This is lecture 16, ok. So, this week we will have couple of lectures today and tomorrow and then Wednesday and Thursday I am out. So, there will be no class on Wednesday and Thursday. So, it is two lectures, let us see you will be ok. So, the last thing we saw in the previous class was this square root of race cosine ok. So, I am going to write that down once again real quick, but before that I want to draw the whole system once again it is good to just keep reminding ourselves as to where this where this where everything fits in it is quite important ok. So, this is the kind of picture block diagram that you should keep in mind when you are thinking of this whole whole ISI and all these things ok. So, you have what I called as a vector b ok b 0 through b l minus 1 n times l bits ok and then you have a constellation script x ok. So, the size of this constellation is what 2 power n ok. So, that is how I am imagining my constellation to be ok. So, as a result you get ok a sequence of in general complex numbers a k plus j b k ok.  So, g of t this is my transmit filter it is also sometimes called a pulse shaping filter ok. So, it shapes your pulse ok and ok. So, there are various choice ways of picking it first of all it has to fit into the bandwidth of your channel under consideration and then it is also good to have g of t and g of t minus k t being orthogonal ok. So, if you do all that then you will have no ISI it is almost as if you are dealing with the same picture as before ok. So, let me qualify that more, but anyway that is the transmit filter. So, in general you can think of g of t without worrying about anything as a square root raise cosine filter ok. So, it is simple response is actually given by square root of the raise cosine ok. So, the only situation that it would not take into consideration is the very first situation we saw what was the very first setup for us and when a signaling time is extremely large compared to 1 by w ok. So, I am choosing a very very small bandwidth in that case what was g of t? What was g of t? It was a constant between 0 and t right. So, we could choose a very simple g of t at that case ok. So, now when we want to increase our bandwidth to a signaling rate close to the bandwidth we cannot do that anymore we will have to deal with ISI if you want to get rid of ISI also then you will have to have a square root raise cosine ok. So, that is the setup there ok. So, then you do then you do what? Then you do an up conversion and then a down conversion ok. So, I am simply going to ignore that just for sake of space in this picture ok. So, you do an up conversion down conversion ok some noise gets added and all that ok.  Assuming I took care of ISI ok well I should put a channel here I am sorry I will put a channel here. So, I will write my channel in base band right. So, since I did not write the up conversion down conversion this is the base band channel they assumed the bandwidth of minus W by 2 to W by 2 ok. So, this was my ideal channel ok. So, very ideal channel and phase when you can assume 0 phase or we will say linear phase for ideal for an ideal channel adjusting for delay layer ok. So, then a noise gets added to it ok. Assuming orthonormality is satisfied for g of t and g of t minus kt and all that all I have to do here is what? Match filter ok. So, you do g star of minus t ok and sample every t seconds ok. If it was not true if it was not true that g of t and g of t minus t and all that are orthogonal then this is not optimal anymore you cannot do these things ok. You will have to do something else, but since I chose my g of t to be a square root trace cosine and I chose my bandwidth suitably I know that I can do g star of minus t and sample every t ok. So, what will I what will I get? Once I do that I can be sure that what I get will be s of k plus noise. If you did not know that I might get something I do not know what I would be getting ok. So, that is the next thing to keep on right ok. So, a few more things I want to point out ok. Suppose instead of choosing so, when I do match filter by g star of minus t I am doing correlation with some orthonormal basis. What is the orthonormal basis? g of t g of t minus t and so on. So, can I choose any other orthonormal basis for the same set of signals and do correlation? Can I do that? Will I lose optimality in any way? Some other set of yeah as long as they are orthonormal you should not lose optimality, but then what will you lose? Will there something that you will lose?  Yeah the ISI you are not sure if it will go away or not right right. So, you might have to do more complicated detection ok. So, this may not be just s of k plus n of k it might be s of k plus some constant times s of k minus 1 some other constant times s of k plus 1. Then you have to do a complicated detection we do not know how to do detection for that it ok. So, we might see it later on, but for now we only know how to do detection when my symbol only noise gets added to my symbol ok. Since I chose my orthonormal basis to be g of t minus k t again and I am having to do only this very simple detection as in there is no ISI ok. So, fact that we eliminate ISI is important for the detector ok. So, that is the those are the things to keep in mind ok.  So, you can run this detector for each k ok. If I had ISI I cannot do this ok and it would not be optimal anymore ok. So, you should know which part of it is optimal for what reason ok. So, do not have to simply take each block to be as it is you could choose another orthonormal basis as long as you know how to detect the resulting signal resulting symbol values you get ok. So, that is the main thing to keep in mind ok. So, this is ultimately will give me B hat ok. So, this is the picture and just to complete this picture let me draw let me write down the square root raise cosine expression because one could pick that as opposed to anything else. So, the square root raise cosine g of t is 4 beta divided by pi root t cos 1 plus beta pi t by capital T plus t sin 1 minus beta pi t by capital T divided by 4 alpha t whole thing divided by 1 minus ok. So, suddenly I put alpha there 4 beta t capital T square ok. So, this is a fairly complicated looking expression from what we had before. So, previously when you were willing to so what is t what is t that is important 1 by t we choose to be equal to what w by 1 plus beta ok and this is true for any beta between 0 and 1 ok. So, this is all this is very important do not ignore this ok. This is an important design choice you are making ok. So, you cannot happily throw that out 1 by t the signaling rate symbol rate ok we are choosing to be w by 1 plus beta you could choose to be equal to w in which case this g of t should become a sink ok. There was some question as to whether that works out or not I think at the end people agreed that it works ok. So, it should work out hopefully you see that alright. So, like I said before when t is very very large when you choose your signaling rate to be extremely small you can get away with the g of t which is flat between 0 and your symbol time 0 to t ok. So, that is good in one way it simplifies your correlator and all that even your transmitter gets detected and this is more complicated in the sense that every t seconds you are producing a signal which lasts for a long time ok. So, well this will not be causal. So, you will have to shift it to the right by suitable amount to get it causal. Maybe it will last for 4 or 5 symbol intervals maybe 4 or 5 is too less maybe it is 10 symbol intervals ok right. So, that is fairly complicated when you think in terms of implementing at the transmitter right. So, every signal you produce at every for every symbol will last for how many symbols say some 10 symbols ok you will have to choose that how will you make the choice why did I say 10 why cannot it be 100 ok. So, you have to plot this and see after how many symbol symbol times does it become very small and I can ignore it ok. So, 10 seems like a good number to pick ok. So, maybe it lasts for 10 symbol. So, it complicates your transmitter right. So, whenever you transmit a symbol not only do you have to add the contribution from that symbol you have to add the contribution from 10 previous symbols. But since I chose my pulse shape to be specifically a square root race cosine and then I correlate on the receiver with G star of minus t my S of k what I get after sampling at t will only have that symbol corresponding to that particular ok. So, those are little bit of a complicated picture in mind, but I also drew a simple picture to show why at every t seconds the pulse shape is going off to 0 and why it does not get any contribution ok. So, that is a simple way of thinking about why it is working out that way ok. I also asked another question at that point is it settled? It is settled any answers for why something like that is ok. Suppose, I do not have a low pass filter then yeah then noise will go through the roof ok. So, if your noise is very very large bandwidth compared to your signal if you do not use a low pass filter there then noise ok. So, those are things to keep in mind. An intelligent question to ask which you might face in a quiz or an exam is I pick G of t as sum square root race cosine ok with beta not 0 and then I use only a low pass filter right an ideal low pass filter at the receiver what do you think will happen ok. So, how do you quantify that? Do you think you have all the tools to quantify that is some question you have to ask yourself ok. Did this question make sense to everybody or looks like enough people are staring at me like I asked a very complicated question ok. So, that is an interesting thing to do because in the receiver you may not want to do this G star of minus t which is fairly complex ok. So, you might want to know at what point can I get away with a simple low pass filter even though I am doing a square root race cosine. So, that seems like a reasonable design question to ask ok. So, you will have to answer that with what are you paying for? Will you get something? What will you get? Can you detect that very easily ok. See remember low pass filter sampled is also an orthonormal correlation. So, technically