Okay, so this is what? This is lecture 27, 27. Okay, so the last thing we were seeing was this update rule at the check node. How do you quickly compute it? How do you write it down? We try to simplify it. Finally, we had some expression, we had to deal with this function. And I want to talk a little bit about that function, right? What was this function? Log tan hyperbolic, sorry? Yeah, mod x pi. Okay, so I think it's good to, I think people when trying to invert it had some trouble with signs and all that. I want to talk about it first of all. Another thing I want to point out is we are only worried about the magnitude here, right? The sign of f of x is not that relevant. So I might even think of this as that being a model as outside. Okay, but usually, you don't put that, I'll tell you why it's not really necessary. Okay, so how will tan hyperbolic x look if you plot it versus x? I don't know, maybe x by 2. Okay, how will that look? What is the value at 0, 0, not 1, it is the infinity, it will get to 1. Okay, and then it will rise and what will be its slope at 0, I think it will be something non-zero. So it will get some, it will start off somewhere and then go this way. If it has just to x by 2, you get up to minus 1. If I do mod x by 2, it will only go in that way. But anyway, I'll plot x by 2. So I'll get something that looks like this. Okay, so what's important is it lies between plus 1 and minus 1. Okay, so to be able to take logarithms and all, I have to do modulus, but what will happen if I take logarithm of tan hyperbolic of x by 2? Will I get a positive value or negative value? It will all be negative, right? Because tan hyperbolic is less than 1. Okay, so if you take logarithms, you're always only going to get negative value. So log of tan hyperbolic of x by 2, after you take logarithms, will always be negative. Okay, so you can as well add, I mean you can take absolute value and add, that's what we want. It's the same as just adding and then ignoring the sign at the end, just taking the positive magnitude value. Okay, so if you had to plot this function f of x, if you want to be careful about it, it would look something like this. If you just plot x versus fx, okay, for the positive part, it will look something like this. Okay, it will be a function like this and it will be symmetric around the x equals y line. Okay, so that's what I claim by saying it's its own inverse, right? If you swap the x and y axis, the function doesn't change, it looks exactly the same. Okay, so it will be symmetric that way and that you can show. Okay, yeah, the value is negative always. Yeah, when you might have to do minus f of x, minus f1 or something, but it doesn't matter. If you worry only about the magnitude, you might as well flip it up and put it back. Okay, so you'll have some minus sign issues, but for simplicity, I'll simply write f as being its own inverse and I'll write f of x is log tan hyperbolic mod x by 2. Okay, so the sign problem is understood and you have to take care of it when you do your, okay, hope that's clear. Okay, so there'll be one issue. So when we deal with this function f of x, I'll simply write f of x is log tan hyperbolic mod x by 2 and they'll say f of f of x is x. Okay, so there is a sign, up to sign these things are true, we'll just take sign only, only magnitudes. Since all of it is negative, this will work out properly. Okay, so there's one comment I wanted to make about the derivations we did last class. So let's proceed now. So let me rewrite what is it that we had. Okay, so if you have, okay, so this is the recap of what we did last class. If you had x being y1 plus y2 plus, so until y, let me say d, okay, then and if pi 0 is probability that pi is 0 and let's say there's one more thing. So and yi is the log likelihood ratio, right, so log of pi 0 by pi 1. Okay, then yx we are able to write as, write in two ways, basically the magnitude of yx will be what? f of summation i equals 1 to d f of yi. Okay, and then what about sign? What? Product of the signs. Okay, so is that clear? So there's one more, so this is one minor point here, I don't want to beat about it too much, but one thing that you can observe it's very interesting. So sign you typically think of as what? Sign is sign of x, so I want to write down what sign of x is. Okay, I want to put i here. Sign of x is usually think of it as plus 1 if x is greater than 0 and minus 1 if x is less than 0. Okay, yeah, put greater than or equal to somewhere. Okay, so that's how you think of sign of x and this product rule holds. Okay, so suppose I do something else, suppose I say sign bar of x is 0 if x is greater than 0 and 1 if x is less than 0. Okay, suppose I define another function which is 0 when it's positive and 1 when it's negative, the same product rule can be written in a different way. Okay, so you can write sign bar of yx is as what? So in fact you can notice sign bar is what? Minus 1 to the power sign x. Am I right? No, no, no, sign x is minus 1 to the power sign bar of x. Do you notice? Okay, so if you do this replacement here, you will see minus 1 to the power sign bar of yx equals product of minus 1 to the power sign bar of y. So when you multiply it out, you will see you will get addition. Okay, and then addition I can do modulo 2. The reason is minus 1 squared is 1. So I will get the whole equation to be consistent. Okay, so this is sign bar of y1 plus sign bar of y1. Okay, so basically the reason why you do this is in your implementation or your program, you can deal with the sign separately and the magnitude separately. Okay, so that is an advantage in some cases. The sign will go in one way and then your magnitude will go in one way. Then you multiply the sign and magnitude to get the final actual value. Okay, so that those are things to keep in mind when you want to implement. So you can deal with it in different ways. Okay, so bit is always better. Storing minus 1 and plus 1 might be a little clumsy in implementation, but 0 and 1 is always easy to understand. Okay, so those are a few comments. So let me go back to the message passing decoder now. So I am going to go to the soft message passing decoder. When we last left it, we were looking at what? What were we looking at? We were looking at step B of iteration 1, right? So it is what we were looking at. So let me write down what that is. Okay, so I was looking at a check node. Okay, well check node of degree E, right? Okay, and I said the messages that it would have received in step A, we will suppose are yi1, yi2, yiE. So those are my log likelihood ratios of the corresponding bits that are connected on the other side of those edges. Okay, so that is what it would have got, right? So let me just see. And now some processing needs to be done. So what is the processing? Suppose you concentrate on the first edge. Okay, we wanted to figure out the message that needs to go there. Okay, so I will call it v1. Okay, v, no, no. Did I have, do you remember the notation, what is the notation we used for in Gallagher A? v is the message from check node to bit node. Did I indicate the iteration number there? I did that. Okay, so v1. Okay, so I will say v1, I will put one here for the edge number. Okay, so this is the first edge. On the first edge in the first iteration connected to this degree, check node. Okay, so this is my message, v1, 1. Okay, right? So I am going to deal with, what do I have to send? Okay, so I already done this computation. This will have to be the log likelihood ratio of the bit i1 calculated using the other log likelihood ratios like before, like using what relationship? Using the relationship that bit i1 is the XOR of all the remaining other bits. Okay, so how will I do that? I will do it in two ways. I will compute the magnitude of v1 and the sign of v1. How will I compute the magnitude of v1? I will use this f function, right? f of what? Okay, yeah, y1 by 2, am I right? f of y1, right? Okay, I have defined the function to be that itself, plus f of y2. No, I think yi2, no, I am sorry. Okay, yi2, yi3, am I making a mistake? Why is everybody staring at me? I do not have to write modulus, right? Yeah, it is already there, absorbed inside the function. Yeah, right? Let me write it down once again, yi2. Okay, I will just clearly erase the whole thing. Okay, since the modulus is already absorbed into the function, I might as well write it as f of yi2. Yeah, I mean I could have written a sigma, I just did not want to write it, I wanted to write the whole thing out. But remember, this is my magnitude. My f is only going to give me positive values, right? It would not give me negative values. So, this is the magnitude. How do I do the sign? Okay, I can do it in both ways. I can either do sign of v1 or sign bar of v1. Both of them would be the same. I would do sign. Okay, you can convert to sign bar if you want. The sign of v1, one would be what? Product of sign of. Okay, so I want to product, I will just write it out. I will write it out fully, I am sorry for this, just to show how it works, right? Sign of yi2, sign of yi3, so on to sign of. So, this is what I would do for the first edge. How will I do v21? Okay, so how do I do v21? On the second edge, what would I send? Yeah, I just skip the yi2 in all the summation but include yi1. Okay, so the magnitude if you had to do, it will have to be f of yi1 plus f of yi3, right?  