`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`189
`
`A.
`
`I don't know what this program actually
`
`does.
`
`Just because it says: Repeat-accumulate code
`
`simulator,
`
`that doesn't mean it actually is a
`
`repeat-accumulate simulator or has anything to do.
`
`I don't know who,
`
`in fact,
`
`the author is.
`
`I have no
`
`firsthand knowledge.
`
`I have absolutely no idea what
`
`this program does.
`
`Q.
`
`Fair enough.
`
`I'm actually asking you to
`
`set aside the particulars of this program and focus
`
`back on Divsalar Figure 3.
`
`A.
`
`in
`
`Okay.
`
`And what I'd like you to assume is that
`
`you've got
`
`the RA code encoder of Figure 3, okay?
`
`the encoder
`
`A.
`
`Q.
`
`Yes.
`
`And you receive an information block of
`
`length N into the repeater, okay?
`
`A.
`
`Q.
`
`Let's assume.
`
`And inside the repeater the block is
`
`divided into three subblocks: Block Nl, block N2,
`
`block NK, okay?
`
`A.
`
`QO.
`
`Okay.
`
`And each own of these subblocks is
`
`repeated a different number of times, okay?
`
`A.
`
`QO.
`
`Okay.
`
`If those -- under those facts,
`
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`Apple vs. Caltech
`IPR2017-00701
`Apple 1140
`
`Apple vs. Caltech
`IPR2017-00701
`Apple 1140
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`would be an IRA encoder, right?
`
`A.
`
`I have formed no opinion with respect to
`
`how IRA codes are defined in the actual patents.
`
`But, let's say, as a casual observer taking some
`
`very vaguely specified form of what
`
`IRA codes might
`
`be,
`
`that could be perhaps an interpretation.
`
`Q:
`
`Okay.
`
`That would be an IRA code as you've
`
`used it in your report, right?
`
`A.
`
`This would require a lot of assumptions in
`
`mappings between the two pictures.
`
`So I'm not
`
`claiming that this cannot be done. But this would
`
`require a very specific set of assumptions on how
`
`these numbers or how these pictures relate to.
`
`Os
`
`Now, back in '99 and 2000, what group were
`
`you in of the classic code theorists versus the
`
`was hired into Bell Labs into what was called the
`
`computer science physicists?
`
`A.
`
`In my Ph.D., most of my work related to
`
`questions of information theory.
`
`Information theory
`
`is kind of the abstract level of coding.
`
`So
`
`information theory sets limits of what can be done
`
`or not.
`
`And coding can be viewed as the kind of
`
`more applied practical way of how to actually
`
`accomplish these limits.
`
`My background is in EE.
`
`I
`
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`02252225
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`O2:52:329
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`02:52:32
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`OZ2s52%:35
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`02:52:41
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`02:52:44
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`02:52:47
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`02152749
`
`Q27S2051
`
`02:52555
`
`02952255
`
`02:53:02
`
`02753206
`
`02+53212
`
`02:53:44
`
`02753751
`
`02253753
`
`02754:01
`
`O2:354:05
`
`02:54:08
`
`O2¢54¢11
`
`02254212
`
`02354215
`
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`
`02:54:24
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`
`
`mathematics of communications group.
`
`So this was a mix, people of somewhat a
`
`mix of backgrounds, most of them would have an EE
`
`background. But,
`
`for example,
`
`some people might
`
`have had a math -- math background as,
`
`for example,
`
`in the case of Dr. Shokrollahi, who got hired at
`
`some point and --
`
`THE REPORTER: Wait. State that last part
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`Divsalar in?
`
`THE WITNESS:
`
`Some people might have had a
`
`math background, as was the case,
`
`I believe,
`
`for
`
`Dr. Shokrollahi, who,
`
`I think,
`
`I believe, got his
`
`degree in mathematics or perhaps computer science,
`
`but
`
`I think it was mathematics.
`
`BY MR. DOWD:
`
`Gs
`
`So the Luby group was -- was in the
`
`computer science and physicists group?
