This is lecture what 12, okay so the last class we saw some basically I think I was spending quite a bit of time with MPAM to establish the decision regions and come up with some expression for the probability of error, okay so the MPAM that we were looking at I want to do it a little bit I think towards the end I was rushing a little bit so I want to do it more carefully this time, okay so MPAM, okay so you have 0 and the way I took it it was d by 2, right 3d by 2 so on till m minus 1d by 2, okay so minus d by 2 minus 3d by 2 so on till minus m minus 1d by 2 that's my MPAM constellation, okay and the decision regions are fairly simple, okay for the outer points you have two different at certain type of a decision region and okay and for the inner points you have a certain finite decision region, okay so that's clear enough so what I'm going to write down so I did some calculations to show how probability of error given a certain transmission point is simply an integral over the decision region with probability of correct decision is an integral over the decision region probability of error will be 1 minus integral over that decision region, okay so I'm going to do that now so suppose you say x is say m minus 1d by 2, okay so you have to take an integral over the decision region for the conditional pdf, right so that's what I want to find out, okay I want to find probability of error conditional on x equals m minus 1 into d by 2, okay so for that what will the conditional pdf look like, okay so this is the conditional pdf f y given x equals m minus 1d by 2 y, how will the conditional pdf look like, it'll be a normal centered at m minus 1d by 2 and variance will be n naught by 2, okay so that's how the so roughly maybe it looks like this, okay the p equal occur here and what is my decision region, m minus 2d by 2 onwards to the right, okay so that's my decision region, okay so this point would be, well that's not a constellation point but that is my so what is this distance d by 2, okay so that's what's important all this m minus 1 m minus 2 and all that is just convenient notation for denoting the point what's crucial is this distance, okay so the reason is I want this integral which is the probability of correct decision but then what will be the probability of error, the other integral, okay so the other integral is much easier to write using q functions once you know the distance from the mean, okay so you see easily probability of error given given x equals m minus 1d by 2 equals what integral from minus infinity to m minus 2d by 2 the normal pdf with mean m minus 1d by 2 and variance n naught by 2, okay so you can either use one of your standard formulas or can do a change of variables convert it into a suitable unit Gaussian and then find the actual distance there, you can do that work and show this is equal to q d by 2 root n naught by 2, okay so root n naught by 2 is the standard deviation and d by 2 is the distance from the mean silver coat as q d by 2 divided by root n naught by 2, okay so okay so if you want if you want a useful trick to remember this the way to remember this is following for instance the general formula for q gives you something for the unit normal unit variance 0 mean unit normal pdf, okay so maybe you don't have that maybe in a general situation you have say mean mu naught and then variance say sigma squared, okay so I don't know why I'm saying mu naught I'll just say mu, okay mean mu and variance sigma squared, okay so q will give you suppose you have this to be a general I don't know some alpha, okay, right the integral from alpha to infinity of this pdf will work out to what? q alpha minus mu divided by sigma, okay so this is the formula, okay, right so if I pick some beta here and ask you for this integral what will it be? Yeah, okay is that clear? q of beta minus mu is 1 minus I'm sorry what will it work out to? Yeah, okay so that integral should also work out to something very similar I don't know why I'm struggling a little bit here what will this work out to? Minus infinity to beta normal mu sigma squared, okay so you can write this as 1 minus integral from yeah beta to infinity normal mu sigma squared, okay this is working out okay am I writing it fine, okay so finally I think the correct answer will have to work out to q of mu minus beta by sigma, okay, right is this fine, okay so there'll be a half term missing so you should use q of 0 is half and all that, okay so it involves a little bit more of work at all it'll be a very simple derivation but anyway you see this will have to work out to q of mu minus beta by sigma is that clear? Okay if you want you can show this you can write this as q of beta minus mu but then it'll be negative q of minus x is half plus q of plus x and all that, okay so you do that you'll get this answer, okay so play around with this so these are the two expressions to remember, okay so these two are the expressions to remember so what matters here you see notice alpha minus mu is what? What is this alpha minus mu? It's this distance right deviation from the mean likewise what is beta minus mu, mu minus meter is deviation from the mean, okay whenever you're calculating what's called the tail probability what matters you can write this as q of deviation from mean divided by standard deviation, okay that's for the tail probability, okay if you're calculating the other probability it'll be one minus the tail probability so this is useful to write everything in terms of q, okay that's one expression, okay you can also use this to write integral from beta to alpha of the normal PDF what will this be, okay so anyway this is an assignment for you, okay try this it's not too difficult write it in terms of the q function, okay so it's okay to write, alright, okay so that's the that's the probability let me go back once again to that page and remind you what we got this is conditional on transmitting one of the right most extreme points probability of error given x equals m minus 1 d by 2 this has to be equal to q of d by 2 divided by root n naught by 2, okay, alright so you see once again the formula at work, okay so what's the distance from I mean I'm interested in this tail probability, right and what is the distance from the deviation from the mean it's d by 2 and divide by 0, okay so use that it's easy to work this out, okay, alright so the next thing is to look at probability of error conditional on the other extreme point is very easy what should it be should also be the exact same thing q of d by 2 divided by root n naught by 2, okay so then I'm going to argue now I'll do for one interior point and everything else will be the same, okay so I will do probability of error conditional on x equals d by 2, okay so this is what I'm going to do let's draw the conditional PDF this is f y given x I think I've been using all kinds of different notation, okay hopefully it's clear to you, right it's going to be mean d by 2 and variance root n naught by 2 and what's the probability that I'm interested in I'm actually interested in two probabilities, two different areas one is this area, okay and what's the other area after d, right so I'm interested in this area, okay so you can visualize this from various points of view from the constellation if you see if you transmit d by 2 if your y is less than 0 then you're closer to minus d by 2 if your y is greater than d then you're closer to 3 times d by 2 in both cases you'll make an error, okay so I'm interested in the integral over that area what is that integral going to be there are two tail probabilities, right so it's going to be q of but you notice the distance is the same, okay the deviation from the mean is same for both, right d by 2 so it's going to be 2 times q d by 2 by root n naught by 2 is that okay, right simple enough formula, okay so now that we've found the conditional PDFs we can find the probability of error itself, okay so how many extreme points do I have I have two of them okay so it's then and they occur with probability 2 by m 2 by m q d by 2 by root n naught by 2 plus what m minus 2 by m q of okay there's a 2 I'm sorry 2 q of d by 2 divided by root n naught by 2, okay it's a simple simplification from this point to show this will be the same as 2 times 1 minus m q d by 2 divided by root n naught by 2 is that okay is that right is that okay all right so this argument of q is quite important to me okay so for m when m is large or even if for any m what's outside the q is not going to matter that much because it's a constant it doesn't change if I change my power at the transmitter it doesn't change if I change my bandwidth it doesn't change if I change any of my other parameters right so remember why did I calculate probability of error I want to understand all the tradeoffs very carefully what's the tradeoff between power of the transmitter bandwidth of the transmitter and all that okay so bandwidth turns out we can't really understand okay so I was trying to write down expected value of n square of t but it turns out since we assumed a huge bandwidth that doesn't make much sense okay so we simply define something based on n naught and we'll proceed for for now later on I'll fix the bandwidth thing so for now we'll we'll ignore the bandwidth part of it I want to understand how the power of the transmitter and power of the noise okay power of the noise is represented simply by n naught the level of the noise all these things tradeoff and give you an expression for probability of error that's what I want to understand right so I should clearly look at this expression very closely and figure out what is important and what's not important okay outside on the left hand side you have coefficients which don't change when any of those things change when will it change when m changes right when m changes it will change okay why is m crucial for me what does m determine number of symbols or the rate okay the bit rate is going to be determined by m okay so that's a that's an expression which you might want to write down so so maybe I'm sorry let me just write it down here I don't want to lose focus of this on this expression it's quite important okay so this log base to m is the bits per symbol okay so m is crucial but you see I don't have to worry too much about it why is it that I don't have to worry too much about it yeah so as one one reason is that when m is large you can definitely ignore it it's no problem but also look at the other term multiplying it it's q okay q is going to decrease exponentially in its argument okay and for any reasonable value for its argument it's going to be far far smaller than this expression and you can conveniently not care too much about it up to some order you can find the expression just with q okay so q is very important okay what whatever shows up inside q as an argument of q is extremely crucial for me and whatever design I do I do in my transmitter and receiver I should take care of that argument whatever shows up inside my q is what's going to give me my performance okay so that quantity is extremely crucial okay so hopefully you're convinced of that okay nothing else appears in the probability of error only thing that matters is what's this argument of q okay so we're going to look at that argument of q very very closely and come up with some expressions for it and relate