[00:00:00] Speaker 01: 2332, Apple Inc. [00:00:02] Speaker 01: versus California Institute of Technology, Mr. Dowd. [00:00:09] Speaker 04: Good morning, your honor. [00:00:11] Speaker 04: May it please the court, my name is Jim Dowd, and together with Michael Smith, I represent Apple in this appeal. [00:00:17] Speaker 04: The PTAB committed. [00:00:18] Speaker 01: Let me start out just expressing my personal opinion. [00:00:22] Speaker 01: I found your reading very difficult to follow, and that you didn't explain the technology in a way [00:00:30] Speaker 01: that made it easy for me to understand what was going on. [00:00:33] Speaker 01: And I mention that to you because I hope in the oral argument we get past that and that you're able to simplify it. [00:00:42] Speaker 01: It's complicated technology. [00:00:44] Speaker 01: And it's really important that we understand what the basics are here. [00:00:51] Speaker 04: I do plan to address that presently, Your Honor, and give an explanation of exactly what the proposed modification would be. [00:00:59] Speaker 04: I do want to start out by saying there were essentially two errors below. [00:01:04] Speaker 04: The first related to the motivation to combine issue, and the second related to the reasonable expectation of success. [00:01:12] Speaker 04: Those are linked because the Mackay reference really gives both. [00:01:18] Speaker 04: But to Your Honor's question, there was no dispute below that if the modification that we propose, Apple proposes, was made, it would actually teach the claims. [00:01:27] Speaker 04: And I can illustrate that, I think, very directly. [00:01:29] Speaker 01: with respect to... As I understand your argument, and maybe this isn't your argument, but this is my understanding of it, that McKay teaches that not only that overall there should be irregularity, but it actually teaches that the HD should be irregular because that's what is primarily irregular in McKay. [00:01:55] Speaker 01: And that made it create a motivation [00:01:58] Speaker 01: to make the HD in PING irregular. [00:02:02] Speaker 01: Am I understanding that correctly? [00:02:04] Speaker 04: I believe, Your Honor, has it correctly in the following way. [00:02:08] Speaker 04: The first is that PING itself teaches having two separate matrices. [00:02:17] Speaker 04: There's an HD matrix, and importantly, the D in PING is specifically defined as referring to information bits. [00:02:25] Speaker 04: So in ping, the matrix HD is the matrix that you multiply by a vector of information bits. [00:02:34] Speaker 04: And all of this, your honor, is linear algebra. [00:02:38] Speaker 04: So all of this is about the linear algebraic. [00:02:41] Speaker 01: Yeah, but could you just tell me whether I'm right or wrong in understanding what you're arguing? [00:02:46] Speaker 04: I believe, Your Honor, does have it correct. [00:02:48] Speaker 04: So in ping, HD is a matrix that you multiply by information bits. [00:02:56] Speaker 04: In Makai, specifically in L93Y, that code of Makai, Makai's teaching is to modify that exact same portion of a matrix. [00:03:08] Speaker 04: The HD portion. [00:03:09] Speaker 04: The HD portion. [00:03:11] Speaker 02: And if it doesn't ping specifically make [00:03:15] Speaker 02: HD regular and teaches that it's trying to have a specific, it almost doesn't teach away from the K, but it suggests that it's purposefully, deliberately trying to have HD be regular and HP irregular. [00:03:33] Speaker 02: And that's a design choice. [00:03:36] Speaker 04: I think Your Honor's point that HD is regular. [00:03:40] Speaker 04: It is true that HD is regular in pain. [00:03:44] Speaker 04: But pain does not teach away from making a modification. [00:03:47] Speaker 04: In fact, what pain states is that the column weights of HD are a variable. [00:03:58] Speaker 04: They're T. And it does encourage you can try modifying T. So it does talk about making a modification. [00:04:06] Speaker 03: And what Makai adds... I'm sorry, just changing T from anywhere from one to some higher digit? [00:04:14] Speaker 03: That's correct. [00:04:15] Speaker 03: It would still remain regular. [00:04:16] Speaker 04: It would remain regular. [00:04:18] Speaker 04: But what Makai teaches, and Makai comes out about three months after ping, is that, and you can see this in figures five, six, and seven, [00:04:28] Speaker 03: uh... that if you take a regular code and i'll be seeking assistance question need your petition and supporting affidavit as opposed to the reply making reference to l ninety three one it it did your honor and let me take you to that uh... [00:04:51] Speaker 03: Here's five and six. [00:04:52] Speaker 03: You say it's Mackay? [00:04:54] Speaker 04: It's Mackay is how he pronounced his name. [00:04:57] Speaker 04: So in the petition, this teaching of Mackay is at appendix 9041. [00:05:04] Speaker 04: And what that does is in the petition, it specifically calls out the rapid encoding [00:05:11] Speaker 04: irregular construction. [00:05:13] Speaker 04: And the rapid encoding or fast encoding construction, that is the L93Y construction. [00:05:21] Speaker 04: 9041. [00:05:23] Speaker 04: And there we cite page 1454 of Mackay. [00:05:28] Speaker 04: And that's the page where the fast encoding improved performance of this code L93Y are shown. [00:05:36] Speaker 04: That's discussed with respect to Figure 7 and in the text there. [00:05:40] Speaker 04: And that specifically is this L93Y. [00:05:44] Speaker 02: I just got to 9041. [00:05:46] Speaker 02: Can you tell me where it is that you're identifying on that page? [00:05:50] Speaker 04: Sure. [00:05:51] Speaker 04: So on that page, you'll see right