UNITED STATES PATENT AND TRADEMARK OFFICE
` BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`Page 1
`
` HUGHES NETWORK SYSTEMS, LLC and
` HUGHES COMMUNICATIONS, INC.,
` Petitioners,
` v.
` CALIFORNIA INSTITUTE OF TECHNOLOGY,
` Patent Owner.
`
` IPR 2015-00059
` Patent 7,916,781
`
` DEPOSITION OF SOLOMON W. GOLOMB, Ph.D.
` Los Angeles, California
` Wednesday, October 14, 2015
`
`REPORTED BY:
`CHRISTY A. CANNARIATO, CSR #7954, RPR, CRR, CCP
`JOB NO.: 97924
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`Hughes, Exh. 1073, p. 1
`
`
` BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`Page 1
`
` HUGHES NETWORK SYSTEMS, LLC and
` HUGHES COMMUNICATIONS, INC.,
` Petitioners,
` v.
` CALIFORNIA INSTITUTE OF TECHNOLOGY,
` Patent Owner.
`
` IPR 2015-00059
` Patent 7,916,781
`
` DEPOSITION OF SOLOMON W. GOLOMB, Ph.D.
` Los Angeles, California
` Wednesday, October 14, 2015
`
`REPORTED BY:
`CHRISTY A. CANNARIATO, CSR #7954, RPR, CRR, CCP
`JOB NO.: 97924
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` Wednesday, October 14, 2015
` 9:21 a.m.
`
`Deposition of Solomon W. Golomb, Ph.D.,
`taken on behalf of Petitioners, held at the
`offices of Wilson Sonsini Goodrich &
`Rosati, 633 West Fifth Street, Los Angeles,
`California, before Christy A. Cannariato,
`CSR #7954, RPR, CRR, CCP.
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` A P P E A R A N C E S
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`Page 3
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`ON BEHALF OF THE PETITIONERS:
`
`BAKER BOTTS
`BY: ELIOT WILLIAMS, ESQ.
`1001 Page Mill Road
`Palo Alto, CA 94304
`
`ON BEHALF OF THE PATENT OWNER AND THE WITNESS:
`
`WILSON SONSINI GOODRICH & ROSATI
`BY: MATTHEW ARGENTI, ESQ.
`650 Page Mill Road
`Palo Alto, CA 94304
`
`ALSO PRESENT:
`ORAL CAGLAR, CALTECH ASSOCIATE GENERAL COUNSEL
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` I N D E X
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`Page 4
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`EXAMINATION BY PAGE
`MR. WILLIAMS 5
`MR. ARGENTI 77
`
`----------------------------------------------------
` EXHIBITS
`EXHIBIT DESCRIPTION PAGE
`
`Exhibit 1200
`Single page with Examples (a) and (b) 31
`
` PREVIOUSLY MARKED EXHIBITS
` Exhibit 1011
` Exhibit 1005
` Exhibit 2024
`
`----------------------------------------------------
` QUESTIONS INSTRUCTED NOT TO ANSWER
` None
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`Page 5
`Los Angeles, California; Wednesday, October 14, 2015
` 9:59 a.m.
`
` SOLOMON GOLOMB, Ph.D.
` having first been duly sworn, was
` examined and testified as follows:
`
` EXAMINATION
`BY MR. WILLIAMS:
` Q. Good morning.
` A. Good morning.
` Q. My name is Eliot Williams. I represent
`the Petitioner in this case.
` A. Let me get my glasses.
` Q. Can you tell me when you first became
`involved in this matter?
` A. In what?
` Q. In this matter.
` A. I think I was contacted sometime this
`past spring.
` Q. How were you contacted?
` A. By telephone.
` Q. And who contacted you?
` A. I think Mr. Argenti.
` Q. At the time you were contacted by --
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`first contacted, were you aware of this patent?
` A. No.
` Q. Did you, at that time, know Robert
`McEliece?
` A. Yes.
` Q. How long had you known him?
` A. Since roughly 1963.
` Q. Where did you meet Mr. McEliece?
` A. I think he started in my group at JPL
`shortly before I left JPL for University of Southern
`California.
` Q. So when he started at JPL, was he
`working under you?
` A. Yeah. He claims I was his first boss.
` Q. How long did you work with him at JPL?
` A. I think only a few months.
` Q. Have you kept in contact with him since?