it to the various quantities that we're interested in okay that's what we'll do okay all right so let's let's see what what shows up inside is d but d is a little bit misleading the reason is what we are more interested in is in transmit power and yeah d is also related to the transmit power okay so I I think I wrote down this relation yesterday but I may not remember it very exactly so signal energy e s worked out towards some m squared minus 1 d squared by 12 am I right okay okay so you notice this is this is very interesting so this on the left hand side you have energy of the signal on the right hand side you have two quantities that are of very great importance to you the quantity d which is the minimum distance in your constellation which plays a crucial role inside my argument of q which determines my probability of error and then also m which is related to my rate okay and the next quantity is n naught by 2 I'm going to make a definition and say en is n naught by 2 like I said at this point I can't exactly relate it what is n naught by 2 n naught by 2 worked out as expected value of n squared some n squared what is that n after the correlation okay so it's not clear what it relates to in terms of n of t okay the only thing I can say is it's the level of the power spectral density okay just take it as a level of the power spectral density for now okay later on when we put in the bandwidth assumption very strictly and try to fit everything properly we'll see we can definitely talk about energy in the energy or power of the n of t itself okay so at that time we'll make it more concrete and all that for now let's take it as level of pst okay so let's try to write it in terms of these two quantities which are definitely measurable in my transmitter and receiver so you can put a power meter or something of the signal that you're putting out you can definitely know what es is it's no doubt about that likewise you can also know the level of the pst so these two are realistic quantities that I can relate to in a physical system okay in my model also it's good to relate everything to these guys okay so let's see what happens okay so the probability of error works out as what 2 1 minus 1 by m okay q what okay so let's try to write this the denominator I have root en case no problem the numerator I would have yeah root I think it should be 3 something no 3 es by m squared minus 1 is that okay okay so another way to write it is 1 minus 1 by m q root 3 by m squared minus 1 I will call I will first I'll define this quantity for the first time I'll call it signal to noise ratio okay so that's my snr okay it is signal to noise ratio is to be es by en okay so it's very clear why this quantity signal to noise ratio is so crucial okay because my probability of error is a function of the signal to noise ratio and not es separately and en separately okay so es by en is what really matters to me okay so that's why I've been saying always it doesn't matter you can pick a d arbitrarily okay as long as you allow n0 to be orbit I mean you can fix your d and then let your n0 be arbitrary okay if you do that what can you get you can get all possible snr's if you can get all possible snr's you can get all possible probabilities of error so your tradeoff is not limited by that in your model your tradeoff is not limited by keeping d as a general d okay you can pick d gen d fixed but what should you do you should allow n0 to vary as long as you allow n0 to vary it's okay so this quantity is very very crucial and you have to pay attention to this in all your design yeah yeah so okay so it's right so what he's saying is in reality you might be able to tweak only some things I'm not talking about what I can tweak okay so I'm trying trying to tell you whatever you tweak I can model that just by this okay so it's just in the model in the model it's enough if I fix d and vary n0 if you vary things in some other way you'll give me some snr right ultimately and my probability of errors is a function of only that snr I can achieve that same snr with a different setting here it doesn't matter only the snr matters okay so that's the reason for fixing d arbitrarily as 2 or something okay so that you don't have to worry too much about all these variables floating around but if you want to have a d you can have it it just doesn't make any difference okay it's the same thing all right so snr so but like he points out in reality what will happen in the receiver so I'll tell you how the receiver will work you know you're going to put a power amplifier in the transmitter and you're going to pump it okay so it's going to go out and the receiver usually you put something called a low noise amplifier after you filter out some things you put a low noise amplifier and after that you'll get your signal okay so that signal will have a certain energy that is my es right at the receiver it will have a certain energy that is my es so maybe based on your power amplifier setting at the transmitter based on your low noise amplifier setting here you can vary the power a little bit that's how it will work okay but typically there will be a target power level after the lna which will be which will have to be met lna is by the way low noise amplifier okay so you have that okay so that's how your signal power will work so you won't know what your d is right it's very difficult to know what your d is you can figure it out by doing some processing at the receiver okay in general if you don't know how far your transmitter and receiver are separated by you don't know all these settings it's not possible to know an exact d and you don't have to know it you only have to know the ratio okay so all these things don't matter too much right but you can figure out the d using some careful single processing at the receiver it's possible okay so that's the those are the things to keep in mind so all these models are nice in your head but in practice they will come up in a very different way okay so you can plot the constellation and all that and figure out how it works okay anyway so this expression is very very crucial when m is large you can make a very convenient approximation what is that you can say probability of error is approximately 2 times q 2 3 s n r divided by m squared minus 1 okay all right so so I want to I want to point out the first of all the simplicity of this expression okay well there is the q function which you can't get a good handle for but again think of it as e power minus x squared okay q of x is of approximately e power minus x so it's an exponential fall and look at the simplicity of the expression it's got probability of error on the left hand side a quantity which you really really care about and inside the q argument you've got the other two quantities you care about okay in fact maybe three quantities power of the signal power of noise and the rate that you're transferring so in just this one simple expression all the tradeoffs are accurately represented okay so so that's the power of modeling things in a very simple way okay if you don't want to do that if you want to take all the complications of your transmitter and receiver and mind hold on to continuous time and do all these things you will never get a nice expression like this okay so you'll never understand how the tradeoffs actually work okay what happens when I double m okay suppose I want to increase my bit rate by one okay right if I want to increase my bit rate by one what should I do I should double m right so what happens when I double m it's a question that can be beautifully answered once you look at this expression okay otherwise if you just you have to do too many experiments to figure out these things things like that are very crucial in practice and let's show you answer okay so there's another is it okay is this expression fine any comments okay all right so there's another related quantity which I'm going to define as normalized SNR okay so that's my definition it's just take it as a definition for now later on maybe we'll look at deeper meanings of this normalized SNR so what's normalized SNR okay I'll denote it SNR norm this is SNR this is for actually m PAM okay SNR divided by m squared minus one okay and you see the motivation is very clear why am I doing it I just don't I want to get rid of m okay I want to normalize by SNR with rate okay so that's my normalization so you see SNR norm becomes viable okay so I'll make more comments I'll show you some plots and then make a lot of arguments about why this is working out why that is working out okay so this is SNR norm and in terms of SNR norm and for large m you see probability of error has this very very simple expression 2 q root 3 SNR norm okay I put equality here so maybe you want to put it wheel that shows approximately that all right okay so let me show you a plot of this hopefully this should work out okay is this picture clear is it okay okay most of you see it so if the guys at the back can't see it I'm not going to make any excuses because there are like tons of seats in the front and you're choosing not to sit in front okay so can you see it this plot is extremely crucial okay whatever else you don't understand you should understand this plot in this course because every digital communication system today one always provides a plot like this okay so what do you have well the title is MPAM so this plot is for MPAM okay on the x-axis I have SNR norm in the db scale okay and on the y-axis I have probability of error which I've called p sub e in what scale logarithmic scale okay so one linear unit is 10 power it's a it's a detection by 10 okay you divide by 10 when you go down one linear okay so it's that's the that's the log of them log of the mic unit and I have two curves there one in red and one in blue okay so the one in red is for m equals 2 okay and the one in blue is for large m okay so you notice it's okay right it's an okay approximation the approximation that we made by ignoring m even for very small m it seems to hold it's roughly the same okay so all these differences it might seem like exactly not the same but in practice when you're dealing with a system these differences don't make much of a difference okay so they don't kill you all that much okay so it's not a big deal so you can you can accept them okay so so this point I don't know how well you can see it maybe if you're close you can see it this this point is 10 power minus 6 okay and that's a crucial point okay the reason is in most practical systems it's accepted as a rule of thumb that 10 power minus 6 is a very low bit error rate or bit error rate or error rate in general an error rate of 10 power minus 6 is considered very very good okay so at least symbol level symbol per symbol symbol error rate of 10 power minus 6 definitely a very good point okay so where is that achieved okay roughly about okay 9 dB okay so this point is roughly about 9 dB 9 dB of what normalized SNR okay so you see the advantage in normalized SNR what is the advantage though in terms of normalized SNR why did I have to divide by m squared minus 1 okay now I can talk about this 9 dB independent of m okay and well actual SNR it's dependent on actual SNR but I can talk about this 9 dB as a requirement for 10 power minus 6 symbol error rate independent of m whatever m you have what should you