Okay, so likewise you can write that expression for sign. The product will involve yi1 to yiE, it will not have yi2. Okay, so likewise if I keep on writing, what will be magnitude of vE1? Okay, so I will have to do the summation from yi1 to yiE minus 1. Okay, so those are my update rules in step B of the first iteration for a degree E check node. Okay, all the E messages that it will have to send out back to the bits that are connected to it, you will have to do this. Okay, if you had to actually implement this, right? If you do it brute force, if you compute each magnitude separately, it will involve a lot of additions. How do you simplify your computation here? Add all of them and subtract one at a time to get each of your magnitudes. Okay, all of them are positive, it will work out that. The same way for the sign, what will you do for the sign? Multiply all the signs and then you multiply out one after the other to get the individual things. Okay, so those are simplifications you can do in your actual implementation. Okay, so that does not look too scary now. Okay, so for any E one can do this without too much confusion. Okay, so let us go to iteration 2, sorry, with suffix i. So, well I am taking an arbitrary check node and I want to say it is connected to bits i1, i2, i3 so on till iE. I want to say that. If I say they are connected, if I put y1 through yE, if you go back and look at the way I wrote down the channel LLRs, I said yi is the LLR of bit i. Okay, but if you put y1 there, it is not bit 1, it may not be bit 1, it is some bit i1. So, initially I put y1 through yE, people objected to it. So, I changed it to yi1 to yiE. Okay, so that shows you something about, well, about consensus. Okay, so let us move to iteration L now, step A. So, what is going to happen to a degree D? Okay, bit node I need to put a circle, degree D bit node which received yi from the channel. Remember, the channel is always there. Okay, it got yi as the channel likelihood ratio. Okay, so in step B of iteration L minus 1, I need to see what would have happened. Right, the same bit node would have received, what? It would have received D different messages and in my notation, I am going to see, there will be a notational ambiguity here. I am going to simply call it with VL minus 1, I am going to say 1 to D. Okay, so hopefully you won't confuse with the previous thing, I am simply calling them just for ease of notation. It is possible to be consistent, it is possible to number all the edges if you want and then put that suffix as the edge suffix. Okay, I am just simply, so you see what I mean, right? You number all the edges and every edge you can put a suffix there. I am just not doing that, I am simply calling it V1 through VD for convenience. Okay, so it is possible to do that. Okay, those are its messages. Okay, so now I have to figure out how will this guy process, I am sorry V2. Okay, again once again I look at the first edge and then we will figure out the other things as we go along. Okay, so I will call this U1L, okay, the message from bit node to check node. So what are all these Vs, VL minus 1s, what are they? Are they bits or they are all LLRs, right? What are the LLRs of? Estimates of what bit? Bit i, the ith bit. What is yi, yi is also? Another LLR which is again an estimate of bit. Okay, so I am going to assume now, I am going to make my iid assumption now. I am going to say all these estimates are independent, they have come from different parts of the code word. They do not reuse any received value in deriving all these estimates. So this goes with the neighborhood tree like assumption. If your neighborhood tree like up to depth 2L, depth L or depth 2L, whatever depth that is. Okay, so depth 2L I think then all these LLRs would have come from different received values of your code word. There would have been no repetition in my neighborhood, so all of them will be independent. So when I get probabilities from independent events, what can I do to get a consolidated probability? Can multiply all of them. Okay, so I can multiply the probabilities and if I do in terms of LLR what will happen? After multiplying, if I take log it will become summation. Okay, so the message U1L should be an updated LLR which uses yi V2L-1 through VDL-1. So a very simple nice thing using the iid assumption to do is to say U1L will be yi plus V2L-1 plus so on till VDL-1. Okay, I am simply going to add all the remaining. The reason is I can multiply those probabilities because they all come from independent constraints and independent received different received values. They do not overlap. Okay, so maybe I will try to give you a different interpretation based on the neighborhood and talk about this independence and I need to be a little bit careful when I talk about it, but hopefully the slightly hand-waving argument is clear enough. Is that a question? So I don't have a, okay, so the question is, see what I am doing here is very different from what I am doing at the check node. Do you agree? This is not what I did at the check node. Okay, so here all of these LLRs are for the same bit. The check node does not receive all LLRs for the same bit. It receives LLRs from different bits and it has to update one of the LLRs according to the condition here. All the LLRs are for the same bit. Okay, so using the other, so the way to think about it is, okay, so I will do it just so that you can get a picture in your head. Okay, so think of the tree, okay, the neighborhood tree. This UV2L-1 is coming from one part of the tree which means it will include all the constraints of the check nodes in that part of the tree and all the received values from the bit nodes in that part of the tree. V3L-1 will come from another part of the tree. Okay, it will include all the constraints of the check nodes in that part of the tree and it will include all the received values in that part of the tree. As long as these parts don't overlap, I can simply multiply those probabilities and say that the overall value I get after multiplication includes the entire tree. All the constraints have been included and all the received values have been included. If you do all that, so what am I trying to compute? Remember, I am trying to compute APP, LLRs, probability that bit i is 0 given the entire received vector and all the constraints are satisfied, all the constraints of my parity check are satisfied. So the way this is going is, I am doing depth by depth on my neighborhood tree. Okay, so I am consolidating at each part. I am including more and more received values, I am including more and more constraints. Okay, so that's the way to think about it a little bit further. So I think that's clear enough. But you can be convinced at several levels. You should be convinced at this level also. Yes, why do I multiply? Yeah, so what you have to compute is, see, so the way to think about it is, this is something, some probability, this is a ratio of what? Ratio of some probability that C i is 0 given R i, this event. This is some probability of C i is 0 given R i alone. What will this be? C i is 0 given what? That's the question you have to ask. Given all the other checks and bit node values in that part of the tree from which it came from. Okay, so that's what it will be. Likewise, you have to ask for each of these questions. This will also be probability that C i is 0 given something else that the other part of the tree. What do I want this to be is the next question. I want this to be C i equal to 0 given R i and all these other guys. Okay, so maybe I call this as some M1. Okay, so maybe I call this as this entire thing. What all it includes? Maybe I'm going to call it as some capital M1. All that is included here, maybe I'll call it MD. Okay, so maybe I should be consistent. I'll say M2. Okay, what do I want U1 to be? I want it to be the probability that C i is 0 given R i, M2, so on till MD. All those conditions have to be satisfied. Okay, that's what I, you know, all those conditions have to be included in the computation. That's what I want to do. And since all these guys are independent, when I write it down as probabilities and events, I can multiply those probabilities. Okay, so usually you must have been used to independence probability of AB is probability of A times probability of B. Okay, this is also something very similar. Okay, something very similar. I have, I'm conditioning on independent stuff and evaluating probabilities independently and I want to consolidate everything I can multiply. Okay, so when I do that, it works out this way. Okay, so think about it. It's a little bit, maybe I'll write down an actual tree example at that point. Maybe it'll be a little bit more clear. Maybe later on, maybe sometime next week, we'll see a proper example where these things work out very nice. Okay, so the question is, so he's asking what I really want is what, what do I want finally? I want CA equals 0 given the entire received vector R. Okay, so this is what I want finally. So he's saying, can I stop when my neighborhood includes all the bits? Okay, the point is one needs to be a little bit careful. See, remember, you're assuming that your neighborhood does not have repetition and all your computations are based on that repetition. So this probabilities will be accurate only when there's no repetition. If there is a repetition, these calculations that you did are not accurate. See, what did you do at the check node? You made the independent assumption