`
`A.
`
`No.
`
`The Luby group was squarely in the
`
`theoretical computer science and math group. There
`
`were various physics groups. David MacKay might be
`
`considered,
`
`to some degree, part of the physics
`
`group. But there were also other people working in
`
`physics being interested in these topics.
`
`Q.
`
`And what was -- what group would you place
`
`PLANET DEPOS
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`
`
`
`LS2
`
`A.
`
`I would say he was working at JPL,
`
`if I'm
`
`not mistaken,
`
`so he would be probably considered
`
`towards the standard classical coding group with EE
`
`backgrounds.
`
`THE REPORTER:
`
`If we -- I'm sorry.
`
`THE WITNESS: With EE backgrounds.
`
`Electric engineering.
`
`BY MR. DOWD:
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`had strong connections to this group in -- at
`
`Q.
`
`Okay.
`
`So you were in the classical coding
`
`EE background group, right?
`
`A.
`
`My group was mixed.
`
`I myself, have that
`
`background. But
`
`in -- within Bell Labs,
`
`that group
`
`was mixed.
`
`Os
`
`And Divsalar would have been in the same
`
`group as you the way that you've divided the world?
`
`A.
`
`He has this -- sorry.
`
`I would assume
`
`without knowing exactly his training that he is
`
`trained more classically with EE background.
`
`Q.
`
`But Dr. MacKay would have been in a
`
`different group, according to the way you're looking
`
`at the world, right?
`
`A.
`
`Dr. MacKay played a special role because I
`
`believe he was either a student or -- or postdoc of
`
`Bob McEliece.
`
`He has a background in physics but
`
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`
`
`
`Caltech and at JPL.
`
`Q.
`
`But all of the groups, yourself,
`
`Dr. MacKay, Dr. Luby, were looking at irregular LDPC
`
`codes, right?
`
`A.
`
`I became aware of irregular LDPC codes via
`
`Dr. Shokrollahi when he got hired,
`
`I believe it was
`
`in '99 or perhaps late '98, whenever it was that he
`
`got hired. That's when I
`
`learned about
`
`the work of
`
`Luby and that group.
`
`Q.
`
`My question was, all of you were looking
`
`at irregular LDPC codes, correct?
`
`A.
`
`In a very specified sequence of timed
`
`events which had to do with how people got
`
`connected.
`
`Q.
`
`And your Richardson '99 paper,
`
`that was
`
`before Dr. Shokrollahi got hired at Bell Labs?
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`Which paper?
`
`No.
`
`So he was already there by that point?
`
`He's there or must have had visited.
`
`I
`
`don't know if he was already permanently hired or
`
`not. But we had met him. That's how we learned
`
`about these works from Luby.
`
`Q.
`
`Okay. And that paper was in March
`
`Gf 1999, right?
`
`A.
`
`PLANET DEPOS
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`
`
`
`Q.
`
`A.
`
`Your Richardson '99 paper.
`
`I -- I don't know the exact date.
`
`I have
`
`seen a preprint which dates April
`
`'99.
`
`Q.
`
`A.
`
`Okay.
`
`So April-ish 1999?
`
`Yes.
`
`I don't know if that was, you know,
`
`the exact
`
`inception date.
`
`It's a preprint that
`
`differs from the final 2001 version in some fairly
`
`substantial ways.
`
`Q.
`
`So at least as of April 1999, you knew
`
`about Luby, right?
`
`A.
`
`Yes.
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`I believe it was Exhibit 15.
`
`You knew about Divsalar, right?
`
`I would believe so, yes.
`
`And you also knew, obviously, about your
`
`own paper,
`
`the Richardson '99 paper?
`
`A.
`
`Q.
`
`Yes.
`
`Okay. And at that point,
`
`if we go back to
`
`the MacKay Ambleside '99 paper, you would have been
`
`aware of his work as well, right?
`
`A.