look for your actual SNR normalized by m squared minus 1 should be 9 dB for for achieving 10 power minus 6 probability of symbol error okay so that's a good number to keep in mind so what's dB conversion I'm assuming you've done enough dB conversions in your head so 9 dB is roughly what 10 times right so 10 times 10 dB is 10 times 9 dB is also you can take as 10 times if you want you can reduce by 1 and say 9 times okay so it doesn't matter okay so there's another thing 3 dB is considered 2 times so maybe it is 8 okay so maybe 8 is a good number for you okay so 8 or 10 times so what it says is what this plot tells you finally is finally it tells you everything that you need to do okay right suppose you know what your receiver you have a certain n naught by 2 you have measured your measured your power spectral density as n naught by 2 okay in your transmit power and your LNA at your receiver you have to keep knobbing moving the knobs till you have a signal power which is roughly 10 times if you if you're interested in a 10 power minus 6 symbol error rate suppose you're interested in a 10 power minus 5 symbol error rate what would you do yeah I just go up and then find the related SNR norm remember this has to be SNR norm okay so it has to be normalized with respect to m squared minus 1 okay so once you normalize it it doesn't really matter this plot captures every single m-pam that you can think of okay so that's the nice thing about this plot any questions about this plot and it thinks the thing that is disturbing people everybody understood so this is very crucial if you understand this plot it's okay it seems very simple right so most people on the field most engineers working on the field work with plots like this case this is a language that's very understandable okay and this 9 dB is a very realistic number right it's an actual number so it has a meaning in reality in a physical system it's not just the number that you got from your from your model all right so I'll tell you it's just to just I mean I know this is too early but even at this point you should know something okay so this 9 dB is not an optimal number okay suppose I ask you a question how low can my SNR norm be so that I can still achieve 10 power minus 6 is that a reasonable question to ask yeah you should ask that question as engineers right you want your SNR norm to be as low as possible and still achieve 10 power minus 6 symbol error rate right is that a reasonable question to ask that's a very reasonable question to ask and that's a question you should ask and most systems when you evaluate it you'll have to find its SNR norm and then find out how far it is from this optimal value what do you think that number is the optimal value of SNR norm at which you can achieve 10 power minus 6 error rates just take a guess what do you think it can be since it's 9 dB sorry 3 dB, 4 dB okay so in in 1949 when Shannon published his paper on communication mathematical theory of communication he gave an answer to this question okay an accurate answer and that answer turns out to be 0 dB okay in fact even 10 power minus 6 is not there the proof the way it works you can achieve arbitrarily low probabilities of error okay but it's not at the symbol level well it's also at the symbol level I should say arbitrarily low probabilities of error can be achieved at 0 dB normalized SNR okay it seems reasonable to you okay so somebody gives you a plot like this and says hey I'm at 9 dB I'm doing 10 power minus 6 what should you tell him well you're doing really bad right that's what you should tell him reason is you can achieve that 10 power minus 6 at 0 dB okay and this was known at the very start of the whole communication problem people were trying to solve this people knew that but it was very very tough and today we can get very very close to this number you can get like at 0.51 dB or so you can get 10 power minus 6 very easily okay without too much of a problem okay so in one way the problem of digital communication has been solved you know we're solving we're looking at a problem that's been almost completely solved and still there are some unsolved issues here and there and of course there are other areas related to it which might be useful for you okay so the ideas that are involved in getting from 9 dB to 0 dB are these powerful ideas of error control coding and all those pretty much you have to pick a very powerful error control code and do them so that's where coding fits in but we won't see coding pretty much till maybe till the end of the class maybe a few examples okay so that's the power of this okay the reason I gave you this information is you should know that what we're studying right now is not the optimal thing it's just one way of doing it so optimal scheme will be a modification of this where you'll introduce something called coding to get very low symbol error rates okay so that's the that's the theory there all right so something else I wanted to do yeah so one some some more computations in terms of actual SNR as opposed to normalized SNR okay so roughly you should know so this once you know these 9 dB numbers you're comfortable with normalized SNR but you should know what it means in terms of actual SNR okay so that that we'll see one rule of thumb which is which is quite useful okay so it's very easy to see okay so I want you to think about this the probability of error expression 2 times q root 3 SNR by m squared minus 1 so roughly for large m you can think of m square minus 1 as m squared itself so the denominator works out works out like that okay so so what rate does this achieve okay so from a useful rate to think of is in terms of bits per symbol okay bits per well yeah bits per symbol I think this is good okay there's also a bits per dimension type quantity I'll introduce that later but anyway bits per symbol is the is a good unit to have okay so suppose I want to increase my rate by 1 bit per symbol what should I do I have to double my m right if I multiply m by 2 I get an increase of 1 in rate if I double my m by 2 to get the same probability of error how much should my SNR increase do you see that do you see how I'm making this argument this is a very crucial argument okay so you see inside q there is an argument and that completely captures all of my probability of error okay when I want to increase my rate my 1 I have to double my m but I want to keep my probability of error is the same okay which means my SNR has to increase four times do you see that it's a very simple argument but still the way it works out is is very nice to see okay so if I want to increase my rate my 1 increase rate by 1 I have to double m okay and to preserve my same probability of error SNR has to increase by how many dB increase by 6 dB okay so the 6 dB number is often quoted as a rule of thumb for doubling your signal constellation okay so increasing your rate by 1 so remember all this is in a very simple m-pam situation the place for m-pam there's no coding or anything it's just simple m-pam it's not optimal or simple simple m-pam you do it okay so it's possible to do that at very very low SNRs without coding okay that's also coding one might say but there's some one can think of it close to modulation but yeah any reasonable rate you have to do code okay so so this is a good good rule of thumb to remember okay so any questions are okay all right okay so so a couple of things to do next is to go to m squared qam okay so you'll see m squared qam and m-pam are very very closely related and one probability of error completely pretty much controls what the other probability of error will be okay so that's that's one thing so let me do that first then I'll do the other thing okay so let's do m squared qam okay so so what's the constellation constellation oh my goodness okay my constellation is actually made of two different m-pam constellations I'm gonna really draw the first quadrant okay so you fill out the other quadrants if you're interested simply draw the first quadrant okay so that's my m squared qam I have say d by 2 3d by 2 m minus 1 d by 2 likewise here d by 2 m minus 1 d by 2 okay so once I assume all my points are independent okay right once I assume all my points are independent my x-axis and y-axis symbols are also chosen independently I can think of an m qam m squared qam symbol right symbol x as 2 p-am symbols this is a p-am symbol m p-am symbol and this is a also an m p-am symbol and once I assume all the m squared points are independent these two will be independent as well so in my detection I can detect my i-channel separately using an m-p-am detector and q-channel separately using my m-p-am detector again okay this is only if I assume they are independent okay if I don't assume they are independent then the whole decision regions will change it's a big headache okay so but it's very common to do this okay so even if you know they are dependent it's just common to finish this off then take care of the dependence in some other way okay so for instance I've been talking about coding I want to briefly point out when you do coding this dependence will be independence will be lost okay but people typically make a sub-optimal decision and take care of the dependence in the decoder for the code okay so that's how it works okay but anyway for now let's assume it's all independent once you assume it's all independent there's no big deal you don't have to build a separate m-squared q-am detector okay you just build two m-p-am detectors one for your i-channel and one for your q-channel then run it okay so your probability of error will be controlled by probability that either x1 is in error or x2 is in error okay and those two are simply probabilities of error for the m-p-am detector okay so this is a very simple way for the independent case if it's not independent what do you have to do find the actual decision regions in two dimension right which is quite complicated okay if you're not independent you have to take care of the probability you can't do ml anymore if you want it to be optimal right you have to do m-a-p okay so if you do m-a-p for optimal detection it becomes more complicated all right so anyway so let's write down probability that x bar is in error okay this will be what okay yeah so the way I can write it is one minus one minus probability that x1 is in error squared is that okay right so this is the probability that either x1 or x2 will be in error assuming their iid right iid distributed okay so this is the probability of error for m squared qam this is the probability of error for m-p-am is that okay all right okay so let's let's write down probability of error for m squared qam it's going to be one minus one minus what did we know probability of error for m-p-am is two times q d by two divided by root and not by two okay so this is again rough because I'm not taking care of m if you want to take care of m it'll be two times one minus one by m okay so I'm ignoring that okay so once again ignoring certain terms this will roughly be four times q d by two root and not by two is that okay okay what term did I ignore q squared I ignore because I know it's going to be power minus so if I need reasonable value it's going to go much faster so I can ignore okay all right so now we have to do the conversion back from d2 esn en okay so I'm going to say