to be able to multiply all of those things up. If those assumptions are not true, then your computation is wrong. The probability that you're sending is not the actual probability. Okay, so that's why this is not the MAP decoder, but it's some message passing decoder which is an approximation of the MAP decoder. So when I write this down, you should be careful. See, I'm not saying these are the accurate probabilities. These are accurate if my neighborhood tree like assumption holds. The moment that fails, this is not accurate. Okay, but what I want to be able to do in real life is even when it fails, I want to be able to run the message passing decoder. Okay, so you remember Gallagher A, right? I showed you simulations. Even when those independence assumptions fails, what happens to the message passing decoder? It succeeds. So I want to be able to do a similar thing in the soft decision decoding also. Even if those assumptions are not true, I want to keep it ready, hoping that it'll do something good for me. Okay, and that actually happens in soft decoders. So that's why you make the IID assumption and come up with rules which are valid under the IID assumption. And then even if it is violated, hopefully it won't go too far, of course. Okay, any other question on this? Okay, so we can only approximate this. Okay, again approximate also I'll put in brackets because nobody has really shown that these things are true, but CE or SE? I don't know, check that. Okay, I think it's CE. Okay. All right, so after all that explanation, hopefully the rule is a little bit clear. So you notice I'm including YA always. Okay, so I have to include YA always, right? Because I mean the way my assumption went YA would not have been included in all of these other things. Okay, that's how I did my calculations. Okay, so let's do U2 now. How will I do U2? U2L will be what? Okay, so it's very easy now, YI plus V1L minus 1 plus V3L minus 1 plus so on till VDL minus 1. Okay, so on till UDL which would be YI plus V1L minus 1 plus V2L minus 1 plus VD minus 1, so maybe I'll reproduce this U1L here just for completeness.  So the update at the bit nodes is decidedly simpler than the update at the check node, right? You don't do any non-linear lookup or anything. It's just simple addition and how will you actually implement this addition? If you were to do it, you don't have to do it. Yeah, add all of them and subtract one at a time. That will always be more efficient than doing the entire addition individually. Okay, so that's the update rule at the bit node. So I can write down step B now for iteration L. Okay, so it's not very different from what I wrote before. Instead of YI1 through YIE what will I have? I'll have U1L through UEL, that's all. So then just replace YI by this. Okay, so replace YI1, YI2, YIE with some U1L, U2L and repeat same steps. So now you can keep on doing iterations. Go on and on and on forever, right? As many iterations as you want, you can do. You'll keep getting better and better values. Okay, so there's also a question of decisions. What about output LLRs after a particular iteration? I want to be able to make a decision after every iteration. So how do you do that? So I'll write down here, decision after iteration L. Okay, after the, in iteration L after step B, okay, what will a particular bit node get? It will get V1L so on till VDL, right? Suppose you say this is a degree D bit node it would get. Okay, so when I want to make decisions, right? When I wanted to pass a message back to some bit node, I had to ignore one information. But when I want to make decisions overall, I don't have to ignore anything. I'll just simply take everything together. Okay, so I'll say output LLR equals YI plus V1L plus V2L plus so on till VD. So what will be CI cap after L iterations? Yeah, if 0 if this is positive and 1 it is, if this is negative. Okay, and how do you decide if you can stop after iteration L? You take your CI cap and calculate H times CI. The H times CI cap works out to 0, what can you say? Maybe you can stop saying that I've achieved the code. Okay, so CI cap after iteration L is 0 if output LLR greater than 0, 1 else and CI cap after iteration L will be C1 cap L, C2 cap L, C and cap L. Okay, so you can have a stopping condition. There's also other things that possible. So typically in a VLSA implementation, there's usually no point in stopping ahead of time. Usually you have a clock and you always wait for the whole thing to end. So you can say after 10 iterations, I'll stop. I don't care about checking this in the middle. But you can also have an optional stop condition. In software, this might be useful. If you're writing a C program for simulation, this might be useful. Okay, H, C cap L transpose equal to 0 can be a stopping condition. Then you know that your output is actually a code word and you can stop. Okay, so those are ways of implementing this. So it's also good to visualize the stop soft decision decoder in so many ways. On the tanner graph, if you were to visualize, what's happening? You're getting soft values on the bit nodes from the channel. In the first iteration, soft values are going on the edges. Then again, step B, soft values are coming back on the edges. Step A of iteration two, soft values are going back again. Okay, in the first iteration, step A, from a bit node, all the stop values, all the soft values that are going out are all the same. But from iteration two onwards, that'll no longer be true. Okay, the values can be different on each edge. Okay, so that's the way to visualize it on the tanner graph. In an actual implementation on C or something, usually sparse matrices are easy to represent. Okay, so you can think of those edges as being positions on my sparse matrix, just like I showed you the animation with Gallagher A. So each of these ones of my parity check matrix can actually represent the message that is flowing on that particular edge. Okay, so and the zeros on my edge will not be anything, they'll be black and then they can be positive or negative. You can visualize it on the matrix also. It goes back and forth, back and forth, you update the matrix. So in fact, a lot of people think of bit node processing, the update of the bit node as column process, update of the check node as row processing. Because in implementation, you always think of a matrix, right? So the graph, well, it's a useful tool to visualize it. On an implementation, maybe the matrix is what is easier to think of. Okay, so people will say row update, column update, row update, column update, things like that. Okay, there are so many other modifications for this when it actually comes to implementation. Okay, so actually, I mean, I could have done an animation for this also, but I don't know if there's much point in it. Just give me one minute. So we'll look at something else. Yes, sir, question. Okay, so the question is what happens to the messages that are passed as the iterations go along? Can we say they converge, etc., etc.? So things like that are very, very difficult to answer. Okay, so it's an immensely complicated system. This depends on too many parameters. So the only thing we'll do is we'll try to do an analysis like we did before. Remember, what did we do for gallery? We were only, we first assumed all zero code word. And then we were worried about the probability that a particular message is 1 at iteration l. Okay, so we'll do a similar thing for this also. Okay, but now the messages are actually soft values, right? They are real numbers. So what is the exact thing that we have to look at is something that we have to worry about. But if you want to look at the whole system in terms of convergence of the set of messages, I don't know if you'll get very meaningful results. It's tough. If you actually do the simulations and look at what happens, all kinds of crazy stuff happens. So it's tough to analyze these kind of complex systems. Any other question? So in an actual implementation, in C or something, you can do floating point representation for the messages and actually implementation VLSIP usually do fixed point. And it's okay, man. It will all work out. It will all work out quite well. Okay, all right. So let's start off with the analysis. Okay, so density evolution for soft message crossing decoding is the tricky thing. And we'll do that. Okay, what do you want to do it? Yeah, so you can do it with intensity of color. See, another thing to keep in mind about these LLRs is suppose I say LLR for a particular bit is one. Okay, that is one thing I can say plus one. Okay, what does it mean? I mean, how confident am I that that bit is zero and not one? Okay, I'll have a certain degree of confidence. But if I say LLR is 100, okay, suppose I say LLR for a particular bit is 100, what does it mean? It's almost zero. Okay, so when LLR is plus 100, the way I define it, it's zero. I mean, I know that for sure. I don't have to worry about it. So the magnitude of the LLR tells me something about how sure am I about that particular bit. Okay, same thing is true. If the LLR is minus 100, what does it mean? It is one. You can do the calculation. You do e power 100 and all. That's it. You don't have to worry about the other probability. You don't work on it. Okay, so the magnitude of the LLR tells me something about how strongly I believe that this is zero or one. Okay, the sign is what? Sign is whether it is zero or one. It's not a problem. So for instance, this question was, how do you represent it in an animation? So in an animation, when I want to show something, I should use different colors. I should previously, I had I think green for zero and red for one. I should have a whole bunch of colors between green and red in different proportions mixing as the LLR increases. The LLR increases, I should go towards green. Magnitude of the LLR increases and it's positive. Magnitude increases and it's negative.  