that is optimal should not lose anything, but your detector will become more complicated ok because you may not get rid of ISI may not ok you will not right. So, because Nyquist criteria will not be satisfied anymore if you do G of t and not if you do not do G star of minus t right. Remember how Nyquist criteria are satisfied for what? Mod G of f squared ok. So, assuming at this point whenever you sample right at this point when is Nyquist criteria satisfied only if you have mod G of f squared if you have something else there that may not satisfy the Nyquist criteria ok. So, you should remember that all right any other comment that I wanted to make does anyone want to make any comment about this anything that is disturbing you it is fine ok. Yeah, you should span that is something important ok. So, yeah I am sorry that is that is an important point ok. Only you can any other correlation with respect to any other orthonormal basis will be optimal only if it spans the entire signal space. So, in the in the Ray's cosine sync case you might lose information I am not saying all right ok. So, another thing to keep in mind is if you if you just want to get rid of ISI it seems like the most important time domain criteria is every t seconds your signal corresponding to every symbol should go off to 0 ok. Pretty much that seems to be the important thing ok. So, you have to make sure your 0 crossings occur every capital t seconds and your signal falls off fast enough ok that seems to be a rough way of satisfying the ISI condition right at the transmitter end at the receiver end if nothing else is getting added and if you if you filter properly it should work out ok. So, that is one more thing to keep in mind ok. Next question I am going to ask is very simple, but we will quickly do that I want to I want to emphasize that suppose instead of this w by 2 and minus w by 2 I say minus w and w does not mean anything right. So, wherever you have w by 2 wherever you have w you should put 2 w ok. So, notice if you notice in the pulse shape nothing will change because it is in terms of capital t ok. So, if you look at the definition of my race cosine and square root race cosine everything is in terms of capital t ok and t is related to the bandwidth, but everything is in terms of capital t ok. So, that is a good lesson to have any algorithm you have for transmitter and receiver it should be as a function of symbol time capital t ok. Do not make it a function of bandwidth ok then what will happen anytime you change your bandwidth you have to change all steps of your algorithm, but if you make it a function of your symbol time big advantages all you have to do is one big change in the beginning t equals change that according to your bandwidth everything else will adapt on its own. So, such subtle things might be crucial ok particularly sometimes when you solve problems or when in the lab for instance when you write your code these things might be easy. Tomorrow if you want to change your bandwidth it is the code software that you write see remember all these things are being implemented by software on some processes ok. So, that is how you should think about it and it is easy to change that if you have such notations ok. So, only thing that will change here is this w will become 2 w ok. So, when you when you go to minus w to w that will become 2 w everything else pretty much remains the same ok. So, another thing I have done here is to assume that this is a complex constellation right. So, that is something people like to relax later on, but anyway so we can stick to the complex constellation for good ok. Is it fine everybody is happy so far. So, this picture is very important and a similar picture for the previous case when we were signaling over a very long time ok. So, that picture is also important ok. So, both those pictures should be clear in your mind because that is the first cut implementation for any digital communication system ok. So, that you should know very clearly ok. So, I think it is pretty much all I wanted to say ok. All right. So, let us so the next few things we will see is to write down some ok. So, next things we will see is notions of capacity SNR and a quantity called EBOR and not ok. So, these are important because these are ultimately the figures of merit that we will be shooting for ok. So, whenever we want to communicate you want to communicate close to capacity because capacity tells you that that is the maximum you can do ok. So, you want to communicate close to capacity and SNR is an important parameter that we saw and this EBOR and not also turns out is a very crucial parameter. So, I will define that and then we will fix the whole thing up ok. So, first thing is capacity what capacity for the ideal band limited AWGN channel like I said was given by Shannon in this 1940 49 paper. So, it has been known for a long long time ok. So, this is ideal band limited. So, I am assuming my H of F is I will say band limited to minus W to W because that is the standard assumption that most books will make. So, I have been doing W by 2 I do not know why I did W by 2 maybe I should also done minus W to W anyway it does not make any difference ok. So, it is the same thing. So, this is H of F. So, which means what my X of T is such that bandwidth of X of T is less than or equal to W ok. So, I have fixed that So, what is my maximum signaling rate? Signaling rate can be 2 W ok. So, one can imagine using a 2 W signaling rate. So, now we are looking at capacity. So, once you want capacity you are going to use the maximum signaling rate there is no point in using something less than that ok. So, it will work ok. So, a few definitions before we define capacity we will call P as power of X of T ok. So, this is the power in the signal ok. So, remember Y of T is your received signal ok. So, power in the signal component of the received signal ok. So, that is what X of T is ok. So, I am assuming it is come to that ok. What about power and noise ok. So, we have been thinking of the power spectral density of noise as what? Flat at N naught by 2 this is the PSD of noise ok. So, now I have a bandwidth minus W to W. So, what is PSD? It is power spectral density basically power per hertz per unit frequency. So, if you want total power and noise I should take N naught by 2 and multiply by the total frequency ok. So, N naught by 2 times 2 W you will get N naught W. So, you see N naught W is power of noise ok. So, that is this is crucial ok. And if you do all this and if you choose your symbol rate you can choose your symbol rate to be 2 W ok. So, this is symbols per second ok. It turns out you can show the maximum rate that you can transmit ok. So, the maximum rate with arbitrarily low error rates ok. So, this is called capacity. This guy has a very very simple nice formula works out to be W log 1 plus p by N naught W bits per second ok. So, it is difficult to do a proof of this and so log base 2 ok. So, it is difficult to do a proof of this in this class if at all you get to do a course in information theory this is definitely a standard proof which will be done in that ok. So, like I said it is a proof it is a theorem and a proof it can be stated very clearly it is not one of those hand waving formulas which you use ok. So, it is an exact result ok. So, it is not under this channel model this is an exact result you cannot do better ok. So, it works both ways as in there is also a converse. What do I mean by that? If you transmit at a rate higher than this then you cannot achieve arbitrarily low error rates. Your error rate that you can achieve is bounded away from 0 by some finite number you cannot keep on decreasing it ok. So, since it is a strong relationship. So, this is the best you can do and you can do no better than this both ways ok. So, keep that in mind this is the operational meaning of capacity. One nice thing to notice is capacity is a function of I can write it as function of two quantities ok. So, well you might say 3 p N naught and W, but the ratio p by N naught W also has an operational meaning which is the SNR ok. So, the SNR is defined as p by N naught W for this waveform channel ok. So, this is remember this is for the waveform channel right continuous time channel ok. So, one can say capacity is a function of two things bandwidth and SNR, but remember how is my SNR defined SNR also has bandwidth in it ok. So, you cannot just throw that away ok SNR also has bandwidth in it. So, just by increasing bandwidth what will happen to my SNR? It is going down does it make sense? Why does my SNR go down if I increase bandwidth? Increase my signal rate ok I am changing only time rate I am signaling faster. So, why should my SNR go bad? You are letting in more noise ok. So, that is the way to think about it when you are signaling faster you are using a larger bandwidth which means you are letting in more noise for the same signal power that you had ok. So, it makes sense that SNR should go down if you either increase bandwidth or decrease your power ok. Alternatively there are two ways to improve your SNR ok. What are the two ways to improve your SNR? One is to increase your signaling power or decrease the bandwidth or slow down your transmit rate ok. So, reduce your symbol rate there is one more way ok which is that way ok. So, you control N naught what is N naught? Now it is ambient temperature noise right. So, how will you control the ambient temperature noise? Reducing the temperature. So, you will see a lot of receivers particularly for satellites and all that will be cooled by liquid nitrogen and all that ok. So, they will keep the receivers at such low temperature so, that is N naught you can control ok. So, but somewhere something has to give you know I mean if you go all the way down to like 0 Kelvin or something. So, you can do some such calculation and come up with the minimum N naught possible, but that is one more way of decreasing your improving your SNR ok cool your receiver ok. Do not cool the transmitter ok. So, cool your receiver to some very low temperature. So, N naught will not automatically go down and you can improve your SNR. So, all these tricks are used in practice. So, if you see most receivers will always be