` A. From time to time.
` Q. How often would you say you speak with
`him? Let me withdraw the question.
` How often do you communicate with him?
` A. I would say an average of at least once
`a year.
` Q. I'm going to ask you about a few other
`names. Aamod Khandekar. Do you know him?
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` A. It doesn't ring a bell.
` Q. What about Hui Jin?
` A. You will have to speak louder. I don't
`hear well.
` Q. Hui Jin, J-i-n. What about that person?
` A. No, I never met him.
` Q. What about Dariush Divsalar?
` A. Yeah, I have known him for some time,
`not well, but enough that we occasionally exchange
`emails.
` Q. How did you come to meet Mr. Divsalar?
` A. I don't specifically recall.
` Q. Was it when you were at JPL?
` A. No, no. It was long after I left JPL.
` Q. And you said you communicate with him
`from time to time?
` A. By email occasionally, yes.
` Q. What is the subject matter of those
`communications?
` A. It varies all over the map.
` Q. Let me show you what was previously
`marked as Exhibit 1011. Are you familiar with this
`document?
` A. I have seen it, yes.
` Q. What is it?
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` A. It's the text of a talk that Divsalar
`supposedly gave at an Allerton Conference.
` Q. Did you attend -- do you know what an
`Allerton Conference is?
` A. I have never attended an Allerton
`Conference.
` Q. Have you ever heard of the Allerton
`Conference before this matter?
` A. I vaguely heard of it.
` Q. But you never attended it?
` A. I never attended. I'm not aware that
`anyone in our large communications group at
`University of Southern California ever attends.
` Q. Before you were retained in this matter,
`had you seen this paper before?
` A. No.
` Q. Had you, before you were retained in
`this matter, ever heard of repeat accumulate codes?
` A. I'm not sure.
` Q. Have you heard of repeat accumulate
`codes now?
` A. Yes.
` Q. What are they?
` A. Hmm?
` Q. What are they?
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` MR. ARGENTI: Objection. Form.
` A. Well, how short or long an answer do you
`want?
` Q. Well, do you know what repeat accumulate
`codes are?
` A. Well, I have a general understanding.
` Q. So I will just take your general
`understanding of what repeat accumulate codes are.
` A. Well, these are typically a type of
`convolutional code where one or more bits are
`accumulated during the encoding process.
` Q. Do you know who invented repeat
`accumulate codes?
` A. What?
` Q. Do you know who invented repeat
`accumulate codes?
` A. No, I don't.
` Q. What were you asked to do when you were
`retained in this matter?
` A. To look at the patent, to look at the
`opinion or decision of the PTAB, to look at the
`Divsalar paper, and to render my own opinion on
`matters raised by the PTAB.
` Q. This paper that's in front of you lists
`three authors; correct?
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` A. (Nods head up and down.)
` Q. And Robert McEliece is one of them?
` A. Yes.
` Q. Did you ever discuss this paper with
`Robert McEliece?
` A. No.
` Q. Did he ever show it to you?
` A. No.
` MR. ARGENTI: Objection. Outside the
`scope.
` A. I had never seen this paper before, and
`I haven't discussed it with any of its authors.
` Q. Thank you.
` You said you looked at the patent, the
`PTAB decision, and the Divsalar paper. Was there
`anything else that you looked at in the course of
`doing your work on this matter?
` MR. ARGENTI: Objection. Scope.
` A. Well, I looked at -- I didn't study, but
`I looked at the Declaration of Dr. Pfister.
` Q. When you said you didn't study it but
`you looked at it, what's the distinction you're
`drawing there?
` A. Well, the difference between reading
`something through just to get a general sense of it
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`and reading it critically.
` Q. Okay. Did you know Dr. Pfister before
`this matter?
` A. No.
` Q. And what was the purpose of reading his
`declaration?
` A. Well, the PTAB, I think, relied on some
`of the points that he made.
` Q. And so you were looking at it to
`understand the points that they were relying on?
` A. Yeah.
` MR. ARGENTI: Objection. Form.
` A. Looking to see what has been referred
`to.
` Q. Before this matter, had you ever been
`engaged to work on patent matters?
` A. Yes.
` Q. How many times?
` A. More than a dozen.
` Q. More than a dozen. Have you given a
`deposition before?
` A. Yes.
` Q. How many times?