So that's the advantage of this soft. I mean, that's the whole point of soft decoding. So the fact that you're not just worried about the bit being zero or one. You're worried about how confident you are that the bit is zero or one. Okay. All right. So now density evolution becomes more difficult. So now I have to previously, I only had to track the messages that were flowing, well, the messages that were flowing on the edges for Galaga A where very simple random variables, they just took two values, zero or one. Okay. So I could simply track the probability whether actually I was tracking the PDF of that random variable, PMF of that random variable, right? But that PMF of a binary random variable is just one value, right? We know the one value, I know what the other value is. I was actually tracking that. Now, also, I will try to track the random variable which represents the message that's flowing on an edge. That's what I'll try to track once again. Okay. But now that random variable is actually a continuous random variable. So I love to track its PDF. Okay. So that's what density evolution in this case will try to do. We'll try to track, track or find just give me one minute, track PDF of, sorry. No, I don't know that thing is not coming. So I don't know, I've not figured out how to make it come. But I think it's getting recorded. So do you know how to make it come? I don't know how to make that disappear. Yeah, recording is going on, but I can't figure out if audio is getting recorded or not. Maybe you should have make this, can is it possible in Windows to make this disappear and show up only when it's needed? Yeah, I think you should do that. If you can do that, then maybe, maybe then that'll be okay. So we'll try to track PDF of messages. Okay. So that's what we will try to do. So it's good to start with the regular graph and think of this properly. So on a regular graph, what happens? On a regular graph, every neighborhood, see first question to ask is this is the same question I asked last time also, right? So it's okay. So it's possible for me to just hand wave through this, but before that, I want to just point out why all these things that we are handling through are slightly meaningful. Okay. In the previous case, we had neighborhoods for the regular case. So we'll start with the regular case. So I could just track one random variable for the message, right? Because the reason is every neighborhood is identical in the regular case. And the message after l iterations is a function of that neighborhood. And all the neighborhoods are identical. And if they are all tree like, the random variable I get for the message or the message will be identically distributed across all bits. Okay. So it's enough if I define one random variable for the message that's flowing on an edge. Okay. So that's the first question you should ask, right? I mean, if you have a graph, maybe you should have asked this in Gallagher A itself, but maybe people don't worry about it. If you have a graph, there are messages flowing on different edges. And in real life for a practical thing with finite n, the different messages will have, will probably have different probabilities, right? But we don't, we don't worry about it. We're saying we're going to let n tend to infinity since the messages, the graph spars for a finite l, all my neighborhoods are exactly the same. So the PDF of the random variable or the message that's coming out on the top will be exactly the same. So we'll depend on the exact same things in the exact same way. So if I denote a random variable for a message, I can have the same random variable for every edge. I don't have to keep using different random variables to track all of them. Okay. That another thing that helps me there is the all zero assumption. Okay. If I cannot make the all zero assumption, all these things will, will be problematic. Okay. So we'll once again make the all zero assumption. Okay. Again, this is justified by the symmetry of the channel, whether it is plus one or minus one, the channel doesn't care. It adds the same Gaussian random variable to it with the same mean and the same variance. Okay. So another assumption we'll make is neighborhoods are three like okay. Since I have a regular graph, I'm saying neighborhoods are three like all my neighborhoods will be exactly the same and all the random variables and all the messages will be according to the same distribution. Okay. So I don't have to have different distribution for different messages. If we go to irregular, what will I do? How do I take care of these neighborhoods being different? You average over all possible neighborhoods and then you say I have a concentration result that says any one case is very close to the average. So I don't have to worry about it. Okay. So that's the way to do it in the regular case. But for the regular case, you'll make all these assumptions and proceed. Okay. So that's one thing. You're tracking the PDF of the message. So, so the thing will get more complicated. Okay. So you'll have to worry about when you add random variables, when you add independent random variables, what happens to the PDF gets convolved. Right. So when you do some complicated function like f function that we had on a random variable, what happens to the PDF? How will you find it? So our function f is a nice monotonic function, right? Log tan apolic. So you can use one of those standard Jacobian formulas to convert from one PDF to another PDF. Okay. So all that all those tools we already have so one can possibly imagine tracking the PDF through your check node update and the bit node update. Okay. Previously, it was very easy, just simple, discrete probability. Now you have continuous random variables, but the random variables are only being added and some nonlinear function is being applied to them. You know how to handle all those changes on random variables in terms of PDFs. Okay. So you know what to do to the PDF and all these things happen happen to random variables. So we should be able to track the random variables. That's one thing. The other thing is what can I say about probability of error from the random variable and its PDF? Suppose I give you the PDF of a message. Okay. How will I compute probability of error? What is the probability that that message is in error? What's the meaning of saying the message is in error? When will the, when is the message is, when will the message be in error? Yeah. So I've already made the all zero assumption. So I know my code word was all zero. So when is the message in error? If it is negative. Okay. So that's the thing. Any message is in error because messages are LLRs. Any message is in error if that message is negative. So once I have a PDF for the message, I can quickly find what's the probability that the message will be less than zero. What will you do for that? Integrate from minus infinity to zero PDF. You'll get the answer. Okay. So that's another thing to keep in mind. Message is an error if it is negative. Okay. So what should the PDF be for the, for the message, if my probability of error needs to be zero? So how, how will it look if I plot the PDF for a message? Yeah. So it's, it's support will be purely positive. Right. So it will not have anything on the left side. Okay. It'll go off to something like that. Okay. So, so that's the thing that we will be tracking. So previously, what did we do for Gallagher? We had this PL and we wanted that PL to tend to zero as L tends to infinity. So what will we want for the PDF as L tends to infinity? We will want it to move to the right. Okay. So initially it will not, it will not be in the right, right? You know how to find the PDF for BPSK, WGN. It'll have some part which is negative also. Right. Slowly you will want, as you iterate, that PDF you will want it to move to the right. Okay. As it keeps moving to the right, eventually the probability of error will become zero. Okay. It will, well, we'll see, we'll see how it works out. Okay. So I want to stop here. I don't want to do a pickup with that later. We'll start looking at this next week.


The oxygen reduction reaction, ORR, is the core reaction of numerous sustainable energy conversion technologies such as fuel cells and metal-air batteries. It is crucial to develop a cost-effective, highly active, and durable electro-catalysts for ORR to overcome the sluggish kinetics of four electrons pathway. This article was authored by Chen Ren, Hui Wang, Shuo Fenglu, and others.


At least four people were injured on May 15 after a blast occurred in the Russian-controlled city of Luhansk, in eastern Ukraine, the authorities reported. The local media said that a grenade went off in one of the barbershops in the center of the city without providing any further details. Russian media reported later that the acting head of the Ministry of Internal Affairs of Luhansk People's Republic Igor Kornet was injured in the explosion.