in the middle there is some discussion. [00:05:56] Speaker 04: To that end, McKay investigates improving Gallagher codes so that they can be rapidly encoded. [00:06:02] Speaker 04: And then we cite McKay exhibit 1102 and page 1454. [00:06:08] Speaker 04: We examine regular and irregular constructions which lend themselves to rapid encoding. [00:06:14] Speaker 04: L93Y, that code, is McKay's rapid encoding irregular code. [00:06:21] Speaker 04: It's the only disclosed rapid encoding regular code in McKay. [00:06:26] Speaker 04: So that's... My understanding of the board's point here is [00:06:32] Speaker 01: that based on testimony from the patentee's expert witness that the regularity in the HD portion of PING is beneficial and that it would be inconsistent to make that irregular. [00:06:54] Speaker 01: And there is such testimony. [00:06:56] Speaker 01: The question is whether it finds any support in PING itself. [00:07:00] Speaker 04: And, Your Honor, it does not find support in PING itself, because what PING itself teaches is that the benefit is from decomposing PING's language, separating the parts of an LDPC code into the HD portion, which is a matrix that's multiplied by information bits, and the HP portion, where P stands for parity bits, that portion performs accumulation to produce parity bits. [00:07:29] Speaker 04: So that's the benefit. [00:07:31] Speaker 04: Ping says if you separate that out, it makes it easier, it makes it faster. [00:07:39] Speaker 02: can achieve the same performance as McKay with significantly reduced complexity. [00:07:44] Speaker 02: Your view is that borne out just by simply having two different sub-matrices? [00:07:50] Speaker 04: So Ping doesn't say that it's producing the performance of Makai. [00:07:55] Speaker 04: Makai comes after. [00:07:57] Speaker 04: Ping does refer to the author of Makai as having reinvigorated interest in LDPC codes. [00:08:02] Speaker 04: But what Ping is saying is, if we separate into the HD portion, the portion that deals with the information bits, and the HP portion, the portion that produces the parity bits, that's what gives the benefit, the simplicity, and the performance gain. [00:08:18] Speaker 03: There's nothing. [00:08:18] Speaker 03: So these claims are the ones that are at issue here are about encoding, right? [00:08:24] Speaker 03: So they are ultimately about the generator matrix, which I don't. [00:08:29] Speaker 03: correct the following. [00:08:30] Speaker 03: Anything I say is wrong. [00:08:32] Speaker 03: Makai does not talk about generator matrices. [00:08:35] Speaker 03: It talks about the decoding low density parity check matrices. [00:08:42] Speaker 03: Ping talks about the low density parity check [00:08:47] Speaker 03: decoder matrices of which a portion, namely HD, is also going to serve as the generator matrix. [00:08:55] Speaker 03: So why aren't you essentially saying or wasn't your theory that what Mackay says about the decoder side of things, the parity check, [00:09:06] Speaker 03: matrices. [00:09:07] Speaker 03: In some instances, particular ones that he constructed, provide a benefit. [00:09:12] Speaker 03: Not all irregularity do it. [00:09:15] Speaker 03: He found one that, by lots of computer testing, worked. [00:09:19] Speaker 03: Translates into changing a portion of the decoder low-density parity check matrix in PING, which is the portion used for the generator matrix. [00:09:33] Speaker 04: So I agree in part, but let me come to the, I think the key issue is, Mackay is not limited to decoding. [00:09:43] Speaker 03: Mackay is talking about LDPC codes in general, which is... But isn't it entirely all the matrices talking, spoken about, about the parity check matrices, not the generator matrices? [00:09:54] Speaker 04: It has both, Your Honor. [00:09:55] Speaker 04: And actually, if I take you to Appendix 1004 and 1005, I can walk, Your Honors, through that. [00:10:03] Speaker 04: If you look at figure five on page 1004, that is describing the encoding procedure. [00:10:11] Speaker 03: Right. [00:10:11] Speaker 03: Can you help me on that? [00:10:12] Speaker 03: Actually, this is one thing. [00:10:14] Speaker 03: One of the pieces, maybe the only, I'm not sure, notations I've never seen before. [00:10:19] Speaker 03: M sub less than sign. [00:10:21] Speaker 04: What does that mean? [00:10:23] Speaker 04: All that means is that what's happening in Figure 5 is Makai is... Just explain the notation. [00:10:29] Speaker 04: Yes. [00:10:30] Speaker 04: So the M there is looking at... I understand what M is. [00:10:35] Speaker 03: What is M with a small index of the form of a caret? [00:10:41] Speaker 03: What does that mean? [00:10:45] Speaker 04: Your honor, I'm not sure, but it also, I don't think, makes a difference in terms of the analysis. [00:10:51] Speaker 03: Speaking for myself, I have spent days working through the details of this. [00:10:55] Speaker 03: And when there's a key figure, this is absolutely key to your argument, and there's a notation that is not explained in anything I have seen and I don't understand it, it's a problem for me. [00:11:07] Speaker 04: No, I understand where you are now. [00:11:09] Speaker 04: So if you look, it says, [00:11:12] Speaker 04: that the bits tk plus 1 through tn minus m, and then there's the carrot that you, Your Honor, talked about. [00:11:21] Speaker 03: Yes. [00:11:21] Speaker 03: That m... It's in the picture, too. [00:11:23] Speaker 03: It is. [00:11:24] Speaker 04: It is. [00:11:25] Speaker 04: That m-carat portion is referring to the rows associated to the left there. [00:11:29] Speaker 04: And so I believe... So the caret means to the left? [00:11:34] Speaker 04: It's just