cooled they will never keep it hot ok. All right. So, this is capacity in terms of bits per second ok. So, we have to translate this into our vector model into our constellation ok. So, that is important once you do that then we can then we do not have to worry about X of t and N of t and we can work with our model itself and be happy about it ok. So, let us see how to do that ok. So, what was our discrete time no ISI model ok, our discrete time model remember it is no ISI right now my assumption is Y of t is X of t plus N of t. So, I have chosen my signaling rate and my transmit filter and all that suitably so, that ISI is avoided ok. So, in the discrete time model Y equals X plus N this is my model. One thing I know that will be carried over is energy ok. So, energy in the signal ES is what we saw it is expected value of X squared ok right. This energy is being put out every t seconds ok. So, well it is an average energy, but everything is average ok. So, average energy is being put out every t seconds. So, what will be my power ES by t ok. So, that is a good way of relating ES to power ok. So, P the P that I had before the same P that I had before can be written as ES by t ok. And then what do I know about t? T is 1 by 2 W ok. So, if I use this relationship I see that my waveform SNR which is P by N naught W becomes what? ES by N naught T W which is T W is what? 1 by 2 ok. So, it becomes ES by N naught by 2 ok. So, in my discrete time model what is N naught by 2? It is the variance of noise per dimension remember it is not the some total variance in 2D or anything right. In each dimension I have a variance N naught by 2 ok. So, that is how I showed it right you remember I said N of t when filtered by a bank of correlators at the output in each dimension I will get N naught by 2 as the variance ok. So, ES is my energy every t seconds ok depending on whether or not I do PAM or QAM or QPSK this quantity will be evaluated differently ok. So, if I do MPAM what is it? If I do MPAM ES is what? M squared minus 1 D squared by 12. If I do M squared QAM what is ES? Same guy multiplied by 2 you know I mean you calculate it differently ok, but what about the denominator N naught by 2? It remains the same, but it is per dimension ok. So, N naught by 2 is noise variance or noise energy per dimension per signal space dimension ok. So, this is a conversion that one needs to be aware of ok. Sometimes people use ES by N naught instead of SNR ok what will be the difference between those two measures? It will be a factor of 2 ok. So, ES of SNR is 2 times ES by N naught some people use that instead of these things ok. So, we will quickly see all these things do not matter just shifting of the curve and I will tell you how to get rid of all these things ok. So, it is very easy to not worry about these things ok. So, the next thing is to look at capacity ok. So, it seems to be confusing if you use bits per second I want to be able to convert capacity into bits per signal space dimension. Once I convert that into bit once I convert that into bits per signal space dimension then everything works out perfectly fine. So, then I can I can I can also look at my constellation and figure out my probability of error rate and all that per dimension and then I can compare ok. So, that turns out you have to divide the capacity by 2 W ok. So, why once again we will see maybe we will see later on maybe in this course or if it will be done rigorously later on if you do an information theory course ok. So, capacity in bits per dimension turns out to be the previous guy divided by 2 W ok. There are easy ways to motivate this, but I am I do not know maybe later on if we have time we will do it ok. Remember this is bits per dimension dimension of signal space ok. So, that is the way you define capacity. So, so you see you are divided by bandwidth you have divided by bandwidth right. So, this unit can also be thought of as bits per second per hertz right this way I divided by bandwidth and I said dimension, but instead of that you can also retain that bits per second per hertz. Remember second times hertz becomes a dimensionless quantity. So, it is ok to simply call it bits, but but it is common also to say bits per second per hertz ok. So, anything in this units is typically called spectral efficiency ok. So, how efficiently you are using bandwidth ok and this is some kind of a maximum right you can never do better than this if I give you W hertz of positive bandwidth you can never do better than half log 1 plus SNR bits per dimension ok if you have an SNR of whatever SNR that you have. Remember W also plays a role here in SNR ok W plays a role there. So, you should be careful about the computation. So, you should not get carried away by this is half log 1 plus SNR ok. If you if you reduce your signaling rate SNR will actually improve ok alright. So, that is the capacity and we will come back to this soon enough ok. So, before that we want to do a few more things ok. So, so what are all these things useful for like I said whenever you design or develop a communication system or evaluate a communication system you are always interested in probability of error versus some quantity which which is like SNR. So, far we just saw SNR right and you want to do that and then you want to compare against capacity ok for the same SNR what is the best I can do and then you compare those two things ok that is where these things are useful. So, one more quantity which is very related very very often used much more than SNR is this EB over N naught ok. So, what is this EB? EB is defined to be energy per information bit ok right. Suppose you are using see now the number of bits in the constellation becomes important ok. So, I am defining EB as the energy per information bit what is this information bit will come to later ok. So, but right now just take it as a definition ok. So, suppose I have a constellation X ok and suppose now say R is the rate in bits per symbol ok. So, if you do uncoded transmission what is R in terms of size of X I am sorry log base 2 size X ok. So, this is equal to log base 2 size X if you do uncoded transmission ok. So, this is for uncoded transmission ok. So, remember that. So, it is a very simple calculation to do if you do uncoded transmission ok. So, later on we will see maybe we will see simple examples or later on I will point out that several times you do coded transmission as in even though you have log base 2 size X log base 2 size X possible you would not do that you will do something lesser than that it turns out to have advantages and it turns out it is powerful enough to take you to capacity. So, that is the idea of coding but for now whenever I say constellation X the rate is log base 2 size X. So, for instance if it is MPAM what is the rate log M base 2 if it is M square QAM 2 times log M base 2 ok M MPSK log M base 2 ok. So, though that is the way you do this computation it is a very simple computation ok. So, once you do that the energy per information bit is very easy to define ok in terms of symbol energy every symbol has energy ES ok every symbol carries R bits per symbol. So, the energy per information bit has to be ES by R ok. So, that is the simple definition for EB ok. So, now one can relate SNR and EB over N naught in a very very easy fashion ok. So, what is SNR? SNR is we saw it is ES by sigma squared ok ES we just now saw is EB times R what is sigma square in terms of N naught it is N naught by 2. So, you see EB over N naught is SNR divided by 2 times R ok. So, this is an important formula ok it seems like a very trivial thing to do, but anyway it is important enough that I should box it ok. So, that is why it is also called rate normalized SNR ok. So, this is EB over N naught is important for various reasons. So, for instance SNR somehow does not have the information about number of bits per symbol which is a crucial thing because capacity is defined in terms of number of bits per dimension or number of bits per symbol ok. So, you should know what rate you are doing and that should be somehow closely related to the SNR. So, somebody says I am achieving 10 power minus 6 symbol error rate right that at some SNR of 3 dB if you have two systems and SNR of 3 dB both of them are achieving 10 power minus 6 symbol error rate you should not say both the systems are doing equally well ok. You should also know what rate each system is doing one system might be doing two bits per dimension while other system is doing one bit per dimension ok. So, in that case one system is better than the other ok. So, one to make a fair comparison you have to normalize by rate. Once you normalize by rate it is enough if you just look at EB over N naught. If you take EB over N naught into consideration you do not have to worry about rate anymore. So, that is the advantage of EB over N naught ok. So, one calculation that is very illustrative in EB over N naught is calculating EB over N naught for MPAM and M squared QAM ok. How will you compute EB over N naught? So, this is uncoded ok. So, it is all uncoded. So, we will take what is EB over N naught now you would look at ES, ES is what? M squared minus 1 D squared by 12 right divided by what SNR right then you divide by 2 times rate ok. So, it is good to write it this way. So, it is a little bit clear ok. So, what do you get the answer to be? M squared minus 1 D squared by 12 N naught log M base 2 ok. So, you see the division by log M base 2 shows up in EB over N naught ok alright. So, now we know for MPAM probability of error is what? Q did we have a 2 in front? So, it is about 2 Q square root of 3 SNR right. So, SNR is what we SNR divided by M squared minus 1 is that right? Is this the formula we had? Ok. So, if you do the simplification and write it in terms of EB over N naught what do you think you will get? It is not a very difficult thing to write down ok. So, remember EB over N naught is SNR by 2 times log M base 2. So, you will multiply by 2 times log M base 2. So, you will get square root of 6 by M squared minus 1 EB over N naught ok. So, the uncoded plot for MPAM with respect to EB over N naught will be slightly different from PE versus SNR. So, if you plot PE versus SNR ok. So, you will get a certain picture ok. So, this suppose this is 10 power minus 6 this point will be roughly around let us say 14 dB ok some number ok. So, if I do the same plot with respect to EB over N naught what will happen? Ok in dB ok what will happen? This curve will shift to the left or right to the left by both 3 dB right factor of 2 ok. So, this you will get the same picture except that this point will be around will be around roughly 11 dB ok. So, that is the it is a picture I think I believe this this this is for say M equals 2 ok. So, so it is very standard to do this in dB remember this plot is much more standard than SNR ok. Particularly when you do coding and all that you have to take care of R ok the rate R. And for those cases PE versus EB over N naught is much more standard than PE versus SNR ok you do not have to worry too much about this is just a 3 dB shift ok. But in terms of when you do coding and when you do more advanced of EB over N naught turns out to be a much more natural and important measure to have ok. So, it is always done and you know how to go from one to the other simply divide by 2R ok.  