Welcome back to the Independent Investor Channel. It's easy to get caught up in the recession in specific stocks, especially this one. It's difficult to keep your eyes on the prize. It's difficult to focus on company improvements, company successes, and it always is unfortunately overshadowed by the stock price. The stock price, I think there's a lot of decisions going on right now based on that. I think a lot of positives that are with the company are unfortunately over shadowed by the current stock price just hanging out at these levels. My purchases last week came at around the 116 level. I disclosed that and no promises to suggest that it can't go lower. If it does, I'll be accumulating more shares. I don't expect you to follow my lead. I expect that after this project is all well and done, I would imagine that the few who have been brave enough to follow on this journey will own a company that is looking to revolutionize the class 8 space. Now, can they do that? I think the theme of this video and where I want to take your perspective on where we are right now is something that I think is being missed and it's being missed in a big way. If you pay attention to investing from the investors that really don't follow the crowd and focus on soft spots in the market, we currently have one alive and well right now and nobody's talking about it. You can blame highly on all you want for a recessed stock price, but might I remind you that the microcap space in general is and has been thrown out for a long, long time. There is no credit whatsoever, which puts these companies that where they would have needed time and would have been provided that ample time in the market in a different market, let's say the latter half of last decade, they are not being provided that favor and companies are being reassessed in the marketplace. Some, if not most unfairly, some fairly and I think this washout is super necessary. I really do. I think it's necessary for those who maybe thought that investing was a game, for those that thought investing was easy, for those that misconstrued their own capability in the financial markets. For me, calmly marching on and I've shared this, I shared it on my Friday livestream. I feel no different now than what I did before outside of the fact that I am super, super excited to be where we are now with the prospects going forward as opposed to being disappointed about where we have come from. I really want you to take that to heart. I really do. And as we work through this video, I'm going to show you that I believe we are marching toward multiple catalysts and I don't want you to take my word for it. I want you to kick over to highlyon.com and look at their last 11 slides or so that they presented on the Q2 call. It has this information disclosed and I find this interesting because a lot of people are saying one way or the other that they're not going to do this and they're not going to do that, they're not going to do this and they're not going to do that. When all the while, highlyon is very, very carefully and diligently communicating with their investors through these releases on what they intend on doing. Now, one thing I didn't mention on last week's video, I will clean up this small delta from the release. It was in the interview actually with JP Morgan. Thomas Healy was being pressed on MSRP and Thomas talked about, look, right now we feel comfortable with releasing a less than 400,000 that's with the credit and incentive baked into the equation for the MSRP. And he did allude to the previous projections being way off. And it was the first time that I had ever heard Thomas Healy talk about what was being projected back in 2019, 2018, 2020 when the original investor presentation came forward. And I don't know if anybody else picked up on that, hopefully that they did, that that was kind of an acknowledgement to making presumptions about where they would potentially be with the MSRP and not anticipating such a huge shift in the industry as a whole and how we would be looking at the supply chain issues and the effects over the industry here in 2023 to affect that MSRP. That was a careful but responsible acknowledgement. I was actually happy to hear it because I've been scrutinizing on that data that was released. And I was glad that that was kind of acknowledged about that might not have been the best way of doing it for the reasons that they really didn't have a whole lot of understanding of when the ERX could potentially come to commercialization. So I thought that was a pretty cool acknowledgement. And I thought that would share those insights with you guys on the weekly Healy on video. But the theme of this video is going to be expect the unexpected. And you know what's funny about unexpected is everything that I am going to talk about is not presumptuous on my part. It is as disclosed by Healy on and I am conveying that through the message here with my following. Now, before we get started, I kind of want to set the stage a little bit for who I am, what I bring to the table, why I'm doing this project and why you should join the movement here on either the independent investor or become a steward through Healy on comm sign up for their newsletter really become kind of a steward of this. I think there's multiple things here at play. I think there are cross currents that are probably fighting this initiative. I think that the slow to evolution is probably a partially manufactured in that I think if Healy on were just to come out guns blazing right now, I think they would fall on deaf ears anyway. So a slow approach and allow things to kind of settle out which in my assessment things are kind of settling out a little bit more, at least on the supply chain issues. I think interest rates higher are going to be around higher for a good while. I think the ability of Healy on to really circumnavigate this environment now and not have to aggressively seek out capital from a necessity perspective rather than an opportunistic perspective is huge right now in the short term. And whether or not that's going to pay off, I'm going to talk about that in a little bit with regard to their caste position, but I really want you to understand that expect the unexpected means that there are disclosed catalysts that by all nature is going to happen. Okay. The reason I disclose that is because we are now sitting on a stock price that is priced for liquidation, priced as a company that will not make it, that will not continue to enjoy further progress on their products, will dissolve away and is now currently caught up with the mix of companies that for all intents and purposes over 90% do fail. And I think with these looming short term catalysts, I think you're going to find here that we are on the precipice of at least having the doors open to a number of these different developments with the company. Look, is it going to change the needle? I don't know. I'm not in that business anymore. I never was really in the business. My price targets for this company have never changed. I believe that the first look on this company is going to be about 150% above its SPAC IPO price of $10 at $24. I think with the evolution of the company and adding Carnot into the mix only adds that many more hundreds of millions of dollars of value now in the company right now, not with even the prospects of incorporating the revenue that the company can generate from the Carnot project because that was information that we were not privy to at the inception of this project. But what we do know is fleet trials will start in Q3. We are currently in Q3 now. We are in Q3 now. So the last announcement that Hylian announced was from the beginning of the month that they reported on Q2 earnings. There's been a couple of really nice pieces and segments with Thomas Healy getting out there sharing the story, which I think is good obviously not to move the needle and not to be expected to move the needle. We need results at this point and there is certainly an undertone of calm cry in the community that results are going to be the only thing that moves this needle and then all fair. Like I said at the top of the program, these companies are being put in a basket of prove it and until they can prove it, they're going to remain in the basket. They're not moving from that basket. They are going to continue to deteriorate in value until they can prove that they can rise to the top of the basket and escape from that basket of stocks that have really historically been provided a little bit more optimistic credit as opposed to where we are now in a prove it story. But fleet trials to begin in Q3, is there going to be no news that comes from that? Is there going to be no... I had one comment on my last Hylian video to suggest that it would be cool to see the deliveries of those first ERXs made public. I don't know if they're going to move in that direction or if they're going to keep it private. I really don't know. I don't know if they're going to be reporting out or if the relationship between Hylian and the recipients of the first fleet trial vehicles are going to want to keep that information private. I don't know, but it's going to happen. However way they choose to roll out this program, I know it's going to happen and it should be a positive catalyst in moving toward what they are considering to be commercialization later on this year. The next is to deliver 30 trucks by the end of 2023. We're in August almost to September here, September, October, November, December. We have four months left. Four months. For what? The stock to get cut more in half? I don't know. I don't really care. But over the next four months, I expect the unexpected. And the unexpected is results from this company in way of delivering 30 trucks by the end of 2023. If you think that that's somehow a misconstruence of the fact or a presumption on my part, this information is coming right off of Hylian.com website and they are setting up to be in the position to say, see, I told you so. We declared everything that we were obligated to provide to you and no more in the investor's presentation as well as the summary slide show that was presented on Q2. It's right there. Now, again, I come back to this beat down and probably shared sentiment across the Hylian community in suggesting this. Will it move the needle? Probably not. Now, am I being unfairly presumptuous in that? Of course I am. But the perspective that you have to come with in the investing landscape is to identify the best case scenario and the worst case scenario. We have