en again is n not by two there's no problem there for es I have to be slightly more careful what will this work out to two times m squared minus one d squared by 12 so okay okay what will be my rate two times log m base two bits per symbol okay so those are my various quantities of interest okay so now if I go through and do a conversion what does it work out to probability of error for m squared p a q a m okay I'm doing all kinds of I think my bracketing is gone it's got all kinds of errors okay so it doesn't matter let's say all brackets match each other okay this is for m squared q a m looks out to what the four outside is okay you know I mean it doesn't change it doesn't even play a role in my trade-off arguments for s n r and all that okay so inside there'll be a small change what will it be three by two square root of give me don't don't normalize three times three by two s n r by m squared minus one is it okay okay okay so you see this is small small change in the way the q works but it's okay I mean it's pretty much the probability of error for the p a m it's not a big deal so don't have to worry too much about this so even here if you want to say increase your rate by two okay if you want to increase your rate by two so sort of you want to add two bits per symbol then you have to double m and when you want to double m you pay a six db penalty okay so that's okay those are things you can do you can plot this but typically this is not it's not a big deal okay so you can see why m p a m is more fundamental okay so it's much more fundamental than the way this is gonna work okay so so so so so so so the next thing I want to do is do a similar calculation for m psk or m squared psk and compare it with m squared q a m and see if which is see which is better so for instance you were asking a question if I have two different types of constellations right instead of just independent signaling with constellations how do I decide which is better yeah that's an important question to ask right you might might be given several choices and you have to make a choice of constellation if you're given two different constellations how do you choose which one is better so the way to do that is a very similar approach so you go through and find probability of error in terms of these q functions okay and simplify it come to a certain stage where you can write it as just one q function with a certain type of an argument okay do it for both schemes and simply compare the arguments of the q functions and you will know the answer okay right that's the that's the trick to doing it and that's an important thing to know also okay so if you do for say I'll do for m psk okay so if you go ahead and do it what I'm expecting finally is probability of error for m psk it's a little bit more difficult okay so those are eight regions are I mean the decision regions are a little bit different and you can't split it into two mpsk so you can't do that right m psk how does it look right it's going to be on the circle okay all these points okay okay so you can't you can't nicely split it into two different things that are independent so you can't do anything simple that way so it'll be a complicated expression but you can do a series of simplifications and I'm not going to write down the final answer right now but you'll have some constant q square root right SNR times some other constant okay okay this constant will not really matter unless these other things match okay this constant will not really matter it's not a big deal and then by comparing this constant with the constant you had for the other case you can decide which is better okay so it turns out you can make a simple decision right so for instance if m is 2 psk will agree with 2 p a m if m is 4 4 psk will be the same as 4 q a m it has to be the same right 4 psk and 4 q m are the same but when you go to 8 psk and say 16 psk 16 psk and 16 q a m 16 q a m will be better so we'll see that so I'll give you the expression maybe we won't even see the derivation the derivation is a little bit painful and lots of approximations there okay so I'll just give you the expression for the next class and we'll stop here okay


What's up everyone? It's your girl Kenzie here from Layton Sports Cards and I'm ripping a personal for Antoine G We've got a 21-22 Panini prism basketball first off the line hobby as well as a 2020 Panini National Treasures Football hobby. All right, best of luck here Antoine. Thanks as always for hopping in. We're gonna start with your prism basketball. Let's see some nice shimmers Shimmy shimmies Say your photo sticker right there. Here we go 2020 NT Again, Rich did add some 2020 products in stock We've got 2020 NT and flawless as well as contenders optic and obsidian for 2020 football products Big day for 2020. We've got a John Stockton on the pulsar for the jazz Hyper Wendell Carter, Jr. Fearless Devon Booker Shengyun Rookie Jalen Johnson Black shimmer would be crazy Barrett got silver Narkic Purple Ice Rookie of Davion Mitchell sick color match there for the Kings 110 of 149 Chrismatic Darren Fox and Fleet Trey Murphy the third rookie in Jordan pool I say a Roby. We've got Tobias Harris on the redway Sixers that is not numbered purple Gordon Hayward for the Hornets 31 of 99 Mitchell Robinson Earl rookie and O'Neill. Let's give him something to watch here after he wins that game Let's do something crazy. Nice. I'm gonna silver kid Cunningham. Take that He's Cade Silver We've got hyper Jalen Brown prismatic Giannis Jalen Green on the rookie base Robert Covington and Dirk and y'all about a two hour two and a half hour queue currently no Breaks tonight. Enjoy the Super Bowl. We'll be back tomorrow morning with Magic Matt with some baseball breaks red wave Tyler hero Let's color match their blue ice rookie of Sharif Cooper for the Hawks 45 of 125 Then Forrest will be a back tomorrow night with some group breaks David Johnson Rudy go bear Then we'll be live on drip as well for some personal For real giving each other shout outs on Instagram and everything. I wish I was that cool You mean Lillard what we have here? Hold on. You have silver Julius Randall You've got widescreen Giannis And we've got a Ricky Rubio auto for the Cavs Ricky Rubio is gonna be your first auto here Antoine Yeah, that's awesome Blake. That was really cool. Does soon my rookie Preston rookie Murray Stottemire Eric I'm going Eagles. I'm going Eagles pretty shimmers out. Come on shimmy shimmy's got red wave LeBron That's a cool one. Love the pose in that photo nice LeBron a Jordan pool hyper Jared Butler Lewis I think it'll be a good game. I think so Clarkson some bonus. We've got silver Andrew Wiggins Red Treyway nice color match there a lot of nice color matches coming out of this that is 218 of 299 Deer and Fox Collins sexton Isaiah livers rookie and Danella Banton rookie Yeah, hopefully the the rest don't get in the way or anything like that. Don't see any Any we've got to 30 a Dwight Howard blue shimmer Flakers The white Howard in his Phillies uniform Planned overseas now isn't he 27 out of 30? Yeah, he's been doing really good over there No, yeah Rudy gay on the red 62 of 299 Santiago dama rookie Alonzo morning. That's funny Super Bowl mixer was yesterday six Are we Split it into a bunch of different group breaks throughout the day. Tracy McGready on the silver There's four spore there the greedy We've got Maubury on the hyper white screen Lillard Yeah, it was yesterday Key on Johnson Marovitch and Jaden Springer. No, no breaks tonight. I hope so. Let's see Gary trends Jalen Robinson we have to ten a Nerlin's Noel on the gold shimmer for the Knicks That one is eight out of ten. Thanks for subscribing Kai prismatic hyper Devon Booker and a Joshua Primo rookie Otto Joshua Primo for the spurs Magic Johnson, Bassie and Murray Yanis Curry Oh be we've got silver Hassan Whiteside for the Kings Prismatic Silver Joellen B Pismatic Ant-Man Scotty Lewis Plumlee and Aaron Wiggins Ricky. All right, not the best box of photo for you Grease Antoine Let's see we can get you here on the 2020 NT Good luck big box here Fun one fun one. Let's see. Let's see a big true our shield, huh? That'd be crazy 2020 national treasures Here we go We were up 2016 NT where those the wood boxes They're super nice We've got a 27 of 85 George Kittle Niners treasured moments of Vaughan Miller Denver Lambackers next Super Bowl 50 MVP 74 of 99 Vaughan Miller We have tremendous treasures of Darius Layton for the Giants 47 of 99 No, I don't see any redemptions in this In this box, we've got Century Patch of Jason Taylor. That's a cool one. That is eight of 99 Jason Taylor. We've got Century Patch 49 of 49 bookend Michael Strahan for the Giants. That's a cool one player war news material Look at this dual partial logos here three of five rookie Jerry Judy Part of the Broncos there right off the chest.  Very nice. We'll make that one for you We've got rookie Otto 17 of 99 of Terrell Lewis. Oh Wow This this could be a big card after tonight y'all.  I love the midnight RPA is beautiful hit here Beautiful beautiful Magnus one for you as well. We do have a redemption. Wow. How about two midnight? RPAs here card 190 a Lynn Bowden, Jr Two midnight RPAs in one box. Wow.  We've got dual material 23 of 99 Justin Jefferson Nice J Jeff. You got the football relic and the jersey patch there Very nice Justin Jefferson.  That was a fan. That was pretty pretty darn good box there ending with a Justin Jefferson All right, Antoine that will do it for your own boxes. Thanks so much for your order. We'll get these right out to you


Hello, I welcome you all once again to my channel, Explore Education and I am Dr. Rashmi Singh, Assistant Professor, Department of Education, SS Kandangalsh Rupi College, University of Allahabad. Nowadays, we are discussing theories of motivation in which I have covered already covered content theories of motivation and today I am going to discuss a new theory under process theories of motivation that is rooms expectancy theory of motivation and the lecture will be in bilingual mode and will be useful too. Do subscribe my channel to get more videos of mine, rooms expectancy theory of motivation. Content theories, we have read them, in process theories, today it is the first theory, content theory tells us what motivates an individual and process theory tells us how an individual motivates, means it tells us the process of motivation. So, we will read the theory of room expectancy theory here, so in 1964, a Canadian professor of psychology, Victor Vroom from the Yale School of Management, developed this theory, who has made it? Victor Vroom was a Canadian professor of psychology and Yale School of Management and the theory was given in 1964, in it he studied people's motivation and concluded it depends on three factors, in this theory he found that the person, who is a dream employee, the motivation of that person is given on three factors, expectancy, what is hope, instrumentality, how much is the trust, and balance, how much is the value, you will know, these three factors will be explained later, you will be clear. Abraham Maslow and Frederick Herzberg also researched the relationship between people's needs and the effort they make, before this Maslow's theory, we have read about Herzberg's theory, what did they tell us? They told us about the relationship