You can also do for M squared QAM and you will get some interesting similar results ok. So, the last piece of information is capacity in terms of EB over N naught ok. So, this is interesting ok. So, how did we do capacity in terms of SNR half log 1 plus SNR remember it is all base 2 bits per dimension ok this was my capacity. So, now EB over N naught is SNR by 2 times R ok what is R? R is number of information bits remember per symbol. So, this was my EB over N naught ok any rate R that I can achieve will be less than or equal to capacity ok. So, I can say R will be less than or equal to half log base 2 1 plus SNR which is ok. So, let me keep it as SNR ok. So, the fact that I am able to achieve this rate R with very low probability of error means SNR has to be greater than or equal to what? You do the simple conversion it is 2R 2 power 2R minus 1 ok right. So, this is another way of stating capacity ok any rate I can achieve has to be less than or equal to half log 1 plus SNR bits per dimension or the SNR I am using has to be greater than or equal to 2 power 2R minus 1 ok right. So, if I convert this to EB over N naught what will happen? EB over N naught has to be greater than or equal to 2 power 2R minus 1 divided by 2R ok. So, to achieve any rate R I need a EB over N naught of at least 2 power 2R minus 1 divided by 2R ok. So, a typical point to take is R equals 1 if you take R equals 1 what is the answer you get 3 by 2 ok. So, 3 by 2 in terms of dB will work out as what? So, 1.7 right. So, 1.7 dB ok. So, for R equals 1 EB over N naught should be greater than or equal to 1.7 dB ok right. So, you can do a plot of PE versus EB over N naught for the system that you have and figure out at what point you are hitting 10 power minus 6 like a like the plot I had before ok and then compare that with 1.7 dB if you are achieving R equals 1 ok compare that with 1.7 dB then you will know how far you are from capacity. So, for instance if you are doing un coded BPSK what is R? 1 ok. So, you can do plot of PE versus EB over N naught it will hit that around 9 dB or so 9, 10 dB ok. So, you will see the gap is about 9 dB it is a big gap ok. So, that is the picture to keep in mind ok. So, that maybe I should draw that picture ok. So, if you take un coded BPSK ok I think I showed this picture before and if you plot PE versus EB over N naught you are going to get a plot which looks something like this and maybe this goes around 10 dB to 10 power minus 6 ok. So, this is un coded BPSK and what capacity tells you is you can achieve R equals 1 at around 1.7 dB this is capacity. So, this is the possible coding gain that you can have ok alright this is for if you are doing R equals 1. So, these are plots that are very standard whenever people describe digital communication systems they would put a plot like this and say this is my coding gain this is how far I am away from capacity and all ok. So, an interesting exercise is to say look at this formula EB over N naught ok it is greater than or equal to 2 part 2 R minus 1 divided by 2 R ok. So, now, suppose I say I want to keep decreasing my rate R and find out the lowest possible EB over N naught at which I can have reliable communication ok. So, that is an interesting measure to think of. Suppose I am willing to decrease my rate to as lower point as possible, but I want to still have error free communication. So, what is the lowest possible EB over N naught? So, to answer that question you can take this expression and let what R tend to 0 what do you think it will converge to if you tend to R to 0 2 power x minus 1 by x converges to log 2 base E ok. So, RHS will convert to converge to log 2 base E which is what roughly 0.693 this will work out to minus 1.59 dB ok. So, there you go that is an interesting result reliable communication is possible only if EB over N naught is at least minus 1.6 dB. So, in some ways that is a fundamental capacity ok, but you have to be willing to tend R to very low numbers to get achieve something like this ok. So, but for larger R the capacity is larger ok. So, I think it is pretty much most of the general things that I wanted to say ok. So, yeah this kind of plot I have to emphasize once again that this is this is very important ok. It might seem like a very dumb thing right now, but as you as you see more and more complicated systems it will be impossible to analyze them ok. So, the only thing you can do is do what I call Monte Carlo simulation. So, you repeat the same simulation over and over again and then you measure your bit error rate as a function of EB over N naught and plot it on top of this ok. So, then you get some good comparisons ok. So, that is where we will stop today pick up from here tomorrow.


channel for physics. Please subscribe my channel. Hello and welcome back to another episode of physics partner. Today I joined you with a very unique and extremely interesting topic known as Bremstrahlung radiation. The term Bremstrahlung is derived from the German word Bremsen to break and Strahlung is radiation also called breaking radiation or declaration radiation. Brems radiation is a type of electromagnetic radiation emitted when a charged particles upon getting deflected by another charged particle is decorated. These charged particles are mainly electrons or atomic nuclei. The particles in motion upon clashing loose kinetic energy, the lost energy is emitted as radiation is the form of photons. Thus the law of conservation of energy is also satisfied. This is known as Bremstrahlung radiation. The Bremstrahlung radiation has a continuous spectrum. The peak intensity tends to shift towards higher frequency with the increase in the energy of the decorated charged particles. Let's recreate a historical movement by similar virtual lab to elaborate more about Brems. In 1895 Wilhelm Ronkton discovered that the beam of cathode rays could create a new type of radiation x-rays when allowed to impinge up on an obstacle such as a glass of the tube itself. The present demonstration recreates that discovery. A Melty's cross CRT is the source of cathode rays as well as target. A modern Geiger-Muller counter detects the x-rays. The Bremstrahlung x-rays are emitted when electrons get decorated when fired against a metal target. These charged particles emit Bremstrahlung radiation in the form of photons or Bremstrahlung x-rays. The continuous spectrum form due to bombardment of electron lies in the x-ray region of the electromagnetic spectrum. Let's talk about the difference between Bremstrahlung and characteristic radiation. The two unique mechanism of which x-rays are produced are called Bremstrahlung and characteristics processes. Brems x-rays produce a continuous x-ray spectrum whereas characteristics x-rays are produced as specific narrow bands of energies. In terms of astronomy, one of the most interesting examples of Bremstrahlung radiation in the universe is that, coming from the hot, it's an intra-clustered gas of klexic clusters. The gas has x-rays luminosities of 210 to power 38 watt, roughly 10 billionth to 1 trillionth time the luminosity of the sun and temperatures on the order of 10 million Kelvin. X-rays telescopes can detect this radiation as diffuse light as seen in the image of the comma cluster. Bremstrahlung is one of the processes by which cosmic rays dissipate some of their energy in the earth atmosphere. So, thank you very much for watching and listening. I hope you enjoyed the video. I hope this video is very useful for you. See you in the next video. Take care of yourself. Goodbye.


My name is Mark Shklav. I am the host of Think Tech Hawaii's Law Across the Sea program. My guest today is Troy Andrade. Troy is a graduate of the William S. Richardson School of Law at the University of Hawaii where he is currently a law professor. He is also a litigator and a Hawaiian History Legal Scholar. Troy and I have previously discussed the 1893 overthrow of the Kingdom of Hawaii. Today, we are going to continue that discussion by going back in time to 1843 and events which have shaped the future of present-day Hawaii. The title of our program is Umau Ke'ea Okaaina Ikapono. In 1843, a British Lord, Lord George Paulette came across the sea and seized control of the Kingdom of Hawaii in what is now known as the Paulette Fair. On July 31st, Hawaii celebrates Hawaiian Sovereignty Restoration Day, which commemorates the restoration of sovereignty to the Kingdom of Hawaii following the occupation of Hawaii by Great Britain. Troy, welcome. Good to see you again. Thanks for having me, Mark. Aloha. Aloha. I'd like you to start us off with a recap of what happened during the overthrow with Queen Liliuokalani.  