been doled out the worst case scenario over the last three years. Why is it fair to expect that somehow it's going to change on a dime and start to become positive when the company has rolled out a lot of positive initiatives over the last three years? It hasn't been what the markets wanted to hear. It has not moved the needle. And so why is it to expect that more of the same is not going to move the needle? A reaffirmation for me of what was declared previously that's been completely removed from their website is a reiteration of some of the old deals that were made with some of the fleets. Have all those deals just went away with Ruan, with LeFarge, all of those deals that they've made with the Innovation Council, Wegmans was in the discussion, Schneider was in the discussion, ANG was in the discussion, Agility, I can go on and on and on and on. And this is their opportunity here for us to get some clarity on whether or not these are a mix of new customers, a reaffirmation of old customers or if the old customers have gone away based on the recalibration of the MSRP and just have kind of died and gone a different direction and or these 30 are all brand new customers that have been brought into the fold. That's going to be a real tell for me because a lot of the hype and a lot of the build up is to understand the excitement behind who that Innovation Council was and how that Innovation Council was basically partnering with Eilion through these fleet trials and rollouts. And that has been removed from the website and I don't know if it's a thing or not. We talked about this Founders Program and White Glove Garbage. The only thing that I really care about is who's going to get the trucks and who is going to help provide data back on those trucks. We have not heard anything about that. All that aside, it's going to happen. I believe that there are going to be 30 deliveries by the end of this year by what they're stating. Could they push it? Yes. Is it going to move the needle? No. Back again to sharing with you my insights about having really level expectations about these catalysts, albeit in the face of me disclosing to you that I believe that those catalysts will happen. And with each new door that's opened up, it should open up further opportunity into next year for some of the longer term projects that Eilion has. All right. The Carbon EPA is expected. This is right off of Eilion's website. They expect to nail down that certification. I expect the finalized certification announcement to come any time. Now, any time, does that mean November 15? Does that mean September 6? I don't know. I don't know what they mean by expected. I know that it's expected within this quarter. I would presume it would be nice to have that Carbon and EPA NITS has already completed. Those three certifications would like to believe that we can get those completed and put them in our rear view mirror because now we're working with a commercially viable product that has gone through the rigor of over-the-road certification. And that right there in and of itself should separate the gray matter to black and white in understanding that is there a chance they could fail certification? And then the project, what? Is just a pilot program or it dissolves away all of the money in R&D that goes in? I don't foresee that happening. But I'm just stating, have I thought that the certification has taken longer than what it should have or could have? Or did I wish it was certified six months ago? Sure. Sure. That's just not where we are. All that aside, we look at the facts and we look at the Carbon EPA is expected to happen over the next couple of months. My promise to you when that is going to be, I can't provide to you, however, to be expected. And is that going to move the needle? Is moving from a pilot program, the HyperTruck ERX, to a commercially viable and certified product going to move the needle? Again, I would just have fair expectations and suggest that it won't with the idea that potentially we could be positively surprised. Maybe we get a little bump in the stock of 10 cents. So everybody can sell the stock and it can retrace back 10 cents. And we're back at the starting place again, having had the certification not in place prior to the 10 cent bump up and now having the certification in place and having a commercially viable product, but having the stock price still where it was prior to the announcement. Muted expectations, I would suggest? Absolutely. I'm calmly sitting in the pocket and watching these evolutions happen over time and I'm completely comfortable with whatever reciprocation or whatever receipt of those positive catalysts happen and are made over the stock because I really think that these positives may in the short term have an impact on the stock price, but if anything has proved out, it has been that there has been so much selling pressure on any upward momentum that this company has been and will continue to be in a downward trajectory, if not stabilizing trajectory over the last six to eight months to be fair. Right. Very stabilizing. If you look at a long-term chart, you could probably extend that six months to 12 to 18 months of stabilizing at these lower levels, but there are recessed levels to indicate that the stock market believes that the company is actually going to dissolve away. It's not going to exist anymore. I find that to be an interesting observation here now where we are. I'm not going to suggest that that's wrong or right. I am a bull on the company and I believe that some of these catalysts will start to generate some upward momentum, but whether or not it's sustained upward momentum, Hylian is going to have to do something that I'm going to share with you at the end of the video and I'm going to double down right now. They're going to have to start to produce results. This whole fleet trial thing, the investor day presentation, yada, yada, yada, this whole announcing the Heizen collaboration and whatever dollars have gone into investing in that, it's taken up an entire page out of 11. About 9% of Hylian's Q2 call had the Heizen presentation in it, go to Heizen's website and try to find the word Hylian on their entire website. I charge you to do so. I'm getting kind of tired of this reciprocation on behalf of Hylian saying, hey, Anheuser-Busch is on our team. All these companies are agility. Man, they're on our team. They're on our team. You go to their website, it's very, very difficult to find any information whatsoever of these companies. I would nary up presumed that if I were to call Anheuser-Busch and talk to an upper executive and ask if they have ever heard of Hylian, they'd probably say no. I do think this is an unknown story and I think Hylian sometimes uses, if not throwing a lifeline to Heizen at the time, trading it 50, 60 cents. They know each other, so why not just throw them a lifeline here and say that the big bad Hylian is partnering with them, which benefited Heizen. Heizen ran right past Hylian right after that announcement. Hylian did not move at all. So here's Hylian with this anchor of a cash position and not much else. Heizen has sales. Heizen has amazing technology. Heizen shouldn't need help and it's reflected in their website. If you go there, which I did before this video, I couldn't find any type of reciprocation at all in acknowledging that they're working on some sort of pilot program with Hylian. While Hylian's out there running the Heizen rig around the test track, Heizen, at least in their public-facing forum, has not disclosed whatsoever that they are partnering with this company in Austin that nobody's heard of before. So a little bit troublesome for me. I'm not sure. Maybe they end up just blasting through it. Their expectations are down the line. I'm going to talk about the Heizen project and they've got some pretty short-term expectations for that project, as opposed to Carnot. They're kicking to 2026 for the Carnot ERX, which I think is a great idea, but definitely not one that I'm interested now in the short to medium term to actually move the needle. Because moving the needle off of subpar stock prices really should and if not has already put itself kind of at the top of the priority list. I mean, they can have all the initiatives in the world. They can go save the ice caps for all I care. It's not going to matter if the company goes out of business, right?  At the end of the day, they have to deliver product that people want and people have to want those products. They have to want to integrate them and we have to understand that that follow-on business will potentially be there long-standing for Hylian. Are we there now? Absolutely not. Hylian is still struggling with providing that transparency into the future. Now, the transparency is there. It's just the follow-through on that transparency in their roadmaps about how that's going to actually generate top-end revenue and then potentially profit for the company. They've got to follow through with these promises that are being made. The start of production, the start of production happens by the end of this year. Now, again, with four short months, the start of production was one that I saw, I acknowledged. Look, I'm excited about, but my expectations from a scale of zero to 10 on start of production and what I think that means is zero, maybe a one. I give it a one on the excitement scale. One because they've said it and one because we've waited three years for the start of production, whatever that means. But what I think it means is most clearly articulated through John Pancer's address and the financials in that, yeah, they're going to produce low-volume trucks, but they're not going to make a dime on it. Now, the one comes from every truck that they do turn out. There should be some follow-on value that is made, but I focus on the word production. And I always invested in Hylian to be a tier one supplier to the OEM, not to be a producer of trucks, i.e., buying the trucks from Peterbilt and then outfitting the trucks in Austin, shipping them back to Peterbilt. It kind of sounds like, forgive my French, it's a clown show that is not efficient. And I'm certain that the board of directors probably sat across from each and looked at each other and said, yeah, I mean, this is a clown show, but we're going to do it because this is the only way we can do it because Peterbilt really hasn't brought us in under their envelope. I'm kind of piecing together what I've gleaned from what this start of production is going to mean and anything less than coming off of the OEM