defining that portion as a portion of the total column. [00:11:38] Speaker 04: So there's the total column height m, and then there's the m caret, which is less than the total column height. [00:11:44] Speaker 04: But the key here is what figure five does is it divides the LDPC into a left side, which is the portion that deals with information bits. [00:11:54] Speaker 04: And you can see that because bits t [00:11:57] Speaker 04: 1 through TK are defined to be source bits, which are the information bits. [00:12:02] Speaker 04: And then the bits to the right of this diagonal line are the parity bits. [00:12:07] Speaker 04: And that is the same division that ping makes between HD, which is the portion of the matrix that deals with information bits, and HP. [00:12:15] Speaker 03: And the only reference to all of this in the petition is the passing reference in one sentence to we tried to figure out how to make some rapid decoding. [00:12:27] Speaker 04: No, Your Honor. [00:12:28] Speaker 04: No, that's not correct. [00:12:30] Speaker 04: We specifically call out in the petition that Mackay teaches applying irregularity to the column weights of the information bit portion of the matrix. [00:12:42] Speaker 04: Where is that? [00:12:43] Speaker 04: That's discussed in the petition at... Let me turn it back to that. [00:12:52] Speaker 04: I believe it's 1045 through 10, I'm sorry, 9045 through 9047 of the petition, Your Honor. [00:13:00] Speaker 04: And so I'm reading now from 9045. [00:13:03] Speaker 04: McKay teaches matrices in which each information bit corresponds to a column and where the weight of that column represents the degree of the information bit. [00:13:12] Speaker 04: Then going on to 9046, as a result, in Mackay's irregular matrix, irregular information bits contribute to different numbers of parity bits. [00:13:23] Speaker 04: That is what's shown in the L93Y embodiment. [00:13:28] Speaker 04: where over in Mackay on page 1005, we see L93Y has a left portion that has weights 9 and 3, a right portion which is the portion that deals with the parity bits and performs an accumulation. [00:13:48] Speaker 04: It's that right portion that has the irregularity. [00:13:50] Speaker 04: and irregularity is only applied to the information bits. [00:13:54] Speaker 04: So that is specifically teaching in Makai to change the column weights of the information bit columns. [00:14:03] Speaker 04: And if you then look at Ping, Ping's HD is the matrix that has information bits. [00:14:09] Speaker 04: So it is specifically teaching make the change there. [00:14:13] Speaker 04: And I want to come back to a point that I wanted to make at the outset. [00:14:18] Speaker 04: If you look at the 781 patent, claim 22 is really the representative claim here. [00:14:27] Speaker 04: Claim 22 is a dependent claim. [00:14:29] Speaker 04: It depends from claim 21. [00:14:31] Speaker 04: Claim 21 describes summing subsets of information bits. [00:14:36] Speaker 04: And the board below found PING anticipates claim 21. [00:14:41] Speaker 04: So everything in claim 21 is found in PING, and the patent owner doesn't challenge that. [00:14:48] Speaker 04: The difference between claim 21 and claim 22 is solely [00:14:53] Speaker 04: the limitation that the information bits appear in a variable number of subsets. [00:15:00] Speaker 04: In other words, it's solely that you vary the column weights. [00:15:05] Speaker 04: And so the only question is, would a person of skill have been motivated and have an expectation of success in making that simple change? [00:15:13] Speaker 04: To Your Honor's opening question, the only change that you'd have to make to PING's HD is to add a few ones to at least one column. [00:15:22] Speaker 04: We say that would be exceedingly easy to do. [00:15:27] Speaker 04: Dr. Frye, Dr. McKay lay that out. [00:15:29] Speaker 04: And therefore, it would have been, and McKay specifically teaches that if you do that, you get a faster encoding and you get improved performance. [00:15:38] Speaker 03: Really? [00:15:39] Speaker 03: I thought all it taught was that in the particular ones he created, he got faster, better code, not some generalization that if you take [00:15:51] Speaker 03: add irregularity to anything, you get good stuff out of it. [00:15:55] Speaker 04: What I meant by that, Your Honor, was if you look at Figure 7, for example, what he's saying is on the left, we have a regular version. [00:16:04] Speaker 04: On the right, we have changed that by adding irregularity to the information bit columns. [00:16:09] Speaker 04: And he reports that for that example, we've achieved both a faster encoding. [00:16:15] Speaker 04: It actually is linear time encodable, which is much faster. [00:16:19] Speaker 04: And we get the same performance gain as before. [00:16:23] Speaker 03: By comparing two very specific things, that doesn't mean that the generalization that if you take some other, let's assume it's regular, assume we're talking about HD, which is by itself regular, that changing this would, by that comparison, create a better coding system. [00:16:46] Speaker 04: But it does give you a motivation. [00:16:48] Speaker 04: And it does give you a reason to expect success. [00:16:52] Speaker 04: Because the claim is only reciting the ability to produce some parity bits. [00:16:57] Speaker 04: The claims, like claim 22, if you produce three parity bits, that's all you need to have practiced that claim. [00:17:04] Speaker 04: And so what Mackay gives you is. [00:17:06] Speaker 03: Let's assume you're right that the expectation of success inquiry [00:17:12] Speaker 03: as a separate piece of doctrine which as you started off this argument by saying