Sounds great. So in 1893, Liliuokalani is the Queen, the Sovereign, the Moe of the Kingdom of Hawaii. Prior to that, her brother, Kalakaua, was the King. And Liliuokalani inherited a situation in Hawaii that was quite tenuous. There was a lot of turmoil within the Hawaiian community, within the business community here in Hawaii, particularly against the rule of the monarch and the sovereign. And what happened in 1893 was Liliuokalani sought to propose a new constitution, a constitution that would, in essence, override the 1887 constitution that her brother was forced to sign that had stripped powers away from the sovereign and disenfranchised a lot of citizens of the kingdom. They called that the bayonet? Often called the bayonet constitution, correct. So in 1893, in January, she's ready to propose her new constitution, a constitution modeled after the previous constitution that would restore monarchical power, allow her to take control back from the business community in Hawaii at the time, and to really help her people. So in 1893, what she did was she prorogue the legislature at Liliuokalani Halle, essentially meaning she closed the legislative session, went back to her palace, and sought approval from her cabinet to approve of the new constitution. And unfortunately, none of her cabinet members were willing to do that, to counter-sign her request to have a new constitution, and by law she needed that in order to declare that new constitution. So she begrudgingly, I think, said that she's going to drop the idea of having a new constitution. What that did was it set up kind of the right time for a small group of individuals within the kingdom who were planning to overthrow the kingdom of Hawaii. A plan that they had for over a decade thought about doing and were waiting for the opportune time to do it, and they saw Liliu's action, one to try to restore monarchical power away from, quote, the people. And two, and I think very importantly, they saw a woman come in and really threaten the power that they had accumulated at that time. And they saw that as the time to enact what they ultimately did in overthrowing the kingdom. So with the assistance at the time of John L. Stevens, who was the minister to the kingdom of Hawaii from the United States, as well as the support of the marines from the United States, they successfully executed the overthrow of the kingdom of Hawaii. That's the condensed version. That's the condensed version. Yeah, we've done a longer version before. But the queen obviously knew what was going on. I mean, she had social events with these folks. I mean, she went to church with them, and they were her ministers, some of them, and why not fight back? I mean, why not resist? Why not do something? I mean, what do you think?  So it's interesting. You know, I will say that one of the lead conspirators for the overthrow was a guy named Sanford B. Dole. And Sanford Dole was actually an associate justice of the kingdom's Supreme Court. The day before the overthrow and the day of the overthrow, he was essentially the president of the provisional government. So the secret was a secret that I think the queen had heard rumors, but she didn't think people were going to act on it. And like I said, all of this was accomplished mainly because of the American support that was given to this small committee of safety. So she didn't believe it would happen, but then she didn't put one and one together, maybe, that there would be this military support. For sure. For sure. And you know, when the troops came into Honolulu, marched across in front of the palace, in front of Aliyolani Halle, she started to get on edge a little. And everybody from her ministers were going up to John L. Stevens and saying, what's happening? Why are your troops landing? You usually need our approval to get your troops to land on foreign soil. And his response was this is just to protect the interests of Americans in Honolulu. And it was, in fact, and through information that we've now seen from the Mission Houses Museum, there's documentation that says John L. Stevens was clearly involved in this plot to overthrow from the beginning and used his power as the ambassador to the kingdom and his power over the military, the American Marines that were stationed here to execute on that plan. Okay. All right. So she knew it was going to happen. She saw the troops come in. Why didn't she do something then? Why didn't she fight then? Why didn't she call her own troops, our own people even? So I think that's great. And everything was on the table. She had her cabinet members were there. Again, they were opposed to signing on to this new constitution. But they're very much in support of protecting the kingdom from its demise. And they were throwing out ideas on what to do. One of the options was to fight back militarily. And all of the records indicate that the queen had enough troops. She had enough ammunition to essentially squash any particular rebellion that would happen from this particular USS Boston and the amount of troops there. The downside was had she done that, had she engaged with the American military, there would absolutely be more American military ships coming into Honolulu Harbor and potentially causing a lot of destruction and devastation for the Hawaiian kingdom, which frankly the kingdom would not stand a chance against the might of the American military. So that was option one, which was definitely on the table, which was advocated by Charles Wilson, who was the marshal of the kingdom at the time. He could gather enough troops and they had all of the ammunition ready to go. Of course, that would also mean a lot of loss of lives, a lot of loss of property, all of which the queen would be responsible for, and she would feel responsible for had she allowed this to happen. The other option on the table, which doesn't really get discussed often, is that she could have turned it over to another, she could have turned her sovereignty over to another country, not the United States, but to Britain or to France. The last option was of course to appeal to the higher powers in the United States to try to make amends for what one of their citizens that was given some authority had done in overstepping their authority. That is definitely the option that they took, and it's an option that's based off of action that happened 50 years before then. What's that about? Now King Kamehameha III faced a similar type of a situation. What's that about? In 1843, Kamehameha III, Kawee Kaoli was the ruler, and he had faced aggression from a lot of different countries at that time. In 1840, he passed a new constitution. This was the first constitution. This was really three years into this new experiment by the Kingdom of Hawaii, this constitutional monarchy. France is very much being aggressive with the Kingdom of Hawaii and wants their way. Because of that, Kamehameha III sends two individuals off to America and to Europe to seek recognition of the sovereignty of the kingdom and independence of the Kingdom of Hawaii. At the same time, Britain starts to get a little more aggressive. One of their ambassador to the kingdom, Richard Charlton, comes in and he was apparently given some land from Kalani Moku, who was sort of the prime minister for Kamehameha I, Kamehameha II, and a little bit into Kamehameha III's reign. He was a very powerful man that apparently gave Charlton a 299-year lease to a piece of property in Honolulu. Charlton then executes on that and starts to kick tenants off of the property. Kamehameha III finds out about this and puts a stop to it and says that Kalani Moku had no authority to give you a lease of 299 years on that property, and therefore you cannot be kicking off the native tenants. Charlton is very upset by this and there are a couple other instances where Charlton and other British subjects felt like the Kingdom of Hawaii was in essence discriminating against them. So Charlton took it upon himself to try to resolve this problem. So he made his way across the Pacific and ended up telling a bunch of different captains. One of them was a guy named George Paulette. Lord George Paulette. Paulette was a naval captain for the HMS Carries Fort and he made his way to Hawaii with orders to keep the piece and make sure that British subjects were not being subjected to or were essentially being treated the same as other foreigners in the Kingdom of Hawaii. Paulette lands in Honolulu Harbor and requests a meeting with King Kamehameha III.  So Paulette arrives in Honolulu, wants to meet with Kamehameha III. Kamehameha III is in Lahaina at the time on Maui. It is going to take too long for Paulette to have to meet with Kamehameha III. Kamehameha III sends in Dr. Jared Judd to try to negotiate with Paulette. Paulette is not having it. He is offended and he unilaterally seizes control of the Kingdom of Hawaii. With his military might at hand, he creates a provisional government in essence that consists of himself, the British consul to Hawaii now, Alexander Simpson, as well as Kamehameha III. This is a photo of Jared Judd in the middle here. He was an American missionary. And part of the offensive nature, I guess, that Paulette saw with this whole incident was that Kamehameha III sent an American to negotiate as opposed to himself coming to negotiate. And for several months, Paulette runs the Kingdom of Hawaii. So you basically have a land dispute started out as a land dispute by a British subject who complained to Paulette. And Paulette comes in that he had no authority to take over the Kingdom. He had absolutely no authority to take over the Kingdom. At the time, there was no formal British policy with the Kingdom of Hawaii. And so his goal, his orders to go to Hawaii was just to keep an eye out, take notes, make sure you see what's happening so that we can then report all of that to then Queen Victoria at the time. Well, word gets out about all of this. And word reaches a guy named Admiral Richard Darden Thomas. Okay. Now, did Dr. Judd, he was involved too? He was helping out, getting the word out? Is that basically what happened? So Jared Judd was, he was a translator for the King. I see. And he was sort of the middle person between the King and Paulette. And Jared Judd played a really unique role because at the time, in 1843, the King's sole advisor or one of his advisors was a man named William Richards. And William Richards helped to create the Constitution, taught the Ali, the chiefs about constitutional democracy, about politics in the world. And William Richards, the King's sort of right hand person, was sent off to try to negotiate a treaty with Europe and America to ensure the sovereignty