line for me and very little transparency about the Maud Center, which is supposed to be the intermediary step to getting on to that line. We have been provided very, very little transparency outside of initially, we're going to integrate with the OEMs. And now it's very difficult to integrate with the OEMs, right? So the story has changed immensely to it being just an easy like handshake. And now it's one of the most impossible things you can possibly do. And oh, by the way, don't be surprised if we don't make it. That's kind of the idea that I get. If High Leon becomes a tier one supplier to Peterbilt, game over, game over. Yeah, it's watermelon time. Do I have hopes that that will actually happen? No, not now, not based on the discussions and what is in it for Peterbilt? I could give you a bull bear case on what's in it for Peterbilt. I could give you a long list on both sides of the house. Yeah, there's mandates that need to be met. But why does High Leon have to be the chosen neon green horse that makes those mandates achievable for Peterbilt? Peterbilt has a hundred year reputation and they're not going to tarnish that reputation by going into business with High Leon because High Leon says they're the best leader of powertrain solutions in the industry. They're going to have to prove it. And High Leon's ability to prove things thus far has been subpar at best. All right, now I'm being a little bit scathing here on what they would suggest that the start of production would mean because it's a far cry from what they said the start of production was going to look like when those projections were made in 2020. But here we are, all that aside. The start of production will happen by the end of this year. What that looks like, I have no idea. Will it move the needle on this company? Probably not. It's the same old song and dance, guys. I'm trying to condition your expectations to understand that we are not in hallelujah mode yet. We are not in jump up and down mode. We are in wait and see mode and be very, very careful and calculated with monitoring this company that I believe is extremely vulnerable, extremely vulnerable. They've got a cash position, yes. And that is the very installation that provides them the safety from this current situation from cutting into the flesh. And until that starts to absorb away and we can really get some clarity on what we consider to be positive moving forward, then I think it's just a wait and see game. Now, the start of production and something that I really want to bring to your attention as well, guys, is 10 million. 10 million. It was disclosed from my understanding during the investor conference. Those of you who were there can attest to this. We just came off of a quarter where they were able to generate 255, 235, 200 and something thousand dollars. See, it doesn't matter. It could be three, 400,000. It could be 100,000. It doesn't matter. Why? Because it doesn't matter. 10 million. 10 million matters. 10 million matters for the years end 2023. Now, if we're at the end of 2024 and they're projecting 10 million, we're in trouble. We are in trouble. And I would put about a 16 month, 14 month or so time frame, give them all a 2024 and the remainder of 2023. So 16 months to really get their act together. 10 million is an indication of going in the right direction with revenue projections. Okay. We're not even talking about profit with this company. And I'm just going to make a bold statement to suggest this. If this small company cannot get out of its own way to generate $150 million of revenue, then this project is for naught. It is a waste of everybody's time. It is a waste of material. It is a waste of manpower. It's a waste of initiative. It is a waste of technology. It is a waste of everything we have come to know about our industrial companies. If the onslaught and the attack of this company has driven it so far down that it can't gain any favor in the market whatsoever, then all fair is love in war. Because Hylian was once valued in the billions of dollars on the initial run-up. Do I think it has the potential to get back there? 100%. Will we have the ability to look back on this time now and kind of remember that 10 million projection in 2023 and say, wow, the company is finally starting to proceed toward that billion-dollar revenue mark and finally come to a nice profitability mark, which profitability for the company should come around that break even, 150, 200, 300, 400. Let's just call it 500 million of revenue. 500 million of revenue, CapEx, and starting to expand out on the margins. Yeah, there could be some profit there and some re-fortification of the cash position with the books. I think John Panzer is just the guy to do that. I think he's super sharp. He understands businesses. One thing I will commend both Thomas and John on, I don't sense at all that there is any type of angst. I don't sense that there's a sense of urgency here with this project. It's just we are where we are and I think they're giving their best account of where we are and what I agree with them is being a very, very tough market, very tough market. All that aside, $10 million will be achieved. Now, if they over-achieve, like they under-achieve the last quarter on their quarterly projections, I think that's going to be a problem for the company. I think if they come back and they close out the year at $7.7 million and they say, see, I told you, year over year, sequentially we're up, but we can't project our own revenue projections, I think that's going to be problematic. So they'd better hit the number and I would suggest perhaps maybe that Hylian is probably due for a beat. So if they come in with $12.2 million, I think that will probably be good in consequential in moving the needle as far as I'm concerned. But when they do report the number, it will be actually on the books and not a projection that was made at an investor conference. But all that aside, I expect to be taking Hylian at its word and closing out 2023 with a $10 million bill. I like that. I think it's great. I think when you track, it's funny, you go back and look at NVIDIA when their company first started, their profits were, I think they started with $5 million. I think they bumped up to like $17 million. Then they went all the way back to $5 million. Then I think they reported out a number less than $5 million if I'm not mistaken. And since then, they've turned in hundreds and hundreds of millions of dollars of revenues and profit as well. But you kind of look at Hylian and you think, how much of a pass do we give them as a young company in growing revenue and eventually getting toward chopping down that CAPEX? Me personally, I kind of sit back and I sometimes think about Mrs. Ryan's perspective, what a colossal waste of time, energy, money, initial investment, all of the aboard. What a colossal waste if this company was doomed from the beginning. In other words, wouldn't you think that these guys have a realistic expectation of what they think they can achieve when they sit across from the board who's supposed to be giving them strategic direction? Don't they feel like they've got a better handle on the marketplace to understand that this company actually has a better chance of succeeding than failing? Wouldn't you think that the total addressable market would help kind of facilitate and allow Hylian yet to get out of their own way, which is what they need to do, but also catch a break, catch a break in that I have contended along this way that the Hylian story and the Hylian opportunity in their product is better in the marketplace than not in the marketplace. It's interesting to me some of the schools of thought that would just have this company fail because of what? A stock position that they were hurt on or they think that somehow it's not better for the environment or Thomas Healey's a bad guy. I think the world is a better off place with this company rather than without it. When I talk about $150 million of CAPEX to cover expenditures, that will increase over time. You would expect that those revenue projections to increase relative to their operating expenditures and capital expenditures going forward, but boy, oh boy, like I said, if we can't cover $150 million, then what are we doing? I mean, this is supposed to be an industrial company. This is not a pink sheet company. This company trades on the niece. I think the prospects are there. I think they've been given a really wide swath in the stock market and Hylian needs to deliver. They really do. The daycap variant to meet the ACF early mandate, I think this was a pretty cool initiative. This was the one thing that I put on the list here that I don't expect a lot of progress on. If I get it, I'll be excited. That way they can meet that short fuse mandate that I believe is coming in 2024. You guys can check me if you'd like in California to start to deliver those. I think with the learnings of what has gone on over the last three years should make the daycap variant a little bit more easily attainable. I don't expect that once the certification is met for Hylian that those certifications wouldn't just be a reiteration of the same certifications for the daycap. I don't know. I'm not an expert on the certification process, but I would expect that those processes be a little more streamlined and I would expect that the daycap variant actually to be an easier build. I don't know if that's a fair statement or not, but I often said, I said this many, many, a couple of years ago actually, and for you guys that have been with me a long time on this Hylian community, I will double down on this. Hylian one year from now and five years from now will be a completely different company than what we are evaluating now. Make no mistake. Making your presumptions now based on what you know about the company is only making assessments or projections on where you think they will end up. And if nothing else Hylian has proven their ability to come over the top with things that were not expected, the daycap, Clarno technology, the collaboration with Hyzon and integrating a fuel cell and actually grabbing that market right there, those things were not expected. Those things were not, we were not privy to that in 2020 and 2021 when this company started and embarked on this journey. So I'm reporting out to you now on a company based on my best assessment here on 2023, but it is fair to acknowledge that this company has been opportunistic about taking on a Carno acquisition. They've been opportunistic about establishing another SKU of the ERX