it's not really a separate piece but let's assume it's a separate piece and that it doesn't matter how useless the thing is as long as you can expect to do what the claim says even if nobody that then that remain there there remains the question why would a skilled artisan be motivated to do it and on that question you have to have some notion of success about [00:17:42] Speaker 03: utility or various other words that build off utility. [00:17:47] Speaker 03: And that's what I'm not sure why I think I guess that the board found. [00:17:52] Speaker 03: Your evidence didn't really prove because Mackay was examples of benefits of particular coding arrangements. [00:18:04] Speaker 03: describes in general terms, but it doesn't establish that if you take Ping and make it irregular according to Mackay that that would be something a regular skilled artist, ordinary skilled artist would be interested in doing. [00:18:22] Speaker 04: So two responses on that, Your Honor. [00:18:24] Speaker 04: First is, under KSR, that is an incorrect legal test. [00:18:30] Speaker 04: We don't have to show that in McKay, McKay specifically says change HD. [00:18:37] Speaker 03: Under KSR... You just have to have sufficient evidentiary support. [00:18:41] Speaker 03: So I'll just change the description. [00:18:43] Speaker 03: That the board said you did not have sufficient evidentiary support in McKay or Dr. Davis. [00:18:51] Speaker 03: particularly when considering as required the record as a whole, including Dr. Mitzvah. [00:18:56] Speaker 04: But that's not what the board said. [00:18:58] Speaker 04: The board said Mackay only teaches changing the entire matrix H. And what we've just seen is that's not what L93Y does. [00:19:09] Speaker 04: L93Y focuses on there are two different parts. [00:19:13] Speaker 04: There is the part on the left, which is shown in Figure 5, which is the information bit portion. [00:19:18] Speaker 04: And in Figure 6, it modifies that portion. [00:19:21] Speaker 04: The HD portion. [00:19:22] Speaker 04: The HD portion, Your Honor. [00:19:24] Speaker 04: And then in Figure 7, it shows that that produces both faster linear time encoding as a benefit. [00:19:30] Speaker 04: and improve performance as a benefit. [00:19:33] Speaker 04: So that sets up the expectation of the person of ordinary skill reading this, who, by the way, is a PhD with years of experience designing these codes. [00:19:42] Speaker 04: So it is an extremely high level of ordinary skill in this case. [00:19:45] Speaker 04: And this court's decisions have said, when the level of skill is high, a lot more is obvious. [00:19:51] Speaker 04: So there, you have this highly skilled person looking at this saying, well, he's reporting that I get this benefit. [00:20:01] Speaker 04: It would be obvious to make that change over here to see if I get the same benefit. [00:20:06] Speaker 04: And that's enough. [00:20:07] Speaker 04: That is both a motive to do it, because McKiney has shown that it does get a benefit, and he said, well, that something gets a benefit. [00:20:16] Speaker 04: that specifically making a change to the column weights of the information bit columns gives you a benefit. [00:20:23] Speaker 04: Faster, better performance. [00:20:26] Speaker 04: And that is enough to give you a reason why you would do it. [00:20:30] Speaker 02: One of the things I'm struggling with is your standard of review. [00:20:34] Speaker 02: Yes. [00:20:34] Speaker 02: And that I read the board's opinion as having two different reasons for why there's no motivation to combine. [00:20:42] Speaker 02: One is the sub-matrices point that you just addressed. [00:20:46] Speaker 02: But the other is that King's parity check matrix H is already irregular. [00:20:51] Speaker 02: and that this irregularity undermines the reasons for modifying. [00:20:59] Speaker 02: And so how are you responding to that? [00:21:01] Speaker 02: I mean, and the question here is, again, substantial evidence in whether the board's determination on motivation was reasonable. [00:21:09] Speaker 04: So I think there are two responses, Your Honor. [00:21:12] Speaker 04: The first is, as I understand the board, [00:21:18] Speaker 04: What the board is focused on is this portion HP. [00:21:22] Speaker 04: And in HP, there is some, and this is the part that deals just with the parity bits. [00:21:28] Speaker 04: There is almost every one of the columns for the parity bits has a weight 2, and then just the very last one has weight 1. [00:21:37] Speaker 04: So that, they say, is irregularity. [00:21:40] Speaker 04: The response to that is twofold. [00:21:43] Speaker 03: First... And just to be clear, Dr. Mitzenbacher explains that the irregularity is one, two, and T. It's not just one and two, it's one, two, and T, and T can range, you know, I think the example he gives is nine. [00:21:57] Speaker 04: But 9 is not disclosed, T could be 2. [00:22:00] Speaker 04: Because T is a variable, it's undefined. [00:22:02] Speaker 04: You can set T to anything you want. [00:22:04] Speaker 04: So his example of 9 is not what Ping teaches. [00:22:08] Speaker 04: T is just a variable. [00:22:09] Speaker 03: T calls out 4, doesn't it? [00:22:11] Speaker 04: T gives an example of 4, but I could set T to 2. [00:22:15] Speaker 04: And then the only irregularity would be in the HP last column, which would be 1. [00:22:20] Speaker 04: And Makai on its front page specifically addresses this. [00:22:24] Speaker 04: This is Appendix 1001. [00:22:27] Speaker 04: We will use the term regular, quote unquote, for codes that have nearly uniform weight columns and rows. [00:22:35] Speaker 04: Nearly uniform, not perfectly. [00:22:38] Speaker 04: Quote, for example, codes which have some weight two columns and some weight three columns. [00:22:45] Speaker 04: So Ping says that if you have some weight three and some weight two, that's still regular as far as I'm concerned. [00:22:53] Speaker 04: And the teaching of Makai is we want to introduce more irregularity in a specific place. [00:23:00] Speaker 04: We want to introduce more, meaning let's make it nine. [00:23:04] Speaker 04: Let's make it a weight nine column and a weight three column, specifically in the portion that is for the information bits. [00:23:12] Speaker 04: So there are two errors really with the board's analysis. [00:23:18] Speaker 04: One is it ignores the teaching here of Makai that says that little bit of irregularity they're pointing to, having weight two and then the last column's weight one. [00:23:28] Speaker 04: That is still regular for purposes of Mackay's analysis, and we want to make things more irregular. [00:23:34] Speaker 04: And then the second is the board does not address at all the teaching of L93Y, which is to make that irregularity specific to the information bit columns. [00:23:44] Speaker 01: OK. [00:23:45] Speaker 01: I think we're out of time. [00:23:46] Speaker 01: We'll give you two minutes for rebuttal. [00:23:47] Speaker 01: Thank you. [00:24:01] Speaker 05: Thank you, Judge Dyke. [00:24:02] Speaker 05: May it please the court? [00:24:04] Speaker 05: I'm going to just several points and then some of the new arguments that have come up. [00:24:08] Speaker 05: But starting with the briefing, Apple's entire case on appeal comes down to two contentions that are simply false and not reflective of what's stated in the final written decisions. [00:24:19] Speaker 05: The first contention is that the board failed to engage in the actual proposal that they were. [00:24:26] Speaker 01: Why don't you address the arguments that are being made here? [00:24:31] Speaker 01: My understanding of the argument is that Makai shows irregularity in HD and that is according to the terminology used in Makai is the only irregularity that Makai shows and that that provides motivation to change the HD in ping to make it irregular. [00:24:53] Speaker 01: What's wrong with that argument? [00:24:55] Speaker 05: A lot of things are wrong with that argument. [00:24:57] Speaker 05: There is no HD in Makai. [00:25:00] Speaker 05: This is a new creation that's come up late stage in appeal. [00:25:04] Speaker 05: Makai is talking about a parity check matrix as a whole, as a single entire parity check matrix. [00:25:13] Speaker 05: Ping started with that type of parity check matrix and then advanced the technology by doing very specific things. [00:25:20] Speaker 05: One of the things they did was to break that matrix into two sub-matrices, HP and HD. [00:25:27] Speaker 05: So you don't see any HD until you get the ping, because that's one of ping's innovations. [00:25:32] Speaker 05: There's no HD in Makai? [00:25:36] Speaker 05: No, there's no HD in Makai. [00:25:37] Speaker 05: This is entirely new. [00:25:39] Speaker 03: Well, using different language, the left side of Figure 5 in Makai [00:25:46] Speaker 03: Why is that not enough like HD that somebody would be motivated to do to HD what apparently is description of the encoding procedure in figure five? [00:26:02] Speaker 03: Let's assume that this argument was sufficiently made in a timely fashion, just because I want to understand it, OK? [00:26:08] Speaker 03: That that is just different language for what I think Judge Dyke, my understanding of what Judge Dyke was describing. [00:26:15] Speaker 05: understood and understanding a very strongly do not believe that argument was timely made but going with that [00:26:25] Speaker 05: I think what's happening is there's an attempt to read in content of Ping through that interpretation. [00:26:33] Speaker 05: As I understand what's in Figure 5, and none of the experts have testified on this in a timely fashion. [00:26:40] Speaker 03: There was certainly some deposition testimony, that is, your expert was deposed about Figure 5, certain excerpts in the Joint Appendix about that, and maybe that's already not [00:26:54] Speaker 03: timely, and I think Dr. Fry talks about it in the course of talking about L93Y, which was maybe referred to in the opening petition. [00:27:09] Speaker 03: If you can, just put aside the timing question. [00:27:12] Speaker 03: Help us understand what [00:27:15] Speaker 03: what is going on in Figure 5. [00:27:18] Speaker 05: Sure, and it helps to know what's going on in Makai, generally, to understand what I believe is going on in Figure 5. [00:27:26] Speaker 05: What Makai is doing is taking one pattern for parity check matrix, this so-called 93 pattern, which they describe as an irregular matrix in the sense that it has one column out of 12 at weight 9, [00:27:40] Speaker 05: all the rest, the other 11 columns are at weight 3. [00:27:43] Speaker 05: And what Makai is experimenting with is within that very specific pattern, if there's any performance difference or coding difference based on how the ones are distributed within that pattern. [00:27:57] Speaker 05: So those are the experiments Makai is performing. [00:28:00] Speaker 05: They're going through and randomly generating... [00:28:04] Speaker 05: Yes, I believe that's true. [00:28:05] Speaker 05: The distribution within the nine columns. [00:28:07] Speaker 05: And then looking at different types of distribution through random generation and then empirical testing to try to determine what works in this area and what doesn't work. [00:28:21] Speaker 05: So in that sense, they're looking at distribution within a parity check matrix to try to