`
`I'm pretty sure that I was not at the
`
`Ambleside conference. And I'm not sure to what
`
`degree I was aware of that paper that you showed me
`
`in exhibit -- the Ambleside paper, whatever --
`
`whatever exhibit that was.
`
`QO.
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`
`
`03
`
`A a
`
`e.
`
`03
`
`eO0:
`
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`
`=00%
`
`03
`
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`
`22
`
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`
`500:
`
`25
`
`03
`
`700%
`
`28
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`42
`
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`
`200:
`
`44
`
`03
`
`200:
`
`47
`
`03
`
`200s
`
`50
`
`that you're then transmitting.
`
`Q.
`
`And that means that it has relatively few
`
`ls, mostly Os, right?
`
`A.
`
`QO.
`
`That is correct.
`
`It's called a generator matrix because
`
`it's used to generate check bits, right?
`
`A.
`
`OQ.
`
`It's -- yes,
`
`that is correct.
`
`And the way it works is that you multiply
`
`the information bits by the matrix to get parity
`
`check bits, right?
`
`A.
`
`That is correct.
`
`So you multiply your
`
`information bit and -- with the matrix and whatever
`
`you get out would actually represent the code word
`
`PLANET DEPOS
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`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`A.
`
`Q.
`
`15, perhaps.
`
`02
`
`259:
`
`42
`
`Let's go back to Luby '97, which I think
`
`02
`
`ES he
`
`44
`
`is Exhibit 9.
`
`02
`
`259%
`
`52
`
`a 0
`
`0
`
`Are you familiar with something called a
`
`02
`
`Se
`
`low-density generator matrix?
`
`03
`
`200s
`
`A.
`
`Ox
`
`Yes.
`
`03
`
`ees
`
`02
`
`If I refer to that as an "LDGM," will that
`
`03
`
`O00:
`
`02
`
`make sense?
`
`Yes.
`
`A.
`
`Ow
`
`03
`
`2:00
`
`07
`
`03
`
`200:
`
`08
`
`Low-density means that the matrix is
`
`03
`
`00%
`
`08
`
`sparse, right?
`
`A.
`
`Yes,
`
`that's correct.
`
`03
`
`200s
`
`12
`
`03
`
`cOGs
`
`a5
`
`00:
`
`14
`
`
`
`Yes.
`
`A.
`
`Q.
`
`So on the left column there,
`
`there's a
`
`statement
`
`in the second full paragraph,
`
`the
`
`paragraph
`
`that begins:
`
`"It's a challenge."
`
`Do you have that paragraph?
`
`Yes.
`
`In there the second sentence says:
`
`"In this paper we present codes that
`
`can be encoded and decoded in linear time
`
`while providing near optimal
`
`loss
`
`protection."
`
`Do you see that there?
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`03
`
`oU1s
`
`38
`
`03
`
`2012
`
`39
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`03
`
`202%
`
`03
`
`ses
`
`03
`
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`
`03
`
`202%
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`
`196
`
`Q.
`
`And we said earlier that that code word
`
`03
`
`200:
`
`a0
`
`would be comprised of parity check bits, right?
`
`03
`
`200%
`
`58
`
`A.
`
`You could consider that. Typically you
`
`03
`
`£01:
`
`03
`
`06
`
`14
`
`2 a
`
`L
`
`03
`
`03
`
`03
`
`ge
`
`AD
`
`would simply call it the code word.
`
`Q.
`
`Let's turn to page, using the Bates pages
`
`along the
`
`bottom, Khandekar --
`
`Okay. Which exhibit are we talking about?
`
`03
`
`Ole
`
`22
`
`Oh, Exhibit 9.
`
`Do you have that?
`
`Yes.
`
`03
`
`e013
`
`24
`
`03
`
`sls
`
`28
`
`So Bates page is 937 of the Luby '97
`
`03
`
`O13
`
`ot
`
`reference.
`
`Yes.