of the kingdom. So with that, come on to the third, brought in Dr. Judd to help. To help, I see. So look, we're going to take a break right now. And then I want to come back and find out how Dr. Judd helped and how Admiral Thomas got involved. Okay, so we'll take a short break and be right back. Aloha. Aloha. I'm Jane Sugimura, a host here at Think Tech Hawaii, a digital media company serving the people of Hawaii. We provide a video platform for citizen journalists to raise public awareness in Hawaii. We are a Hawaii nonprofit that depends on the generosity of its supporters to keep on going. We'd be grateful if you'd go to ThinkTechHawaii.com and make a donation to support us now. Thank you so much. Aloha. I'm Sharon Thomas Yarbrough, a host here at ThinkTech Hawaii, a digital media company serving the people of Hawaii. We provide a video platform for citizen journalists to raise public awareness in Hawaii. We are a Hawaii nonprofit that depends on the generosity of its supporters to keep on going. We'd be grateful if you'd go to ThinkTechHawaii.com and make a donation to support us now. Thanks so much. Aloha. Welcome back, Mark Schlauves, with Troy Andrade. And we are talking about 1843, right, Troy? And all right. We have Paulette, Lord Paulette, come in and take over the kingdom. I guess, theoretically, on behalf of the British, what happened? What happened? What did Admiral Thomas do? So Admiral Thomas, who is out in the Pacific, is superior to Paulette, finds out what Paulette has done and makes his way to Hawaii. And when he arrives in Hawaii, he is met by a party and Thomas goes and requests a meeting directly with the king. And the king immediately grants Thomas's audience. And they meet and discuss. And by the next day, Thomas famously restores the kingdom of Hawaii and says what we did was wrong and that we have a British policy now in favor of friendship with the kingdom of Hawaii and recognizing the kingdom as an independent nation and the actions of Paulette were wrong and therefore restoring the kingdom to Kamehameha III. Okay. Now, Admiral Thomas came across the Pacific, across the sea. And what role did Queen Victoria, if any, play in all of this? Was she aware of what was going on? Because she was the monarch at the time. So she wasn't directly aware of what was going on. But I had mentioned earlier that Kamehameha III had sent his emissaries out there before this Paulette affair occurred. And by the time they had reached Europe, everything was coming to a boiling point in Hawaii. And they got not formally signed until later in November of that year, but they got the recognition and a policy from Britain. That policy then came back to Thomas. And Thomas went over back to Hawaii and said, this is inconsistent with British policy towards other nations. Hawaii is an independent nation. And therefore I am restoring the sovereignty of Hawaii back to Kamehameha III. I like all those concepts, friendship and restoration, and doing the right thing. And so what does that have to do with the Hawaii model? And what was the reaction of the king to that? So immediately there are celebrations across the kingdom. Kamehameha III creates July 31st as an official national holiday celebrated as La Hoi Hoi Ea Restoration Day. Every year during his reign it is celebrated as that national holiday. Interestingly, it is stopped after he passes during the reigns of Kamehameha IV, 5th Lunalila and Kalakawa, and is reinstated in 1891 after Liliu becomes queen. So maybe that's telling us where her mind was, huh? So Liliu was very much familiar with what happened with the Paulette affair. She'd only been a young child at the time. She had only been a young child, but still the lessons that were learned were passed on, I believe, from monarch to monarch, from advisor to advisor. And back to the overthrow, that was the precedent that she was working off of, that a superior authority would come in and make right for the wrongs that their citizens had caused. So Kamehameha III created this national holiday. He also, in honor of Admiral Thomas, created the first public park in the kingdom and in Hawaii, and it was a piece of land where Thomas had actually restored sovereignty, and it is now Thomas Square. Today there is a beautiful statue of Kamehameha III in Thomas Square. For a long time Thomas Square, the sidewalks were shaped like the Union Jack in honor of Britain and Admiral Thomas' restoration of the kingdom. It was also during this event that Kawee Kawee Kamehameha III said his famous words, which has been translated, which is now our state motto, and also has been translated to mean the life of the land is perpetuated in righteousness. A lot of Kanaka Maui scholars have gone in and said there's way more to just the life of the land is perpetuated in righteousness, specifically with the word ea, which ea is life. But it also, particularly for Kamehameha III, meant sovereignty. In a speech he did, he delivered after Paulette had taken over the kingdom. He referenced ea as our sovereignty has been taken from us, but it will be restored as long as we go down a path that is pono, that is right, that it's just, all of which really hearkens to this Hawaiian concept of imi haku, which is this notion of gaining and keeping mana, this life force that runs through all living beings. And if you continue down a path that's pono, you will be rewarded with more mana. So again, as I mentioned earlier, this was a real experiment for Kamehameha III, this experiment in shared power with not just one sovereign. And so he was looking for a sign that things were good, things were pono. And Admiral Thomas coming over and making things all right was validation, was reaffirmation for Kamehameha III that what he had done in creating a constitutional monarchy and getting advice from not just his chiefs, but from foreigners, from American missionaries, all of that reaffirmed his path of pono, this path of gaining more mana. Doing the right thing. Doing the right thing. And it came back to him is what I hear you saying. Exactly. You know, if you do it, it'll come back. Exactly. And that's what he experienced in his mind. That's what he thought was going on and when Admiral Thomas and that's why he made a park for him. Absolutely. I assume.  And the Queen was thinking maybe the same thing. You know, it's not clear, but I think that's definitely, you know, this Hawaiian mentality was very much a part of who she was as an individual and as a leader. And I think this concept was right there with her. And this affair, this Paulette affair was right there in the back of her minds and the back of the minds of her advisers. And they frankly thought if they had gone to Washington, D.C., that Congress and the President would see the bad things that John L. Stevens had done in authorizing the Marines to land and they would make amends for it. And, you know, 126 years later, Native Hawaiian people are still looking for that. Still waiting for Pono to happen. Correct. Now, do they still have this feeling?  So, absolutely. I think this idea of finding the path to making things better is still there. There's been a lot of efforts to try to reconcile with the United States, with the state of Hawaii for everything that has happened to, since the overthrow of the Kingdom of Hawaii, to make the lives better for all of the citizens of the Kingdom, but particularly for the Native Hawaiian subjects of the Kingdom who were disproportionately dying off, who to this day have statistics that are, you know, some of the worst statistics and some of the highest statistics for things like incarceration and mortality rates. So, all of that I think is what's driving Native Hawaiians to try to reconcile. It was definitely the push for the sovereignty movement early on, because what happened after the overthrow was this process of Americanization that really in public schools led to this history not being taught and led to people actually forgetting and misremembering what had happened in the past. And that sort of came to to light in the 60s and 70s. That's interesting. Okay. I see. Come back and let's do Pono. Let's do the right thing. And we weren't taught that. The history didn't teach us that. Yeah, I understand. Yeah. So in the 60s and 70s, I think as the elders are dying off, really the ones that were there at the time, the ones that interacted with the Queen, they were dying off and they had their stories to tell. And they started to tell their stories to their children. And those children got older and in the 60s and 70s, that all came to a head, which with what is commonly called the Hawaiian Renaissance, this political, cultural, spiritual revival. And you had some key events that happened in the 70s, like the bombing of Kaho'olavi that really catalyzed the movement for Hawaiian recognition, Hawaiian, the restoration of some form of Hawaiian sovereignty. And there has been some good coming back from doing good things too in the current day. Absolutely. Absolutely. So Native Hawaiians tried. And in 1978 at the Constitutional Convention, there are a lot of changes that happened for Native Hawaiians. There frankly, no one was expecting to happen at the 78 Con Con. Going in, everybody thought the only issues related to Hawaiian affairs that would be addressed were related to the Department of Hawaiian Homelands. Post-78 Constitutional Convention, you get constitutional requirements for making Hawaiian language the official language of the state, the creation of the Office of Hawaiian Affairs, the reaffirmation of traditional and customary Native Hawaiian practices and cultural, religious practices. Education and history is now mandated to be taught in Hawaiian language, in public schools. So all of this porno stuff comes out of this Constitutional Convention despite everything that was thrown in the face of Native Hawaiians. And so maybe in Kamehameha, the third and Queen Naliyo Kalani were right and did the right thing and are waiting for it to come back. And hopefully, it will. Troy, thank you so much. I appreciate your time. And we'll continue this discussion, I hope. Aloha. Aloha. Thank you very much. That's a wrap. I'm Mark Shklav. We're closing a lot across the sea. Aloha.