figure out what works. [00:28:30] Speaker 05: So if we're looking at figure five, I believe what Makai is trying to do is consistent with that notion of researchers trying to understand how distribution within a parity check matrix might affect performance. [00:28:47] Speaker 05: So I think in that sense, [00:28:49] Speaker 05: He's trying to point to different. [00:28:52] Speaker 03: Again, just continue helping me. [00:28:55] Speaker 03: So this is about an encoding procedure, figure five, that's what it's called. [00:29:00] Speaker 03: And the idea here is to try to indicate why if you have something like the parity check matrices we're testing, then the encoding process will actually be reasonably fast, low cost in memory. [00:29:20] Speaker 05: It's a different method, the fast encoding method that's using, I believe, this different parity check. [00:29:25] Speaker 03: The good point of this chart is the little stuff on the right about storage requirements for the encoding process, right? [00:29:36] Speaker 05: I think that's right. [00:29:37] Speaker 05: I think that's right. [00:29:38] Speaker 05: I mean, you're asking the lawyer who hasn't gone through the... hasn't had the experts weigh in on this, but I think that's correct. [00:29:47] Speaker 05: As far as the question as how that relates to each [00:29:50] Speaker 05: Again, I want to be really clear on this. [00:29:53] Speaker 05: The HDHP construction or breaking restructuring parity check matrices is something that first comes up in PING. [00:30:02] Speaker 05: And that's what PING is describing as the difference. [00:30:06] Speaker 05: So if we want to understand if that represents a difference with regard to Makai. [00:30:11] Speaker 01: But I'm still not understanding why [00:30:15] Speaker 01: MacKay L-93Y doesn't disclose the equivalent of irregularity in HD. [00:30:25] Speaker 05: I don't think that it does, but that ultimately, if we're looking at the basis of the board's decision, [00:30:30] Speaker 05: what the board said about no substantiated motivation to combine based on 93-Y or whatever else petitioner was originally referring to, all of that still applies. [00:30:43] Speaker 01: The board's decision seems to be fairly simplistic. [00:30:47] Speaker 01: It says [00:30:48] Speaker 01: that McCoy says irregularity is desirable and some of PING is irregular so there's no motivation to make it more irregular. [00:30:55] Speaker 01: That seems to be the basic tenor of the board decision, which it seems to me is not entirely satisfactory if you assume that McCoy specifically shows that the HD is irregular and the question is whether there's motivation to make the PING HD irregular. [00:31:13] Speaker 05: So, well, I mean, I think the board notes that there were a lot of assumptions made, and there's a lot of briefing on the oversimplification that was believed to occur in the petition. [00:31:24] Speaker 05: I mean, I think the board goes through and takes the very logic that was advanced in the petition materials and then evaluates that in view of the references and the evidence to see if that works. [00:31:36] Speaker 05: And they go through and give really three main reasons [00:31:40] Speaker 05: why the logic as laid out didn't work or why the rationale lacks logical underpinnings. [00:31:46] Speaker 05: One of the reasons is starting with just the notion of what petitioner was pointing to in Mackay, this observation that a irregular parity check matrix performed better. [00:31:59] Speaker 01: and the board is looking at the specific proposal, this proposal to- I think the point I'm making is it seems as though there's more to Makai than a general statement that some irregularity is desirable. [00:32:11] Speaker 01: It seems to show irregularity as being desirable in something that looks like the HD matrix. [00:32:19] Speaker 05: I'm not sure I understand the point. [00:32:22] Speaker 05: I understand some visual appeal looking at the figures. [00:32:24] Speaker 05: I'm not sure that that's accurate. [00:32:27] Speaker 05: Ultimately, what Petitioner was proposing is reaching through the parity check matrix to a very specific portion of Ping's parity check matrix and making a modification. [00:32:38] Speaker 05: And the board very clearly addressed that, went through and explained precisely why they were rejecting that theory for three main reasons. [00:32:46] Speaker 05: there was a disconnect with what was being argued and the content of both of the references, both Makai and Ping. [00:32:54] Speaker 05: One was this disconnect between the general teaching or observation that a irregular parity check matrix as a whole performed better than an irregular one as a whole. [00:33:06] Speaker 05: that didn't connect up with the specific argument that you'd reach in to a periodic matrix and change one particular portion. [00:33:16] Speaker 05: We're looking for support to guard against what really was a hindsight-driven argument here. [00:33:22] Speaker 01: Let me ask you about another aspect of this if I could, and that is your expert said that in PING it shows that there's a benefit [00:33:32] Speaker 01: to regularity in the HD matrix, and that making that change would ignore the constraints of PING. [00:33:43] Speaker 01: But in looking at PING, I don't see that PING says that there's a benefit to regularity in the HD matrix. [00:33:56] Speaker 05: It does, Your Honor. [00:33:58] Speaker 01: Where does it say that? [00:34:01] Speaker 05: in two places. [00:34:02] Speaker 05: One is in the beginning. [00:34:04] Speaker 01: I'm sorry, it's A1010. [00:34:22] Speaker 05: Excuse me? [00:34:24] Speaker 03: Decimal numbers, not binary numbers, 1010. [00:34:26] Speaker 