` A. Two or three.
` Q. On those two or three occasions were you
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`acting as an expert?
` A. Yes.
` Q. Have you ever acted as an expert --
`well, let me withdraw the question.
` You understand that this matter is
`proceeding within the Patent Office?
` A. Yes.
` Q. Have you ever worked as an expert in a
`matter that was proceeding before the Patent Office?
` A. I think so.
` Q. You think so. Do you remember what
`matter that would have been?
` A. No.
` Q. Do you remember when that was? When,
`generally?
` A. I have been asked to be an expert in
`patent cases starting around 1990, and I don't
`remember the details of most of those cases.
` Q. Do you remember --
` A. By the way, I do remember one case where
`Dr. McEliece and I were experts on opposite sides.
` Q. Do you remember the last time, prior to
`this case, that you were acting as an expert in a
`patent case?
` A. About four years ago.
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` Q. Okay. Was there any other material that
`you read in connection with your work in this case
`that you haven't mentioned?
` MR. ARGENTI: Objection. Scope.
` A. Nothing directly related to this case.
` Q. Have you ever heard the term "file
`history" of a patent?
` A. I'm aware of the term. I did not look
`at the file history of this patent.
` Q. So you say you're aware of the term.
`What's your understanding of what the file history
`is?
` A. Well, it's the correspondence between
`the patent applicant and the Patent Office that
`ultimately leads to the issuing of the patent.
` Q. Did you consider reviewing the file
`history in this case?
` A. I never seriously considered it.
` Q. Why not?
` A. I wasn't asked to.
` Q. Okay. Have you ever looked at a file
`history before?
` A. I'm sure there have been a couple of
`cases where I did look at the file history of the
`patent.
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` Q. "A couple cases" meaning a couple cases
`when you have been an expert before?
` A. Yeah, where I was an expert.
` Q. And, in general, why in those cases
`would you look at a file history?
` MR. ARGENTI: Objection. Scope.
` A. The details escape me at this point.
` Q. Can you think of any reason why an
`expert would want to look at a file history?
` MR. ARGENTI: Objection. Scope.
` A. Well, sometimes a particular item may be
`disclaimed by the applicant during the prosecution
`of the patent.
` Q. And that's an example of when you
`might --
` A. Hmm?
` Q. That's an example of why you might look
`at a file history?
` A. That's an example of why it might be
`relevant.
` Q. And so you said you weren't asked to
`look at the file history in this case. Did you look
`at the file history in this case?
` A. No, I did not.
` Q. And why not?
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` MR. ARGENTI: Objection. Scope.
` A. I wasn't sure that it would matter.
` Q. Now, you wrote a declaration in this
`case; correct?
` A. Yes.
` Q. Can you tell me how it was generated?
` A. Excuse me?
` MR. ARGENTI: Objection. Form.
` Q. Can you tell me how it was generated?
` MR. ARGENTI: Objection. Form.
` A. I gave my opinions at least verbally to
`counsel, and there was an exchange of documents back
`and forth that ultimately led to the final
`declaration, which I carefully read and made sure
`that I fully agreed with everything in it.
` Q. Did you bring a copy of your
`declaration?
` A. Yeah, I have it somewhere. Yeah.
` Q. And does it have an exhibit number on
`the bottom?
` A. Exhibit 2024.
` Q. Exhibit 2024. Okay. Now, on the last
`page there's a typed signature?
` A. Yes.
` Q. Did you authorize your name to be put
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`there?
` A. Definitely.
` Q. And this document, Exhibit 2024, this is
`your declaration in this proceeding?
` A. Yes.
` Q. Does it reflect your opinions
`accurately?
` A. It does.
` Q. In preparation for today's deposition,
`have you had an opportunity to read through it
`again?
` A. Yes.
` Q. When did you do that? When?
` A. During the past week.
` Q. During the past week?
` And in doing so, did you notice any
`errors or things you would like to clarify?
` A. There may have been one or two minor
`grammatical things that I would have done
`differently, but nothing substantive.
` Q. Now, you mentioned that there was an
`exchange of documents that led up to this final
`declaration. How many exchanges occurred?
` A. Two or three.
` Q. And do you recall making changes to the
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`document during that tame?
` A. Yes.
` Q. What kind of changes were you making?
` A. Clarifications of all sorts of things,
`including even things related to my CV.