between people's needs and the effort they make, but Victor Vroom distinguishes between the effort people put in their performance and the final result. But Victor Vroom is telling us that the effort people put in and the performance they put in and the final result, there is a difference between them, his theory primarily relates to motivation within a work environment, how a person is motivated in a work area based on this, when employees can make choices in their work, in which the employee can choose their choices. Victor Vroom argues that they will mostly choose what motivates them the most, Victor Vroom gives us the idea that the person chooses what motivates them the most, and this theory says that an individual's motivation is affected by their expectations about the future, and what the person chooses, what is the basis behind it, what is the future on that job place. Vroom's expectancy theory assumes that behavior results from conscious choices among alternatives, meaning that we have a lot of alternatives, in which we consciously choose what we will choose, what we will choose from, whose intention is to maximize, please and minimize pain, meaning that we can increase our benefits, our happiness, our happiness and reduce our suffering. Together with Edward Lawler and Lyman Potter, Victor Vroom suggested that the relationship between people's behavior at work and their goals was not as simple as was first imagined by other scientists. He found that, as we were told by the scientists before, how a person works, what his goals are, how he motivates them, they are not as simple as they have been told. He found that the performance of an employee depends on the individual factors, whereas Banslow, Hulshberg and other scientists were not talking about this. That is, the personality of a person, his skills, his knowledge, his abilities, these are also the basis of our motivation. Vroom stresses and focuses on outcomes and not on needs. Vroom's theory focuses on outcomes, what is coming out, what is the product. You are not focused on the strengths, you are not focused on the strengths, as we were talking about Messell and Hulshberg. That is why this process comes into the theory. This theory states that the intensity of a tendency to perform in a particular manner is dependent on the intensity of an expectation that the performance will be followed by a definite outcome and on the appeal of the outcome to the individual. How will we perform? The intensity of the performance will be dependent on the intensity of the performance and on the appeal of the outcome to the individual. Vroom's expectation is based on the assumption that an individual's behavior results from the choices made by him with respect to the alternative force of action. Done. Which is related to the psychological events occurring simultaneously with the behavior. We will choose the best alternative for our behavior. We have also found out that we have to choose according to which the pleasure, maximization, and pain are minimized. This means an individual selects a certain behavior over the other behaviors with an expectation of getting results they want desired. According to what we want, we start our business. This is our conscious action. That is why Vroom's expectation is that we get the journey in cognitiveism. That is how an individual processes. The different elements of motivation. The theory is dependent on the idea that the more an employee values the outcome, the more motivated they will be to achieve it. If our outcome is that our salary will increase then we will be highly motivated. If we don't even have the means to benefit from the monetary benefit, we don't give money or money to anyone, then we won't be motivated at all. We won't be able to do it easily. This means that we value the reward. The more effort they put into succeeding, the more certain they are of getting their satisfying reward. All the theories built around the concept of balance, instrumentarity, expectancy are not of hierarchy. It can be up and down. There are only three factors. Keep this in mind. That is why we know it as VIE. V for balance, I for instrumentarity and E for expected. There is nothing new in this. The lower part is more important. That is why I gave you more information. If you want to attend a long-questioned theoretical, you will get a matter. Specifically, Vroom says that an individual's motivation is affected by how much they value and reward associated with their action. What is the balance? The balance is that the reward associated with our action, how much we value it. What is the expectancy? How much they believe that by putting effort into something, they will be able to generate good results. We should have faith that if we put in more effort, if we put in more effort, if we put in more effort, we will be able to pass the result. This means that the result should be achievable. If we give them such a result that is unachievable, then it will be useless. And how much they believe that generating good results will result in a reward. And this belief that if they bring in good results, then they will get the reward. This is the instrumentality. It is important to note that rewards could be intrinsic or extrinsic. Our reward, the reinforcement, the reward can be extrinsic too. Intrinsic means sense of fulfillment, sense of achievement, acclimation, recognition. Or extrinsic means money, promotion, transfer, whatever we want. Okay. Now let's know what is the expectancy. There is no expectancy. Faith is that if we give better effort, then better performance will come. This is it. Expectancy is the faith that better efforts will result in better performance. How much they believe that their additional effort will help them achieve the target results of behaviors. That is, we believe that if we put in additional effort, then we will get good results. And what is important for that? Having the right resources, having the right skills and having the necessary support. What should the management do? Must discover what resources training or supervision employees need. We should give that so that the expectancy is increasing. Instrumentality. Instrumentality is that if we believe that if we work hard, then we will get the reward, the valid outcome, the promise that will be fulfilled. Instrumentality is the faith that if you perform well, then the valid outcome will be there. How much they believe their rewards will actually appear should they achieve the desired outcomes of behaviors. I mean, it shouldn't be like if you perform well, if you achieve this task, then you should be given this and not given that. So, instrumentality will end. So, what should happen? Clear understanding of the relationship between performance and outcome. That is, everyone should be clear that if they perform well, then they will get this outcome. Trust in the people who will take the decisions on who gets what outcome. That is, they should be confident that they will decide what they will get. And transparency of the process that decides what they get, who gets what outcome. And this process should be transparent which will decide who will get what outcome. So, what should the management do? Management must ensure that promises of rewards are fulfilled and that employees are aware of that. So, the management should ensure that the promises that he has made for the reward should be fulfilled and this employee should know from the beginning. That is when he will be motivated. And then, the most important thing is that the reward that we have decided is not significant for us. Do we value it or not? If we don't value it, then all things will be void. It is the importance that the individual places upon the expected outcome. The expected outcome gives us so much importance. How much self-interest is in the reward and what is our emotional orientation towards it. So, it is an expected and not the actual satisfaction that an employee expects to receive after achieving the goals. That means, we expect that we should get this. We value the value that we are getting. So, this is the balance. How to use this thing? Before using this thing, we got to know what we have to do for the manager. The balance should be significant for the employee. The employee has the expectation that the results we will be able to see when we make a better effort. So, we should give him a doable and achievable task. And instrumentality means that we must fulfill our promise. These three things can be applied again. And one more thing, that the motivation is equal to balance into expectancy into instrumentality. That is, it is a good and full product. So, if anything is zero, the whole motivation will be zero. If there is no balance, then there is no expectancy. There is no instrumentality. There is no instrumentality. There is no expectancy or balance. There is zero. So, if any of you have zero or more than one, then everything will be zero. So, we should ensure that there are three things. Advantages for motivation and satisfaction. Connection tells us that motivation increases with reward. This is the expectation. It promotes the idea that more effort should lead to increased performance. It is easy. You can read it yourself. It is self-explanatory. You can read it. It focuses on psychological extravagance. It is based on the self-interest individual. This theory helps the manager in looking beyond what Maslow and Herzberg implied. What Herzberg and Herzberg said, it tells the manager to satisfy his employee or motivate him. It is a cognitive theory. It values human dignity. Why?  They consciously choose their alternatives. Okay. There are disadvantages. Home theory is difficult to research and apply in practice. It is difficult. It assumes man to be a rational human being. But sometimes we choose unconsciously. It is an important theory but it is complex. It tells us that idealistic quite a few individuals perceive a high degree of correlation between performance and rewards. But many people do not. And application of this theory is limited. It assumes that effort and performance will result in the desired reward. Sometimes it does not. That is the way it is. What are the implications? The managers can correlate the preferred outcomes to the aimed performance levels. It means the implication for the managers is that we have to trust the employee that if you do a good job the performance will improve. You have to trust that the promise you made will be fulfilled. And you have to ensure that what you are going to give will be significant for them. The non significant things will be kept above the reward and the employees will become demotivated. And they do not motivate at all by themselves. Okay. So this is the matter I gave to you to write. I designed interesting dynamic and challenging jobs. Employees' motivation level should be continually assessed. I did not know that the significance of the work has changed. The balance should have changed. Okay. So I have completed one more theory of theories of motivation and this theory is a new theory because it comes under process theories of motivation. It is an important theory too. Vectors, expectancy theory of motivation and also known as VIE theory of motivation. Okay. So thank you and don't forget to like and subscribe my channel Explore Education today.