03: 1010. [00:34:29] Speaker 03: Yes. [00:34:33] Speaker 05: So in the beginning of the, and PING is a very short article here as you can see, it's a column and a half, but in the very beginning of the PING discussion it's talking about LDPC codes. [00:34:49] Speaker 05: Where are you? [00:34:50] Speaker 05: So in the second paragraph it states. [00:34:52] Speaker 01: This is 1010, second paragraph. [00:34:55] Speaker 05: Yes. [00:34:56] Speaker 05: It's saying an LDPC code, and it's citing to Dr. McKay's work discussing these randomly generated LDPC codes. [00:35:06] Speaker 05: Further in the paragraph, it talks about those codes and some problems associated with them, including [00:35:16] Speaker 05: that they can be very costly in terms of the memory requirements and the operations that are involved. [00:35:24] Speaker 05: So high complexity is requiring a lot of processing and hardware and cost. [00:35:31] Speaker 00: But my question was where does this relate that to irregularity? [00:35:38] Speaker 00: Yes. [00:35:38] Speaker 00: Irregularity. [00:35:40] Speaker 05: And in two places. [00:35:41] Speaker 05: I'm being slow in getting here, but [00:35:43] Speaker 05: In the next paragraph, Ping describes what they're doing. [00:35:47] Speaker 05: They're saying they're taking a modified approach compared to Makai, and that modified approach is they're adopting a semi-random technique, not a fully random technique, but semi-random, where they break the matrix in two. [00:36:03] Speaker 05: Random is irregular. [00:36:05] Speaker 05: No, random is how they generate the distribution of zeros and ones in the parity check matrix. [00:36:11] Speaker 05: Because people didn't know how these things work. [00:36:13] Speaker 05: They would generate them randomly. [00:36:15] Speaker 03: And they can be gigantic. [00:36:16] Speaker 05: And they can be gigantic. [00:36:17] Speaker 05: And you just didn't know what would work. [00:36:22] Speaker 05: So people would generate them randomly. [00:36:24] Speaker 05: So they're saying, let's narrow the universe here. [00:36:26] Speaker 03: We came up with a... So it's making the left side deterministic. [00:36:30] Speaker 03: Fully deterministic. [00:36:31] Speaker 03: Where does it say that the right side, the HD part of it, is beneficially quite regular? [00:36:39] Speaker 05: So early on, they attribute it to both. [00:36:42] Speaker 05: Further, then they walk through and talk about the HP side. [00:36:48] Speaker 05: And then when you get down to equation three, they're defining HD. [00:36:54] Speaker 03: So now we're taking the right side and we're essentially creating a stack, a stack of matrices, one on top of each other. [00:37:03] Speaker 03: Each one, we're going to have t stacks, right? [00:37:07] Speaker 05: I think that's right. [00:37:07] Speaker 03: Right. [00:37:08] Speaker 03: And in each one, each column's going to have a single one. [00:37:10] Speaker 03: So each total, we're going to have t ones in each column, one in each piece of the stack. [00:37:17] Speaker 03: I think that's correct. [00:37:18] Speaker 03: I think you understand. [00:37:19] Speaker 03: Where does it say this is a, [00:37:23] Speaker 05: Right, so equation 3 is HD, and the text right underneath that talks about why they're doing it that way. [00:37:31] Speaker 05: They say, they describe that each sub-block in HD, they randomly create exactly [00:37:41] Speaker 05: one element, one per column. [00:37:44] Speaker 05: So they're making it exactly uniform per column. [00:37:48] Speaker 05: And then they talk about why they're doing that. [00:37:50] Speaker 05: They describe the partition equation three is to best increase the recurrence distance of each bit in the encoding chain and intuitively reduces correlation during the decoding process. [00:38:10] Speaker 05: So both experts have weighed in on this. [00:38:12] Speaker 05: Dr. Davis was asked about this during cross-examination. [00:38:15] Speaker 05: Dr. Mitsimacher addressed this directly and explained what that means. [00:38:20] Speaker 05: Increasing the recurrence distance is what is giving some of the very benefits that PING is talking about right up front and walking through there. [00:38:30] Speaker 01: Well, yeah, but the trouble is there are different benefits from PING. [00:38:34] Speaker 01: And he talks about both kinds of benefits. [00:38:38] Speaker 01: I'm not sure this is referring to the benefit of regularity. [00:38:42] Speaker 01: Why should I understand this that way? [00:38:46] Speaker 05: You should not understand it that way. [00:38:47] Speaker 05: It's not talking about any benefit of irregularity. [00:38:50] Speaker 01: It's talking about a benefit of regularity. [00:38:56] Speaker 05: It's talking about the benefits of the structure and the constraints. [00:39:00] Speaker 05: No, but it's not talking about the benefits of regularity. [00:39:03] Speaker 05: Well, the constraints are what's set in that submatrix, and those constraints are a very regular distribution. [00:39:10] Speaker 01: Explain to me how this is saying there's a benefit to the regularity. [00:39:17] Speaker 05: So it doesn't use those words, but it says this is the construction we've chosen. [00:39:22] Speaker 05: Exactly one element, one per column. [00:39:25] Speaker 02: So the one element, one per column means regularity. [00:39:29] Speaker 05: Yes, it says uniform weight, which under the parlance of Makai is regularity. [00:39:34] Speaker 02: Okay. [00:39:35] Speaker 05: Yes. [00:39:36] Speaker 02: So it says we have this one element per column, so regularity, and then you're saying the next sentence is, when it's talking about this advantage of reducing the