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But so far, the money had dwindled and the take from the claim had been extremely little. One evening at supper, after Fred put in a hard day working the claim, his mother tried to encourage him. John, you haven't smiled since you came in. The winter's setting in past now. I thought by this time I'd have stuck enough paid dirt to carry it over. We'll get through somehow, Fred. I'm sure that before long, you'll make a strut. We run out of money. Food is high, and with the winter breaking on us now, what are we going to live on? Fred, perhaps we could get credit at the treatment post to carry us until the claim does pay off. Why don't you take the dog team right now and go into Dawson to the trading post? But if they should give me credit and I couldn't pay later, we'd lose the dog team and the claim too. You've got to face it here. We certainly can't keep the dogs if we can't feed them or ourselves. It's a chance we'll have to take and then hope for the best. Well, all right, Mom. I'll go to the trading post and see what I can do. They won't give me credit. Well, I reckon the only other thing will be to sell what we have and get back to Seattle somehow. Fred, the hitched up the dog team and set up for town.  Oh, hold on. He stood for a moment hesitating. He could see several men standing around the big stove inside as he gazed through the window. Well, here goes. I don't get credit for this. What can I do for you? Well, I want to get quite a lot of supply. Sure, sure. Now, if you just give me your list and get them together for me in a jiffy. Well, at first, well, I can't pay right now. You'd trust me until my claim pays off better. Yes. But you'll get your money. Just look at that. Isn't that I'm hard-hearted or anything like that, mind you? But the first year of the rush, I got took for plenty by chichacos who promised to pay me off when they made a strike. Now, having myself to think of two, I made it a policy not to stake anyone who doesn't have a pay-in claim. Oh, look, my name's Fred Olton. My mother and I have claimed 20 up in Bonanza. We have a dog team and Fred and a cabin up there. If you could see your way clear in our case... Oh, and I know where number 20 is located. It's one of them secondary claims back off the creek on the hilltop. Well, that's right. Not one of those claims there have paid off, Olton. Sorry as I am to say it. Now, it would be better for you to cash in for the little you'd get on your dog team and cabin right now and save yourself a lot of greed. Winter's setting in. We couldn't get out of the territory even if we decided to. Especially if I sold a dog team. Sure and a good many find themselves in the same predicament, sad to say. Well, I feel sure if you let me have the supplies that I'll make that claim pay off. Sorry, lad, but I just can't do it. There's several useless cabins and bad claims I have on the hands already for unpaid accounts. No, for bitter grub to last a day or two would help you. I'll let you have it. I'm not asking for charity. Just forget the whole thing, mister. I'll find a way to get the supplies I want one way or another. With discouragement in his heart and his mind torn with frustration and unreasonable anger, Fred left the trading post and approached his dog team. For a few minutes, he stood near his sled, dreading to start back home of the disheartening news. As he stood there undecided what to do, a heavy-sucked man came out of the trading post. Hello, Oldman. My name is Jerry Strong. Hi. How'd you know my name? I don't remember meeting you before, Strong. We haven't met before. I happened to overhear you talk with a storekeeper. What I heard, I figured things are kind of tough for you right now. I think that's right. If you think you'd be interested in making some cash, maybe I can help you do it. Just what would I have to do to get the cash you mentioned? I'd like to hire you and your dog team for a few hours tonight, that's all. But I'll pay you well for it. What do you want to hire me and the dog team for? Well, it's a friend of mine over in the cafe. I want you to take him and me a few miles up Wolf Creek a little later tonight. We have some business up there with an old prospect or friend of ours. What do you say? It's lame. Oh, it doesn't make any difference. We'll pay you $25 to take it there and back. $25? All right, I'll do it. Good. You meet us in front of the cafe in about half an hour. I'll see you then. We'll continue our adventure in just a moment. It's to wind up the pitch. The bases are loaded and it's a two-waggle as the game's tied up. Say, kids, come out to the ballpark as guests of a major or minor league team. Right now, you can see baseball games free if you are 12 years or younger. Just bring a paying adult like mom or dad. And you can get your free ticket immediately. No mailing, no waiting. Free baseball tickets are right inside packages of Quakerpuff wheat, Quakerpuff rice, and Muffet shredded wheat. In QuakerPackle 10, you get two free tickets. Names of the teams and dates of the games are on every ticket. Remember, the more packages of these delicious Quaker cereals mom gets, the more free baseball tickets you get. So tell mom you want to eat lots of Quakerpuff wheat or puff rice, Muffet shredded wheat, or QuakerPackle 10. And just think of the fun you'll have at the ball game. Seeing real star players in person and cheering for home run. A few minutes after Fred and Strong separated in front of the trading post, Sergeant Preston and his dog King came up the street and entered. Come along, King. Well, now, it's good to see you, Sergeant. And King, too. I haven't been around for the past two weeks or so. No, Mike. King and I just got in from a trip to Selkirk. I find I'm out of coffee, so I dropped over to get some. Coffee, it is, Sergeant. Yeah. Sure, that's all for now? That's all I can think of, Mike. Oh, Mike, but it's still good. That it is, for anything in the place. Sure, in just a short while ago, a lad came in asking for credit through the winter. Sorry I was to have to turn him down. Only what I know? Oh, that I can't say. The name was, um, you know, let me see. Oh, yes, Orton, he said it was. Fred Orton. Has a claim upon bonanza. One of those hillside claims that never seemed to pay off. The young fellow and his mother will have to claim that thing. It seems to me that was his name. Like his nurse, it's the same chap. Dark, nice-looking. Said he and his mother have number 20 claims. Yes, that is the same one. My conscience has been bothering me since he left for lab. He was that upset he went out and slammed the door behind. I see. Things must be rather bad for them, then. Yeah, that's right. He said they were out of money, but he still seemed sure he'd make a go of it if they could get through the winter. Soon he looked so desperate when he left, saying he'd get supplies one way or another. It's certainly to think, and that it is. Must be very hard, Ed. Yeah. You think you'll be heading out that trail any time soon, Sergeant? Why, Mike? Well, now, if we do, stop by and tell Orton I changed my mind. Oh? To come on in and get the supplies he needs on credit. The look on his face will haunt me all winter if I don't give him the credit he had for it. I'm glad you changed your mind, Mike. You're not losing by it. I think I'll go up there in the morning and give him the news. Good. That'll be a relief to me, Mike. I'm sure it'll be a relief to them, too. Good night, Mike. Good night. Come along, King. Jerry Strong and his friend, Baldi, found Fred Orton waiting outside the cafe with his dog team as he promised. The three men set out along the well-beaten Wolf Creek trail. The cold, gusty wind swirled the light-dry top snow in white, dusty clouds, obliterating any slight tracks they might have made. Sometime later, they stopped before a remote cabin. Oh, who am I? Well, this is the place. Our business is rather private. I wonder if you'd mind waiting outside for about five or ten minutes. I guess I can stand it. I'm sure you won't be any longer in this. We won't. Don't worry. Come on, Baldi. Let's get inside and get this over with. All right. Fred watched as the two men went to the cabin and entered without knocking. For a few minutes, he heard nothing but the wind. And then his attention was attracted by the voice of a man raised in fear and protest inside the cabin. Oh, no! Get out of here! I'll let you have it! A moment later, Fred was startled by the sound of a muzzle shot. That shot was inside the cabin. I'd better go see what happened. As Fred reached the door, it suddenly opened and strong barred his way. But not before he saw a sight inside that gripped him with a sudden fear. Get back to the sled, old man. Hey, that old man lying on the floor. You shot him. That's right. We did. I get back to the sled and make a friend. Put the sack of cold dust under the blanket on the sled, baldy. Sure. You ride on the sled, baldy. I'll follow along behind the stumpy charcoal and have my gun handed. Now I get it. You took that old prospector's golden and murdered. You're getting a little smarter now, old man. I'll start the dog team and go straight ahead. But that's going away from tossing. I have to get back. My place is in Bernanth and Craig.  You're not going back. We're heading for Selkirk and you're going with us. After the threats you made in the trading post one way or another, they'll blame you for what happened when you turn up missing. I'll get going. All right. Come on. Early the following morning, Sergeant Preston took King and went in the impromptu to deliver Mike's message to the old man. He stopped at their cabin. Good morning, Mrs. Olden. You... you're Sergeant Preston. That's right. I just know you've come to tell me something has happened to Fred. Please, Sergeant, tell me what's happened to our boy. Well, Mrs. Olden, I came here to see your son to bring him a message from the trading post. But Fred isn't here. He didn't come home last night. Oh, I'm so worried. I've been almost out of my mind. Well, I'm sure he's all right, Mrs. Olden. It was a little upset, I understand, because Mike at the trading post refused in credit. Poor Fred. That was his last hope. But Mike changed his mind. I came to tell you and Fred that you may have all the credit you want. Oh, thank heavens. But, Sergeant, where can Fred be? Oh, don't worry. I'll try to locate him. Perhaps you'd better get your rafts and come to town with me. You can wait at the trading post until I find him. Yes, yes, I couldn't stand waiting here any longer. I'll get my things and be with you in a few minutes, Sergeant. Oh, do come again. Thanks. Come on. Oh, uh, you have something of your son's, a glove or something like that. Well, yes, of course. Here's a glove of yours, but why do you want it? Just in case I have to trail Fred, King will be able to get the scent in his clothes. Oh. Now we'll get started for town. Come along, Colin. You'll be warm enough under the blankets on the sled. Here, let me help you. You're so very kind, Sergeant. Thanks. I'll try not to worry. I'm sure everything will be all right. All right. I'm coming. Sergeant Preston took Mrs. Alton to the trading post and left her with Mike's wife. Then, leaving his dog team outside, he and King went through town making inquiries about Fred Alton, but learned nothing. Finally, Preston stopped in at the constable's office. Hello, Sergeant. Hi, there. Morning, Constable. You happen to know young fellow named Fred Alton has claimed 20 up on a bonanza. Well, I've seen him once or twice. Five times? Why? He came to the trading post last night. When he was refused credit, Mike said he looked desperate. As he went out, said he'd get supplies one way or another. He didn't get home last night. That's not that good, is it? No, it isn't. I'm worried about it. His mother's quite upset, too. I seem like fine people. Fred doesn't just sort of do anything out of the way with what a man's been desperate for. Yeah, yeah, I know what you mean. He's gone, is he? Just thought of something. He was at the trading post last night. Probably left his dog, King, right out front. I have one of his gloves. King, he got the scent from that. Then we can go to the trading post to see if King can pick up Alton's trail. I'll say that's a good idea. I'll come along with you. I'd like to see King in action. All right, glad to have you. Let's go. Come on, King.  