line, couple of SKUs. You know, that Carno generator wasn't supposed to, it was just supposed to be an agnostic generators, what they called it. And I think they knew about Carno at the time. It just hadn't been announced. So that was what we were making decisions on. You know, the hydrogen fuel cell iteration of the ERX was just that. Now we have color on, you know, what that product is going to look like, i.e. the release this week of driving the test track at the Toyota facility. That stuff's very, very exciting. So it becomes a lot more real when we start to look at those projections and we start to kind of formulate where this company could potentially be. But the day cab is one thing that I thought we would mention as far as, you know, expect the unexpected and highly honest poised to surprise to the upside. And I'll be eagerly awaiting updates on the day cab variant, early stationary power deployments in 2024. So let's talk Carno for just a second. I'm not going to belingar this point, but all things aside, you can say what you want. I tweeted, I want a Carno generator. I want one. If I get wealthy off of this project, I think we should all buy one, all of us. Let's all buy some property off the grid and we can all film our experience with the Carno generator. This is why you watch me. I have vision. I have vision. I live in my vision. Day to day, I'm just a regular fella. But if this ends up making it, I would love to have a Carno generator at my property to help provide the power to vital services that I expect to have around the house. I would buy enough power to power me till rapture. All that aside, I believe that the Carno generator in the first iteration is coming in stationary power deployments in 2024. Why do I believe that? Because they've told me that's what's happening. That's next year. As an investor, I'm totally fine with that. Most of my projects for long-term microcap investing are multi-years out. So why is Hylian any different? Hylian's cool because I can really just track the progress. I bounce from microcap to microcap and assess catalyst when they happen. Most days, you hear crickets because they're working behind the scenes doing what it is that they do. But when the microcap has a development, it's usually a big development. I'm waiting on a couple of those developments on a couple of other stories that I cover. But this catalyst, I believe, is actually a foregone conclusion. And who's to suggest that it's not going to flip the script on this? Even with that, I say that my expectations are muted to non-existent. Will it move the needle? Of course not. Of course not. Why do we need stationary generators? We have Generac. We don't need to advance technology. We stopped advancing technology in this country 40 years ago. And we've made it so difficult for new companies to come to bear with new technology and we stymie progress as much as we can. That's just what we've written now. So why would we need this product? We don't need it. Just keep the aging infrastructure. We haven't upgraded our infrastructure for 50 years. Why would we need this product? Why would somebody need to actually find an opportunity to lower the cost of their utility bill when, in fact, most households in California are actually under the thumb of the utility companies to operate their outlets and operate their power during optimal times to do just that? Guys, that's ridiculous. It's ridiculous. Can the Carnot solve that? Yeah. Yeah, it can solve it. But that doesn't matter. That doesn't matter. What matters is the political pressure, the political initiatives, whatever foul play is going on with this company, whatever manufacturing of attacks on this company is out there, has really just put us into the position of where we are, where Hylian's just going to have to fight. And that's all in love and war, baby. They're just going to have to fight and they're going to have to find a way out of this hole. And I believe that they have enough prospects to do just that. The Heizen collaboration complete in 2023, late 2023. So the test track provided some insight that that is actually an up and running fuel cell iteration of the ERX. Did it move the needle? Of course not. Of course not. We can all hold hands and sing kumbaya in that we all own the only stock in the entire stock market that actually doesn't go up. I've come to terms with that. No big deal. Hylian has just provided some insight to their hydrogen fuel cell iteration that could potentially be another SKU in their product line for class 8 trucking. All that aside, do I expect it to move the needle? No, not at all. Not at all. I expect to be around these levels indefinitely. I expect Hylian to be turning out that $500 million in revenues and still trading at $1.25. I expect them to be a tier one supplier to Peterbilt and still at the $1.25 level. I expect them to have stationary power deployed. All of these catalysts that I'm talking about, certifications reached, milestones achieved, and still trading at $1.25. Absolutely. Again, we can all continue to hold hands around this project and wonder what is happening. The last thing I will mention here is something that I want you guys to consider in way of their cash position. They're currently sitting at $2.75. By the end of the year, they'll be at $2.75 on their cash burn, projecting $150 million, get them through next year, and even through 2025 by all intensive purposes. They're not burning cash as fast as everybody says that they are. That cash position has really been quite a lifesaver. Unfortunately, a detriment to the company now, I'll explain. If they're burning against a cash position, unfortunately, that cash position takes on a different light in that it's looked at negatively and not as a positive. Now, the $10 million will be turned in in 2023, like I talked about. If they can increase that to $25 million, which lofty, I get it.  Okay, come up with your own. $12.5 million. $6.5 million. They're going to lose money next year. I don't know. $25 million. All right. The more revenues that they can make and generate on the top end, the more that cash position transitions to a position of strength rather than a deteriorating asset. Okay. And I'd really like to see Ilion come to an impasse where they actually start to generate revenues. I think they're too close for comfort right now. They seem to think they're all right. That's no big deal. We can fund the business and we can just go to the marketplace and or dilute shareholders who have, quite frankly, been singing Kumbaya for three years and that's about it. So we're going to dilute shareholders even more. And that's a good thing. And we can just remain calm on it. It's no problem because I'm pulling in a hefty salary, which is kind of a thorn in my side. I think even Thomas Healy is in a prove it phase right now with the company. I really do. I think pulling in over a million-dollar salary is absurd. I think to produce the results that have been produced hasn't been his fault. But in all fairness, you need to be compensated on results. You really do. And to drag this story out three, four million dollars later after four million, four years and four million of salary payouts to produce what, that's half of what they're anticipating, generating for top-end revenue this year, 10 million. I think that's a little bit absurd, but that's just my opinion on it. But I'd like to see the sentiment from what is now perceived to be a negative, actually. They keep reiterating that their cash position is strong and the marketplace keeps coming back and saying, yeah, but your deteriorating your cash is just at such an accelerated rate relative to your projected revenues. And I think once those projected revenues kind of start to materialize a little bit, I think we can look at that cash position with a little different lens. So with that, guys, I wanted you to expect the unexpected. All things aside was the theme of this. When we talk about presumptuous and I'm a really bad guy and I'm a really bad investor, all that aside. These catalysts are coming. Whether or not you decide to take a position in Hylian or not is totally up to you. Your position in Hylian doesn't affect me, nor do I expect my position in Hylian to affect you. You have to be fair about this relationship. This is business. A lot of people will come and they'll blame me for not putting food on the table for you because of your misguidance of a particular position. Most people are like that. Most people want to blame others for their problems and not really just look diplomatically at where we currently sit now with the looming catalyst on the horizon and expect that potentially I could be wrong in suggesting that it does not move the needle as opposed to it will move the needle. And we're just going to have to wait and see on this. My friends continue to be patient on this project. If you enjoy the message, subscribe to the channel, leave your comments at the bottom of this video. I appreciate each and every one of you and your support that is rendered week to week will be back next week for the Hylian Weekly Update. Guys, take it easy and good luck in your investment future.


So today I'm announcing as part of our tech strategy, part of our innovation strategy that the BC government is providing $27 million to UBC through the British Columbia Development Fund and that $27 million is going to support a number of 40 research projects at UBC. It's going to purchase new equipment to enhance diabetes research and treatment and it's going to establish one of the largest DNA computing networks in the world. Today is a very exciting day for research in British Columbia. Many of the projects that are funded by BCKDF are on a path towards the discovery or development of life-saving technologies and methods that could revolutionize industries. This funding from the BC Knowledge Development Fund promises to transform research for us here at the Canucks for Kids Fun Childhood Diabetes Laboratories at BC Children's Hospital. Our youngest daughter Fiona was diagnosed with type 1 diabetes when she was 5 years old. That's why we're here today. We put our hope and our trust and our faith in diabetes research for Fiona living with type 1 diabetes and for all people living with diabetes. That there will be a better, stronger, brighter future for her for tomorrow. So what we see here today is an example of how research enhances the lives of British Columbians and it enhances our position as a world leader in innovation.


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