correlation, it's referring back to the attribute of exactly one element one per column. [00:39:55] Speaker 05: Yeah, as defined in equation three, which it states in that sentence, precisely, Your Honor. [00:40:02] Speaker 05: And it ties that structure to the benefits. [00:40:05] Speaker 01: Did your expert focus on that sentence? [00:40:07] Speaker 01: Yes. [00:40:08] Speaker 01: Yes, they could. [00:40:09] Speaker 05: Where did he? [00:40:17] Speaker 05: I'll turn to what's, see if I can find first what's cited in the board, board's decision. [00:40:27] Speaker 05: This was discussed at length. [00:40:37] Speaker 05: Board citing specifically to paragraph 96 of Dr. Mitz and Mocker's testimony. [00:40:44] Speaker 05: And let me find you the A site, your honor. [00:40:46] Speaker 05: 3049? [00:40:49] Speaker 05: Yeah, 3042. [00:40:52] Speaker 03: Oh, maybe there's several different Mitz and Mocker declarations. [00:40:59] Speaker 05: Yeah, there are multiple different declarations. [00:41:09] Speaker 05: Yep, paragraph 96. [00:41:10] Speaker 00: So I'm supposed to look at 96? [00:41:16] Speaker 05: Is paragraph 96 at 3049 of the appendix. [00:41:22] Speaker 02: Thank you. [00:41:27] Speaker 05: The whole section here from 3048 to [00:41:32] Speaker 05: 305.1 is Dr. Mitsenmacher's testimony on the points regarding the constraints of PING. [00:41:53] Speaker 01: Okay. [00:41:53] Speaker 01: All right. [00:41:53] Speaker 01: I think we're out of time. [00:41:55] Speaker 01: Thank you, Mr. Rosano. [00:41:56] Speaker 01: Thank you. [00:42:03] Speaker 01: You might address that last point. [00:42:05] Speaker 04: I will, Your Honor. [00:42:06] Speaker 04: I want to hit three points that I think came out of Your Honor's questioning. [00:42:11] Speaker 04: The first is about what the board actually said. [00:42:14] Speaker 04: The second is about the explanation of figures five and six, which Dr. Fry does give, and that Dr. Fry's explanation is unrebutted. [00:42:22] Speaker 04: And then the third is, what is the specific benefit that PING says you get from its construction? [00:42:30] Speaker 04: I'll do the last one first, and then I'll come back to the others. [00:42:32] Speaker 04: What Ping says is not that you can't be irregular. [00:42:38] Speaker 04: Ping picks t to be any variable, and it's the same. [00:42:43] Speaker 04: But what Ping is talking about is that the benefit here is splitting HD and HP. [00:42:52] Speaker 03: You use a single T in a given matrix. [00:42:57] Speaker 03: That is regular. [00:42:59] Speaker 04: That is regular. [00:43:00] Speaker 04: In HD, using a single T is regular. [00:43:04] Speaker 04: But this idea that that is a constraint that could not be violated is not correct. [00:43:09] Speaker 04: That's the issue. [00:43:10] Speaker 03: The thing says we did exactly the following thing, and it was terrific. [00:43:15] Speaker 04: And so the chronology is ping comes out. [00:43:18] Speaker 04: A person of ordinary skill reads ping, sees I'm going to separate out HD. [00:43:22] Speaker 04: It's a regular matrix. [00:43:24] Speaker 04: I'm getting some benefits. [00:43:25] Speaker 04: And the benefit that ping says is it requires very little memory to store HD in the encoder if HD is sparse. [00:43:34] Speaker 04: This can be insured using a small t. [00:43:37] Speaker 04: Then Makai gets published, and Makai says, let's make the HD portion, the information bit portion, have irregular column weights. [00:43:46] Speaker 04: And it says that that gives you the same benefit in largely the same language. [00:43:52] Speaker 04: And this is on Appendix 1006. [00:43:56] Speaker 04: talking about his fast encoding code, which is L93Y, both the memory requirements and the CPU requirements at the encoder of our fast encoding codes are substantially smaller. [00:44:09] Speaker 04: And then he goes on, this compares to, and he gives an equation, for storing the generator matrix. [00:44:16] Speaker 04: So MacKay is saying, using his construction, [00:44:22] Speaker 04: where you've made the HD portion irregular, gives you the same benefit. [00:44:29] Speaker 04: It has low memory requirements, they're faster in coding, they can be small just like pings. [00:44:36] Speaker 04: So that idea that ping somehow teaches, essentially they're making a teaching away argument and it's just not there. [00:44:43] Speaker 04: There's nothing in ping that constrains the modification that Makai teaches would give you the benefits of faster encoding and better performance. [00:44:53] Speaker 04: Coming back to the board, the error that the board made was saying, and I'm quoting, Mackay's teachings are only applicable to the full parity check matrices. [00:45:05] Speaker 04: That's at Appendix 26. [00:45:06] Speaker 04: So, quote, Mackay does not suggest that these improvements would have been applicable to the portions of a parity check matrix, e.g., Ping's submatrix HD. [00:45:17] Speaker 04: That's at Appendix 25. [00:45:20] Speaker 04: They never, the board's errors, they never considered L93Y, and L93Y specifically does what they say, that Mackay doesn't disclose. [00:45:31] Speaker 01: Okay, I think we're out of time, okay? [00:45:33] Speaker 04: If I can just make one last citation, Your Honor? [00:45:36] Speaker 01: Okay. [00:45:37] Speaker 04: And that is, [00:45:38] Speaker 04: At appendix 2164 to 65, Dr. Fry specifically explains that teaching of Mackay and that opinion. [00:45:47] Speaker 04: There is no rebuttal from Dr. Mitzenmacher on that. [00:45:50] Speaker 01: Okay. [00:45:50] Speaker 01: Thank you, Mr. Davenport. [00:45:52] Speaker 01: Thank you. [00:45:52] Speaker 01: Thank you. [00:45:53] Speaker 01: I appreciate it.