Preston held out Fred's glove for King to sniff. Then he spoke a command. Finding King, find him, fella. As the two mouties watched, King put his nose to the frozen ground and circled around, trying to find the scent of a similar to the one on the glove. Suddenly, he barked eagerly, ran a short distance, then stopped and looked back, still barking. They found Alton's trail, Jim. Well, what do you know about that? After him, fella, finding King, on King, on you, Husky. King headed along the main street. Reaching the cafe, he circled a few times and then started in the direction of the Wolf Creek Trail. Preston and the constable hurriedly followed King for the dog team to find the approach to the old prospectus' cabin. King had stopped there and came in puzzlement. Then as the two men came along with the sled, the great dog turned toward the cabin and sniffed at the door. Oh, how you doing, fella? I'd say that Fred Alton went on up the trail and had stopped here at this cabin. I'd say that Fred Alton had stopped here at this cabin first. Well, we'll go in and ask about him. Come on. What do you say, will you, sir? Take a look at me now. What, constable? What's there on the floor? The old prospector named Drew. We said to have quite a bit of gold here, his cabin. He's done for all right. Shot through the heart. Constable, you've got to go back to town. Take my team and sled and carry to his body. All right, sir. You're looking for Fred. I'll follow his trail and we'll find him and bring him back.  All during the night and most of the following morning, Jerry Strong and Baldi forced Fred Alton to mush steadily onward over the frozen trail that led to Selkert. During the few short stops they made for food and rest, Fred racked his brain to think of a way out of his predicament. But he didn't have a gun and the two crooks were constantly on the alert. One or the other was always watching him with a gun ready for instant use. Finally, they reached the deserted cabin on the side of a trail and decided to make a prolonged stop. It was late afternoon and they made preparations to hit the trail again. That's a good thing we found that George Venison someone to cash here, Baldi. We'll take what's left along with us. Yeah, we'll need it before we reach Selkert. Oh, that's strong. You've got this far. Why not take my dog team and let me make my way back? My mother's there waiting for me and by the time I get back to Dawson, why do you hear that, Baldi? Olden wants us to let him go back and tell the Monies what he knows. That's a hard one. But all you have is that small supply of dried venison. It won't be enough for the two of you, much less for three. Selkert's still a long way from here. What's more, the dogs will need some food and they'll give out. Hey, there's nothing to what you say, all right? But then you'll not make me go on with you? Nope, I reckon not. Hey, let's come over here, Jerry. As it is, the Monies will be looking for Olden when they discover that dead prospector. But if Olden gets back to tell him the truth, they start a search for us. Who said he was going to get back? I'm not that crazy. I said I decided not to take you along with us from here. In other words, Olden, dead men tell no tales. We'll continue our adventure in just a moment. Hey, kids, wouldn't you like to be in the ballpark and see how a star pitcher makes the ball curve right over home plate? Golly, everything about a major or minor league game is exciting. Get in on that excitement. Come out to the ball game as guests of a major or minor league team. Walk right through the gate free if you are 12 years or younger and have mom or pop with you or another paying adult relative. It's as easy to get a free baseball ticket as going to the grocery store. Get it right inside packages of Quaker Pop wheat pop rice, and Muffet Shredded Wheat. You get two free tickets inside Quaker Paco 10. Names of teams and dates are on every ticket. Golly, why wait? When mom buys breakfast cereal, be sure she gets the kind with a free baseball ticket inside. That's Quaker Pop wheat or rice, Muffet Shredded Wheat, or Quaker Paco 10. To continue. In other words, Olden, dead men tell no tales. In other words, Baldi looked meaningly at Fred Olden as he said. Now I get what you mean, Jerry. You intend to give him the same as we gave the prospect. Let me go. I promise not to say anything. Think of my mother. You can think of her to Baldi gets the meat ready to pack on the sled. After that you won't do anything. Or talk it. I'll take the dry venison out to the sled right now, Jerry. Don't do anything till I get back. I want to watch the fun. The blood doesn't murder strong. I don't care. I'll get your wine until Baldi gets back inside. He'll enjoy it. I'm getting tired of holding this gun all the time anyway. Hey, Jerry. Somebody's coming along the trail. Looks like a mountain to me. A mountain, huh? Let's do some fast thinking. Baldi, when he gets here, you answer the door. See what he says. I'll stand back here and have the gun pointed right at the door. You stand over to one side so he won't see you when Baldi opens the door. I'll get over there and keep quiet, understand? If you don't, I'll... All right, I'll keep quiet. I'll let the money in. We'll leave two of them behind when we set out for Selkirk. Meanwhile, Sergeant Preston, with King running just ahead of him, approached the cabin. He saw the dog team waiting out front. Taking his gun in his hand, he approached cautiously, Oh, hello. I didn't expect to see you, Baldi. You live here? Sure do. I suppose that's your dog team. Yep. It's getting ready to go after more supplies. I'm looking for a young man named Fred Alton. It's all rather dark. You seen him? No. Nobody's been by here for several days. You lie, Mr. Fred Alton came here and entered this cabin. That's what you think. Why not come in and look around? I shall. Stop aside. As Sergeant Preston with a drawn gun stepped across the threshold, Fred Alton yelled out a warning. Preston had been keeping an eye on Baldi, even though the man didn't have a gun. Momentarily gave his attention to the inside of the cabin. As the money stepped past him, Baldi grabbed for his gun arm, at the same time calling out to Jerry Strong. Oh, grab him, Jerry. Use your gun. Holding Joel, pressing aside, Preston lashed out with a slashing blow. As Jerry Strong would help fire a moment to avoid hitting Baldi, he raised his gun. Fred Alton jumped in front of Jerry Strong's gun and took a bullet intended for Preston. The strong raised his gun for another shot at Preston, King without waiting for a command lunged forward, grabbing the killer by the arm and dragging him to the floor. Help, the dog! Get away, will you? Longing, down below, good, King. Fred. All right. I plan to kill you if you came here.  You took a bullet intended for me, Fred. Let me see that. Picture right shoulder. I killed an old prospect and forced me to go with him. I'll take all three of you back to Dawson City. After we get there, we'll learn the truth about everything. Preston handcuffed the two crooks together, put Fred Alton on the sled and started back to Dawson. Fred's mother was told what had happened and though she was relieved that her son had been found, she waited anxiously the next day while Fred was taken to the constable's office to be questioned with the two crooks. Later that afternoon, Preston with King and Fred entered the trading post where Mrs. Alton was waiting. Fred, is everything all right? Well, you finally got the truth, Mrs. Killers, Mrs. Alton. I'm glad to say that Fred's been exonerated. Thank heaven. I just knew my boy wasn't guilty. I felt sure of that too when he took the bullet intended for me. If guilty, he wouldn't have done that. Was a mighty fine thing for him to do. Did you tell him to do so? Yes, Mike, he did. I'll make good at the claim. I heard something else today that makes me think you will, Milad. Two claims right next to yours have struck a great share. And with yours between the two of them, you can be sure there's gold there. Isn't it wonderful, Fred? Golly, it sure is. Of course, you'll have to dig for it. But meantime, anything you want is yours. On credit. Now, do you get those men to tell the truth, Sergeant? Each one blamed the other for Joe's murder and they finally told the whole story. King saved the day at that cabin. You'd have had your hands full with the two of them. He's certainly a wonderful dog. I think because of him, Sergeant Preston was able to trail you and reach you in time. He knows we're talking about him. That he does. Sitting there with his ears perched up and sought a grin and like. I think he's happy, I'm sure, Mike, because he knows things have turned out all right. This case is closed. We'll return in just a moment with a word about our next exciting adventure. Young America keeps his musical knowledge up to date by listening to Phonorama Times starring Johnny Desmond. Every Saturday, Johnny presents a roundup of the planners that are making musical history from coast to coast. In addition, he brings such outstanding big-name guests as Theresa Brewer, the Fontaine sisters, and Bill Haley's comments. Guest disc jockeys from every section of the country appear regularly to report to listeners on the top tunes in each of their hometown areas. And interesting teenagers appear on Phonorama Times to bring their viewpoints on what Young America is thinking about and talking about in music and other fields as well. Everyone loves Johnny Desmond and everyone loves his Phonorama Times show. So gather your friends and fellow music fans around this Saturday and every Saturday for the musical session you can't afford to miss. Phonorama Times starring Johnny Desmond on Mutual over most of these stations. Sgt. Preston knows a strong organization for taxonatorious, curly-tagged. He anticipates problems in this new assignment, but he can't foresee the grim peril that threatens not only himself, but also his dog King and some of his best friends. Be sure to hear this next exciting adventure. These Sgt. Preston of Yukon Adventures are brought to you every Monday through Friday at this time by the Quaker Oats Company, makers of Quaker Pop Week and Quaker Pop Rice, the delicious cereals shot from gun by special recording in cooperation with the Mutual Broadcasting System. They are a copyrighted feature of Sgt. Preston of the Yukon Incorporated, created by George W. Trendle, produced by Trendle Campbell Muir Incorporated and directed by Fred Flower Day. Part of Sgt. Preston is played by Paul Sutton. This is J. Michael wishing you good-bye, good luck and good health from Quaker Pop Week and Quaker Pop Rice. So long. This is Mutual, Radio Network for All America.