` Q. What about things related to the patent?
`Did you make any changes related to -- did you make
`any changes in the document relating to the patent?
` MR. ARGENTI: Objection. Form.
` A. I don't recall any specific changes
`related to the patent.
` Q. Let me ask you about paragraph 16.
` A. Okay.
` Q. You say there that a person of ordinary
`skill in the relevant field is a hypothetical person
`to whom one could assign a routine task with
`reasonable confidence that the task would be
`successfully carried out. See that?
` A. Yeah.
` Q. What did you mean by "routine task"?
` A. That if you give the person detailed
`instructions they would be able to carry them out.
` Q. And then paragraph 17 you say you're
`familiar with the level of skill in the art.
` A. Yeah.
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` Q. Sorry, of the '781 patent. See that?
` A. Yes.
` Q. How is it that you are aware of the
`level of skill in the art of the '781 patent?
` MR. ARGENTI: Objection. Form.
` A. Well, because I work with students,
`graduate students, post-docs, and I have done
`consulting with companies that expose me to people
`that would typically be of ordinary skill in the
`art.
` Q. And then in paragraph 18 you give a --
`you give a description of a person of ordinary skill
`in the art.
` A. Right.
` Q. And that was someone who had, either
`through education or experience, the equivalent of a
`master's degree in electrical engineering or
`mathematics and three to four years of work or
`research experience in the field of error control
`coding.
` A. Yeah.
` Q. Or alternatively, a PhD with two years
`in that area.
` A. Yeah.
` Q. What's error control coding?
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` A. How long a lecture do you want?
` Q. Less than five minutes.
` A. Okay. The modern history of
`communications started with two papers written by
`Claude Shannon in 1948 in which he described the
`limit -- the theoretical limit on performance in
`communications that could be achieved by coding.
`And he didn't describe explicitly the codes that you
`could use in practice to get close to his limits.
` So for the next, whatever it's been,
`close to 70 years, people have been coming up with
`specific systems where you add redundancy bits to
`the information bits so as to be able to detect
`errors, locate errors, correct errors so that the
`encoded message is more resistant to noise in the
`channel, and you have a better chance of decoding it
`correctly in spite of the noise.
` Q. You said two papers. Were those both by
`Shannon or were you thinking --
` A. Yeah, they were both by Shannon. And
`they were originally titled, "A Mathematical Theory
`of Communication," I think Part I and Part II. When
`it reappeared in book form, it became, The
`Mathematical Theory of Communication.
` Q. So by May of 2000, what was the state of
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`the art in that field in terms of error coding?
` A. Okay. Well, for many decades, the two
`leading families of error correcting codes were
`known respectively as block codes and convolutional
`codes. But during the decade before 2000, two new
`classes of codes, one called turbo codes and another
`called low-density parity check codes, have been
`shown to have superior performance.
` And the state of computing had improved
`to the point where it was practical to implement
`these codes. Because earlier the decoding would
`have exceeded the computing capability of most
`people, but by 2000, turbo codes and low-density
`parity check codes have become very fashionable
`because they got you closer to the Shannon
`theoretical limit.
` Q. Are those classes, turbo codes and
`low-density parity check codes, different than the
`two families you mentioned, block and convolutional
`code?
` MR. ARGENTI: Objection. Scope.
` A. They're different from each other, but
`there are certainly relationships between the two.
` Q. So would someone of ordinary skill in
`the art, in your opinion, then have been familiar
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`with turbo codes and low-density parity check codes?
` MR. ARGENTI: Objection. Scope.
` A. I would say that in the year 2000 people
`who were considerably more experienced than one of
`ordinary skill in the art would have already been
`familiar with those two kinds of codes, but many
`people of more ordinary skill would not yet have
`been.
` Q. So would someone with a master's degree
`in electrical engineering and three or four years of
`experience in error control coding, they wouldn't
`have been familiar with turbo coding in May of 2000?
` A. I think it's unlikely that the
`curriculum for a master's degree up to that time
`would have included turbo codes.
` Q. Have you ever taught a class in coding
`theory?
` A. Many, many times.
` Q. What's the most recent time you taught a
`class in coding theory?
` A. About five years ago.
` Q. Was that an undergraduate or graduate
`level?
` A. Typically, it's at a level that's taken
`by seniors and first-year graduate students.