Next question is from McConnell 816 what are your thoughts on massage guns cold tubs and saunas for recovery? So all those three things I'm gonna put in the same category as supplements so what I mean by that is let's change the question what are your thoughts on supplements for recovery? Supplements are maybe 2% of diet and sleep and how you train in terms of recovery same thing with these things can they help yes but do they do they compare to the right training program getting more sleep you know getting enough recovery between workouts no so in other words you can't fix a bad workout or crappy sleep or bad stress with these particular products I think that these are great in their own right in other words if you have everything is going good your training is good you're recovering right you got the right volume you're getting good sleep and then you're throwing cold tubs and sauna you'll get some additional health benefits from them but I see too many people try to make up for overtraining or poor sleep or whatever with these devices and tools and techniques and think oh this is gonna fix everything it's not it's not gonna fix anything no I mean I like the idea of kind of like let's go down this like path of comparing it to supplements because I can get down with that because it when you talk about percentage wise as far as the pie chart of what you know dictates a successful training program as far as recovery and all that stuff like that it would fall in a similar category as supplements now my only thing that I'd challenge that is a supplements what I don't like about supplements now that they're cheaper you know but like a bottle of creatine is much cheaper than a massage gun or a cold tub but the nice thing about those things is once you own them you have them you could use them as many times like supplements I feel like it's like this I've probably spent more money on supplements combined total over my lifetime than eat I could own sure I could have my own sauna my own all those things in my house and have it forever to use that other people can use and get lots of value in so I prefer I think to me those are more valuable than supplements are especially since I think these are just a more natural process of trying to get your body to speed up its recovery but they're all it's also a tool and when used inappropriately and not correctly you don't get a lot of value is with these the value of these things is to add them to a good routine a good diet and a good sleep schedule and good stress management like it I've done this before where I'm like oh I'm a little over trained I'm gonna add these things in thinking it's gonna fix everything it doesn't but when I add them to a good system it does enhance things a little bit like sauna does have health benefits there's lots of studies that show that but it's not this huge recovery tool it doesn't like for example getting more sleep is gonna be way more impactful yeah and it's interesting because I don't really look at these tools necessarily when I'm like physically like beat up as much as I'm mentally stressed and that's a good point I tend to gravitate and it just feels good with like the TheraGun and you know those massage guns it's just something that kind of helps you to kind of relax your state of mind and I guess you know part of that is sort of you know tricking tricking you know that signal so you're in this like constant loop of anxiety and all these things that you're running through with your brain I feel the same way with the sauna just helps you to kind of decompress the the cold one is interesting because you know the cold plunge I thought was just gonna be like an extreme kind of like oh I gotta like you know brace my way through this and grit and bear it which found out that's a terrible way to approach it and that was something that is actually part of the protocol is you got to learn to not do that and you don't feel as much pain and anguish which is a whole value in itself in terms of battling all this like anxiety and everything else because that's usually my go-to is to brace bear down and then you end up like pushing it down you keep it and it just stays with you and it just gets worse whereas it's it's a bit of a release and you know realizing that you know you fighting it actually like makes things worse and so to acknowledge it and breathe slowly and get in the calm parasympathetic state is all part of the training yeah there's there's benefits to these things but I love them I mean I would though I hate that we don't have a cold plunger like I use our sauna all the time and I would use a cold plunge if we had a really nice setup for us to be able to do that I think it would be amazing to do it before we podcast so forget that I this person's asking about recovery I'm like on the page with Justin is like they're the mental benefits of this and the like a performance enhancing that would be to go into the go into a podcast like a shot of caffeine like better than that even right I mean the feeling that you get when you come out of a cold plunge especially if you have the contrast of a hot cold like that oh the feeling is an instant not to mention it has some recovery but the problem with these things is that the science they use to try and sell them is is okay like okay yeah I could help speed up recovery I think they inflate how amazing it is it's like you said it's a very very small percentage but I do think it has tremendous benefit in just how you feel like I everybody who's listening right now if you've never done this do this for one week report back to me on how a cold shower exactly in your shower with a 30 second to one minute minimum okay so we'll minute to two minutes if you can of ice cold water shut the hot water and see how your day is just tell me how the beginning of your day goes for that week and I bet you 90% people report back that they were more productive they had better energy they were more alert like there's a lot of good benefits other than just the recovery piece they sell yep I'll say this about recovery if you feel like you need something to help you recover first of all look at your workouts look at your diet you might be doing too much sleep sleep is so underrated get better sleep or just take a nap or a couple naps that'll do more for your recovery than any other tool you could do or add to your body it's like someone's like oh I'm gonna go do 45 minutes you know sauna you know sessions or whatever take a nap taken if it's for recovery take a nap and you'll get better benefits hey if you enjoyed that clip you can find the full episode here or you can find other clips over here and be sure to subscribe


Item number. SCP-122. Object Class. Keter. Special Containment Procedures. SCP-122 is to be stored in a standard containment chamber containing a single electrical outlet. No personnel dormitories are to be constructed within 500 meters of the containment area. At no time should SCP-122 enter an unpowered state. Several redundant power systems are to be maintained and inspected regularly. In the event of SCP-122-1 manifestation, 35 members of site personnel assigned to enact containment are to be deployed outside the containment chamber. If it becomes hostile, procedure 99 Renmar is to be enacted. Due to the potentially disastrous side effects in the event of cross-contamination, at no point are SCP-122 and instances of SCP-3060 to be stored at the same facility. To enact procedure 99 Renmar, all subjects are to assume specific positions in and around the containment chamber in order to prevent a containment breach. Two subjects are to man a portable generator with which the equipment used in procedure 99 Renmar is powered. Three subjects are to be equipped with chemical irritants, created as a byproduct of SCP-1837, which has been found to have an inhibitory effect on SCP-122-1 instances. After all instances of SCP-122-1 have been reduced to the point where entry is safe, five subjects are to enter the containment chamber and use an electrical extension cord from the generator to return SCP-122 to a powered state. These personnel are to be considered irrecoverable after entering SCP-122's containment chamber due to its effect. The remaining personnel are redundant. They will take the place of any incapacitated personnel. Description SCP-122 is a children's nightlight in the design of a stylized shooting star. When it is in a powered state, SCP-122 lets off between 14 to 20 lux. No manufacturer's mark is present on or within SCP-122's components. When in an unpowered state, SCP-122 will affect all subjects within a 500 meter radius of its location. When the subjects enter REM's sleep, they will move into a comatose state in which they will remain, until SCP-122 is resupplied with power. While comatose, humanoid figures appearing to be composed of a black, slightly translucent mass will appear from any shadows around the subject. These figures are hereafter known as instances of SCP-122-1. Instances of SCP-122-1 exhibit signs of sapience and sentience, with physical abilities roughly equivalent to the affected subjects. They will attempt to locate as many human subjects as possible and expose them to SCP-122's effect. As more subjects are affected by SCP-122, its radius of effect will expand, with the maximum range seen in testing being over 2.7 kilometers. The SCP-122-1 instances will attempt to gather all sleep aids within the area of effect and apply them to the subjects. These objects have included Insomnia medication Traditional medicines known to be used as treatment with insomniacs Pillows, blankets, mattresses, and bed frames Media, such as lullabies When in a powered state, SCP-122 will affect the sleep patterns of all subjects within its radius. If a subject awakens from a state of REM sleep while within SCP-122's radius, they will display signs of insomnia and will complain of unusual dreams. Proposals to determine SCP-2840's effects on these dreams are currently pending approval. SCP-122 was discovered within the Linnel Children's Hospital after several reports of SCP-122-1 manifestations reached locally embedded agents. When the area was investigated, it was found that all subjects within the building had been affected by SCP-122. Recovered documents indicate that a patient brought SCP-122 when being admitted. However, no record of the patient's identity has been found. Agents secured SCP-122 with a portable power source and it was transported to Site-19. Addendum 122-B SCP-122 reclassified to Keter following Incident-122-1 moved to Armed Reliquary Containment Area-2. Incident-122-1 On 11 instances of SCP-122-1 breached containment, causing the death of several members of Site personnel and numerous casualties. Following recontainment operations, SCP-122's containment procedures were put under review. During this review, security footage of several maintenance personnel tampering with SCP-122's chamber lock was discovered. When questioned, the subjects claimed that they had done so under duress, saying that a canary was not allowing them to sleep until they released SCP-122. Affected subjects were given class A amnestics and containment procedures were revised. Upgrade to Keter requested. Lesson complete. If you missed the previous orientation, go watch SCP-121, Concrete Cradle, right now. Or for the complete course, watch this playlist. Thank you for watching.


On the breakfast, President Mohammed Buhari charges the National Institute of Policy and Strategic Studies to surpass the best think tanks policy institutes in the world. Also on the breakfast, I need to meet with the Nigerian Communication Commission to discuss identified blind spot in transmission of the 2023 result. Don't forget to also be going through today's newspaper headlines and analyzing the biggest stories of the day on the breakfast. And we're back with the breakfast and plus TV Africa. It's a beautiful Tuesday morning, reaching live from our studios right here on Victoria Island Lagos. My name is Kofi Bartels. Welcome. And I am messable for this good to have you join us this beautiful Tuesday morning. All right, we'll start off with a top training segment before we go to a major conversation this morning. I said the paper review in between mercy. I want you to help me pronounce the word J-A-P-A. I'm sure you know the name. How do you pronounce the word J-A-P-A? Jack Bar. Jack Bar. It's not Jack Bar. Jack Bar. Jack Bar. Okay. Is Jack Bar a Yoruba word? This becomes synonymous with the traveling abroad, the relocation of Nigerians because of the economic situation, political situation in the country, either or the two together. I hear it's a Yoruba word that means run. You know that social media, I think Tik Tok or Instagram video where somebody just come and then there's somebody singing their voice, you hear a voice saying run, let me start running. So if anyone wants to leave the country, say I'm done with the country at the airport to take a selfie, they say they are Jack Bar in, they are Jack Bar in. We can ask you, so this is training because the video can't quite tell when it was shot, we told the French ambassador to Nigeria wanted to know the meaning of Jack Bar and it got a brilliant answer. So we'll just play that. I'd like to hear the lady pronounce the word herself. Quite interesting. Let's go. Jack Bar in Yoruba, say I'm in Yoruba, Jack Bar in Yoruba, a word that describes to the character of the Yoruba series, describes the character of the Yoruba series of Nigerians. And in that sector, it means that the Nigerians were on our gifts, gifts, prayers, with Oh my God.  He said we want to take our skills, our abilities, our dates, and export it to the world. I'm sure since he's talking to a foreigner, the French ambassador, a white woman, we want to go to Yoruba, Yoruba in this part of the world. Maybe he's giving her all looks, you know, packaged, packaged, let's call it a packaged definition, but the people there were laughing because they know that he's not just exporting our skills so well. People are packing their go-go, their loads, right? No. And they're running away. But if you look at it, so yesterday when I went through, you know, the comments and all of that, really interesting and some people were worried about the fact that the young man was a joke, you know? Why would he be making a joke out of a serious question that the lady asked? And if you look at the lady, she was smiling when she asked the question. I mean, the French ambassador, she was all laughing. It's even possible that she knows what it means, but maybe, you know, she wanted some kind of humor around it. And I'm sure that the young man never expected that kind of question. So it was really good. One would want to say that young man should be an ambassador, you know, of Nigeria. Trying to put out the story there, not necessarily painting a bad light of the country or putting us in a bad light or putting out the story entirely there, which is also not wrong.  They are resilient, talented Nigerians leaving the country, most of them. And so I think that he took him by surprise. So it was quite a lot of creativity to come out. Put out all of that thoughts and then try to convince her. I like the fact that he actually saw Nigeria in a good light, you know, in all of that. Because, I mean, we understand what it is, but it's also not a way from the reality. He's such, you know, a delight to look at if you ask me. Absolutely. Absolutely.  You sometimes you have to, you have to be in such form, you know, while you say it as it is, but you also look for diplomatic way to put things because, you know, you don't want to be spoiling the mood. And I think he's out, you know, it's a bit of sarcasm there, you know, but I'm sure that everybody gets the point. You know, everybody gets the point. It's just like the president of Kenya, William Ruto, an interview that's been trending on social online, on YouTube in particular, where he sat with Christina Mampo, CNN, and was asked about same-sex marriages and relationships and rights in Kenya, and he answered it diplomatically. You know, he was basically saying, no, we won't have that in Kenya, but he used diplomacy, tact and diplomacy to answer that. So, I think he said it. He said it all. Nobody can fault this gentleman.  Even he said that for how he kept his school, he's kept his composure and was able to do justice to the question that he wasn't prepared for. Let's move on to the next one very quickly. This is a class presentation gone wrong at the Krumlea Adjasi University where Akoko, where lecturer and his students had to run for their life. This is something that you can only see maybe in movies. We had terrorists pulled up for lectures in understate. My God. Let's go to that. We have to report that this is user-generated content. The first video, of course, the quality was low. I will apologize for that, but it's user-generated content, and that's why. The second one is, of course, you had music background, user-generated content, and that's why. But we have to avoid speculation that may lead to misinformation. But what we're putting out is what the people who were there, they shared on their statuses and all that. They felt that the person who you see in the camouflage with a bandage around his face was a terrorist. It kind of reminds me of Kanye West, how he covers his face. I was a terrorist. This is understate. I don't know if there's a bandage tree or terrorism in understate. I think we had some attacks. You remember those attacks in a war? Always in understate. So I do not know if that is part of them. But someone said, so this is what happened. We have a political science presentation, and the group was to present on terrorism. They decided to do the presentation in a different way. Look, like to portray the whole terrorism thing now.  Or more people ran out, got injured, someone fainted, me say if I ran under the chair, started shouting, blood of Jesus, my mind went straight up to the over stuff. Class don't scatter or shout because some people, phones got spoiled in the process, escaping and some got injured. I mean, so you can look at that. Probably the lecture was so strange to have some, the practicals, you want to call it that. But this is the situation here. Like I said, understate message had its own fair share of, you know, terrorist incidents in recent times. I'm not even surprised that, you know, that's from the Department of Political Science. It should have been from... It should have been meteorites maybe. No, no, but I'm not even surprised that, you know, it's the Department of Political Science that's putting out that stunt across the country. A lot of people, students would want to agree that this department is extra. But would you blame the people? I mean, actually some of you were in that situation. And if you know the current situation that we're in and the things that are happening, you would tick off. Now, recently, University of Calaba, I think that was Unical. I'm not sure if it was Unical or Crutek, one of them. Is it an initiation? No, it wasn't an initiation. No, it wasn't. There were reports. No, I don't know why that didn't really have the media presence as it should. But there was a video that went viral. This was not a joke. There were unknown gunmen who stormed the school and people were just running. People were just...  