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` Q. Did that course include a discussion of
`turbo codes?
` A. Actually, no.
` Q. Did it include a discussion of LDPC
`codes?
` MR. ARGENTI: Objection. Scope.
` A. I didn't hear you.
` Q. Did it include a discussion of LDPC
`codes?
` MR. ARGENTI: Objection. Scope.
` A. No.
` Q. LDPC. I meant low-density parity check.
` A. Yeah.
` Q. Let me ask you about the next paragraph
`of your declaration, which is paragraph 19.
` A. Okay.
` Q. The first sentence you say, "I've been
`advised that in the present proceeding the '781
`patent claims are to be given their broadest
`reasonable interpretation in view of the
`specification." Do you see that?
` Now, before this matter, had you ever
`encountered this standard, "broadest reasonable
`interpretation"?
` A. I'm pretty sure I had.
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` Q. You had. What's your understanding of
`what it means?
` A. The purpose of a patent, as I understand
`it, is to enable someone of ordinary skill in the
`art to be able to reproduce the invention. The
`claims alone will rarely give enough information to
`do that. And the purpose of the specification is to
`give the additional information needed to interpret
`the claims in sufficient detail that one can realize
`the invention.
` Q. So when you say the claims are to be
`given their broadest reasonable interpretation, then
`what do you consider that to mean?
` A. Well, they should be given the broadest
`interpretation consistent with the specifications.
` Q. Now, starting in the next page of your
`-- on page 6 of your declaration, there's a section
`A.
` A. Yeah.
` Q. So generally can you explain to me what
`opinion you're providing in this section A?
` MR. ARGENTI: Objection. Form.
` A. Was there a question?
` Q. Yeah. Generally can you explain to me
`what the opinion is that you're providing under this
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`section A?
` MR. ARGENTI: Objection. Form.
` A. It's how I read claim 1 of the patent in
`light of the specifications, and my conclusion is in
`paragraph 35.
` Q. So okay. So just as I understand it,
`you're interpreting, then, a claim term in this
`section?
` A. Yes.
` Q. So let's look -- do you have the patent?
`Did I give that to you?
` A. I have it.
` Q. So that's Exhibit 1005. And you have a
`copy; is that right?
` A. Yeah, I have it.
` Q. So claim 1 is at column 7 of the patent.
` A. What page is that?
` Q. Page 11, if you're using the numbers on
`the very bottom.
` A. Okay.
` Q. And so the language that you're
`interpreting in section -- that section A of your
`declaration is the language that appears in the
`portion of claim 1 that begins, "performing a first
`encoding operation."
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` A. Yeah.
` Q. So, in particular, you're interpreting
`the language "a first encoding operation being a
`linear transform operation that generates L
`transformed bits;" is that right?
` A. Yeah.
` Q. So now, if you hadn't read the
`specification, is that language that would have made
`sense to you?
` MR. ARGENTI: Objection. Form.
` A. If I didn't have the specification, I
`would have very little understanding of what it's
`telling me to do.
` Q. Is the phrase "linear transform
`operation" one that's used in this field?
` A. Well, I know what linear transformations
`are in linear algebra. I teach courses in linear
`algebra fairly frequently.
` Q. Is linear algebra related to the field
`of this patent?
` A. Linear algebra is related to most of
`coding theory.
` Q. Before I forget, have you written any
`papers yourself in this field of coding theory?
` A. Yes.
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` Q. What about in the field of turbo coding?
` A. No.
` Q. What about LDPC coding?
` A. No.
` Q. What about iterative decoding? Have you
`written in that area?
` A. I haven't written any papers in that
`area.
` Q. Do you have an understanding what
`"iterative decoding" means?
` A. I think I understand what it means.
` Q. Does that relate at all to what's
`described in this patent, "iterative decoding"?
` A. Yes.
` Q. And how so?
` A. Well, the patent describes decoding in
`terms of Tanner graphs, and Tanner graphs are an
`approach to iterative decoding.
` Q. And so the Tanner graphs, just so I make
`sure I understand what you're talking about, is
`Figure 3 an example of a Tanner graph?
` A. Figure 3 is almost a Tanner graph. The
`random permutation in the middle makes it difficult
`to see the direct connection between the circles on
`the left and the -- which correspond to the
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`information bits, and the check bits on the right.
`It makes it difficult to know the exact relation,
`because the information symbols have been scrambled
`randomly.