Unical has had its own fair share of... They come in from the Calaba River. Those bad guys. So we live in difficult times and that's what it is. Trust me. Ask yourself. Why are we going back to talking about it? But imagine that you were in that school. Me, I would tick off. There was no joke about it. Everybody wanted to run because we see the news. We hear the story and you want to imagine, especially, but it was an act. And even also with the fact that these days you have a lot of skid makers making skids and you don't want to take that for granted. But it also shows that there's a lacuna. We need to up up security. We need to beef it up. I don't know if you understand. So I don't know at what point, if when these guys came into the school, or it was when they went to the classroom or somewhere and then they got changed and what have you, because these things can actually happen. I don't know if you understand. So we can also take out the fact that we need to beef up security across different institutions, our schools, what have you, because I looked at that video. I remember that video that made it. It was a satin university. I think it was Crutec. I'm still trying to remember if it was Crutec or Unical. Yes. This is a big one. The video that had the music that we had, you can see the inscription on the screen where the person said, presentation gone wrong, lecture gone wrong. So people have lost their phones. People have lost their, I've got an injured. For this gentleman, what if you had an agent, a secret service agent, SSS in the audience, who was part of the class, but he was there with his piece. He had a piece on him. I think you pulled the trigger.  And then maybe he just brings it out. God, God. Who will we blame? It's very important in this time where the country will live in for institutions to always give warnings when they have things like that. When the military are having their shooting at the military shooting range, it may be quite a distance from the city center. Have you been around? No matter how far it is, whether it's in terms of perimeter fence and everything, they will still tell the public, oh, we're going to be having a shooting exercise, training, routine, blah, blah, blah. From this day at this time, please don't panic, go about your local activities. So I think a warning, some sort of warning should have been given to the students so that no one would lose their lives. People's phones have gotten destroyed because of the economy. Which house would they go to? How much would they pay to treat themselves? I love invention. I love creativity in teaching. I love it. But, you know, we need to have certain precautions. So we don't endanger the lives of the people who are the actors and those who are the students. Very valid, very valid points as you have actually raised. But it actually would appear more like I mean, the kidnap industry, you want to call it that in this country, has been a big one. She looked at those in the terrorism circular sector. Those engaged in terrorism in Banditry have resorted to kidnaping to further their activities. In fact, they have surely left the terrorism in the religious aspect of it, if it's political aspect of it. On kidnaping, you know. Down south, we've had a kidnaping epidemic for some years which has been surpassed by what's happening in the northern part of the country. So it's a big issue. Well, the latest is that suspected government on Sunday kidnapped the Commissioner for Housing and Urban Development in Benway State. A very fine young man, Chief Ekpe Ogbu really sat. He wasn't kidnapped alone. He was kidnapped along with him. Still be signed by the Social Democratic Party candidate for the House of Assembly seats in a door state constituency. Orirri or Cheje Richard said that Ogbu was kidnapped alongside Hon. O'Lago Ode, one of his in-laws and his driver. He said to himself, cross your names because they share border across the state. It's really sad. I just hope that the man will be connected to his family. Now according to the statement he was, or they were kidnapped along David Mack's farm. I'm sure that's a road. After Aqbah Otobi while on their way from Otaupo to Uthongon in Adolo Co. Cabinet in Benway State. It's really sad. It just reminds me of the conversation I had with Nika Guley just before we got on the show. And then he was asking if I've ever been to Benway. I mentioned vividly that I've been to Benway to be precise Otaupo. And trust me getting to Otaupo wasn't even a joke. It was really... Because you travelled from Canapah? No, seriously. Apart from that, getting to Otaupo. You don't even want to hear the stories about Otaupo at the time. It was scary. The car that we're driving was very, how do I even put it highly secured car. It was portable. Was it bulletproof? Let's not even get into all of that. But the fact that the first skirt that we got was that people stopped. Security persons actually stopped. But of course in all of the interaction, you could notice that these guys were up to something very crazy. And just approaching Benway itself, there was a lot of scare. You have to be careful. We had to break the journey in Boko. What do you think? I don't remember. Our pleasurable memories of Benway. So the thing is the journey was actually we had to cut the journey into two. So first we needed to stop at Boko. So we had to sleep at Boko. And even in the hotel that we checked into there was a lot of warning that you have to be careful. So it was like, we're even scheduled to check in. Was it recently maybe? No, it's not quite. It's 10 years ago. My point here is not necessarily to castigate Benway State or any past ones. But I'm just saying that generally security is a major issue for our country in Nigeria. But it seems to say that Benway State is unsafe from what you experienced. No, from that time. Do you know how long it is? It's not up to 10 years. The thing is, it's not up to 10 years but it was really scary at the time. I mean, that was my first experience. You don't want to see it. I've had very pleasurable experiences of Benway State as the breadbasket of Nigeria. Please, when I say pleasurable, don't misunderstand me. It means that we had a experience. No, that's fine. It didn't mean that it wasn't pleasurable. It's just a coincidence that we're talking about Utopo, we're talking about Benway. And then yesterday, Nika Gule who was in Benway State was also asking have I been there? And then it was the year before and all of that. So it's coming. That's why I'm talking about it. So you also had the same view that it was probably it helps security challenges. Yeah, it helps security challenges. Which I think is... In recent time, indeed, you need to look at the attacks in the head of a crisis. Yeah, in recent times. Definitely mercy. But you have to tell me what you went to Benway to do. We'll talk about that. No, no, no. Don't say it on it. My point is, we have to go. But security is very important. And if you look at the constitution, the reason government actually exists is that government will protect lives and properties. Absolutely. We have to run because of time. And that's on top of the list. And so we cannot neglect that. Government of all quarters should pay attention to the issue of security. All right, thank you. I'll be right back.


Bob Trotson here, courtside with player of the game, Sarah Tarbert, incredible performance tonight. You really did things on both sides of the floor. How do you evaluate your performance? I think it was a slow start, and we knew that coming in, they like to pack the pain, and that's mostly my game. But I think we did good getting out and transition eventually. And it just kind of opened up for us. We knocked down some good shots, which really helped open the post play up. You mentioned that slow start. What do you do as a leader, a veteran out there, for your younger team, is to try and get back into a game like this? I think it really comes down to keeping our composure. I don't think we can get rattled when we have a slow start like that, because it's not going to help. And then I think once we do start hitting the shots, it helps build our confidence. But we just really have to keep shooting. And then it comes down to defense to try to hold them when we can't get our shots to fall. What are your expectations based on film work that you may or may not have done so far, heading into this Wednesday's game versus Albright? I'm really optimistic about Wednesday's game. Albright is always a tough competitor, but it's always a close competitive game. So I think they're really good with their guard play, so it'll come down to closeouts and keeping them from going off the dribble. And then it comes down to us. We have to put our shots in. You've got a pretty big fan base here. What does that mean to you for them coming out to a game like this? Oh, it means so much, especially because we're not that. I mean, we're like an hour away. But for the high school team to come down and support me, it just means the world. And I appreciate it so much. Certainly seemed fired up up there today. Congratulations on the win. Good luck this coming Wednesday. Thank you so much. All right, that's Sarah Talbert after a big time win here versus the Saints. Back in action on Wednesday versus Albright. Bob Trossett, Sarah Talbert. Talk to you soon.