` Q. So if instead of the random permutation
`block there were lines connecting the nodes on the
`left --
` A. If you knew what the lines were
`directly, that would be a normal Tanner graph.
` Q. And a person of ordinary skill in the
`art would know, given a Tanner graph, how to decode
`the code?
` A. I would expect that, yes.
` Q. So do you know what the Galois field is?
` A. I think I have known what a Galois field
`is longer than almost any engineer.
` Q. Good. Can you just explain it to me
`what it means?
` A. Well, a Galois field is a field with a
`finite number of elements.
` Q. So if we restrict it to just the Galois
`field with two elements, then what is that
`describing?
` A. The Galois field of two elements is
`usually represented by the symbol 0 and 1, with
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`rules for addition and rules for multiplication.
`And it's really the rules for even and odd so that
`odd plus odd is even. So in the Galois field of two
`elements, 1 plus 1 is 0. All the other addition and
`multiplication operations are obvious.
` Q. So is this patent, the '781 patent,
`describing operations that occur in the Galois field
`of two elements?
` A. Most of coding theory describes
`operations in vector spaces over Galois fields, and
`most typically over the two-element Galois field.
` Q. And this patent is describing the
`two-element Galois field; correct?
` A. Yes.
` Q. So now you said you know what linear
`transformation is in linear algebra.
` A. Yes.
` Q. Is linear transformation in the Galois
`field with two elements something that makes sense?
` MR. ARGENTI: Objection. Scope.
` A. The linear --
` MR. ARGENTI: And form.
` A. -- transformation makes sense in vector
`spaces over Galois fields.
` Q. And so in such a case would a linear
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`transformation, then, -- could a linear
`transformation be used to map k binary variables to
`n binary variables?
` MR. ARGENTI: Objection. Scope.
` A. In general, yes.
` Q. And you could describe that
`transformation in matrix form?
` A. Yes.
` Q. Now, in general, if you were to talk
`about the linear transformation such as the one I
`just described to you, does that require irregular
`repetition of the k input bits?
` A. In the Abstract, you know, if you ask,
`in general, does a linear transformation require
`anything else, the answer would be no. But in the
`context of claim 1, it talks about performing a
`first encoding operation that involves a linear
`transformation. And to understand the first
`encoding operation, you have to look at the
`specifications. And that was the basis in which I
`reached my conclusion in paragraph 35.
` Q. All right. Well, tell me about that,
`then. What is the first encoding operation --
` A. Hmm?
` Q. What is that first encoding operation in
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`the specification that led you to reach that
`conclusion?
` A. Well, I have many paragraphs in which I
`discuss that starting in paragraph 21. The
`specification consistently refers to the invention
`comprising two main aspects, an outer code and an
`inner coder. The Abstract starts by stating serial
`concatenated coder includes an outer code and inner
`code. Later on, in both the Abstract and the
`Summary of the Invention, state that the repeated
`and scrambled bits generated by the outer code are
`then input into the inner code.
` The next paragraph I explain, "With
`respect to the outer coder, the Abstract explains
`that irregular repetition is one of two key
`functions it performs, along with bit scrambling
`'the outer coder irregularly repeats bits in the
`data block according to a degree profile and
`scrambles the repeated bits.'"
` So the specifications repeatedly describe
`irregular repetition as an essential feature of the
`patent, and you can't read any of the claims without
`understanding that that's essential to the nature of
`the patent.
` Q. So what is different about that than any
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`linear transformation encoder?
` MR. ARGENTI: Objection. Form.
` A. Well, the specifications describe more
`than just the linear transformation. They describe
`irregular repetition of bits.
` Q. So while we're on this subject of
`irregular repetition of bits, what would that
`actually mean? How would I know if there was
`irregular repetition of bits in my coder?
` A. In contrast to the Divsalar paper, where
`it's disclosed that you can repeat bits the same
`number of times, the patent explicitly describes
`repeating different sets of bits different numbers
`of times.
` (Exhibit 1200 marked for
` identification.)
` Q. You don't know what exhibit we were up
`to by any chance, do you? I'm just going to mark
`this as 1200, which is safe.
` So on Exhibit 1200, there are shown two
`different linear transformation operations. Do you
`see that? Are they both irregular? Do they both
`include an irregular repetition of input bits in
`
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