`
`03
`
`2012
`
`38
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`What does it mean to encode in linear
`
`03
`
`202%
`
`08
`
`03
`
`ees
`
`12
`
`What
`
`they meant
`
`in that paper was that if
`
`03
`
`202:
`
`12
`
`you take the block length of the code, which
`
`03
`
`e028
`
`15
`
`sometimes is referred to as N, and if you look at a
`
`03
`
`202%
`
`18
`
`family of such codes where N is varied and might
`
`03
`
`U2
`
`25
`
`take on different values,
`
`that the effort that is
`
`03
`
`202:
`
`30
`
`needed to do either the encoding or do the decoding
`
`03
`
`202
`
`234
`
`would be a linear function of that parameter N.
`
`03
`
`OZ
`
`40
`
`So perhaps if you had an input that was
`
`03
`
`Oz:
`
`45
`
`only 100 long, it would take you, let's say,
`
`just
`
`03
`
`202s
`
`47
`
`100 operations,
`
`to keep it simple. But if you had
`
`03
`
`SU:
`
`50
`
`03
`
`54
`
`Do you have that?
`
`an input that was a thousand long,
`
`then it would
`
`take you thousands.
`
`So it would be proportional to
`
`the length of the input.
`
`Q.
`
`And that's the same explanation of an
`
`encoding and decoding in linear time that you give
`
`in your report, right?
`
`Yes.
`
`Now,
`
`if we go over to the right column --
`
`Yes.
`
`—-— the last full paragraph in the right
`
`column that begins:
`
`"Our encoding."
`
`PLANET DEPOS
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`
`202%
`
`03
`
`“Og:
`
`57
`
`03
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`203s
`
`29
`
`
`
`paper, Luby '97?
`
`"Our encoding and decoding algorithms
`
`are almost symmetrical."
`
`Do you see that?
`
`Yes.
`
`What does it mean for the encoding and
`
`A.
`
`Q.
`
`decoding to be symmetrical?
`
`A.
`
`What
`
`they mean in this paper is that they
`
`use a similar type of operations to perform both,
`
`and that's what is meant with "almost symmetrical."
`
`Okay.
`
`In Luby the encoding is irregular,
`
`In -- you're talking about this particular
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`03
`
`203%
`
`48
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`30
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`198
`
`A.
`
`The last -- sorry.
`
`The last on the right
`
`03
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`"Our analytical tools"? Sorry.
`
`QO.
`
`The one above that,
`
`that is our
`
`encoding --
`
`THE REPORTER: Wait. Wait. Wait. One at
`
`03
`
`US
`
`36
`
`a time. Start again.
`
`THE WITNESS:
`
`The paragraph:
`
`03
`
`203:
`
`41
`
`03
`
`s033
`
`41
`
`"Our encoding and decoding algorithm."
`
`03
`
`703:
`
`42
`
`Yes,
`
`I see that paragraph.
`
`DOWD:
`
`Okay.
`
`It says:
`
`03
`
`-o3¢
`
`45
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`41
`
`Sorry, are we still on the same page?
`
`"As
`
`in many Similar applications,
`
`the
`
`graph is chosen to be sparse, which
`
`immediately implies that the encoding and
`
`decoding algorithms are fast."
`
`Do you see that?
`
`PLANET DEPOS
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`
`A.
`
`It's not quite clear to me what do you
`
`mean by that.
`
`Gs
`
`A.
`
`Q.
`
`That doesn't make sense to you?
`
`No.
`
`Okay.
`
`Now,
`
`if we continue in the right
`
`column,
`
`same paragraph, Page 937, it states:
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`QO.
`
`A.
`
`Correct.
`
`What do you mean with encoding is
`
`irregular? You mean whether the code is an
`
`irregular code?
`
`QO.
`
`Well,
`
`let me start there.
`
`03
`
`704:
`
`32
`
`03
`
`704:
`
`34
`
`03
`
`704:
`
`36
`
`03
`
`304%
`
`38
`
`03
`
`704:
`
`42
`
`In Luby '97 the code is an irregular code,
`
`03
`
`ees
`
`44
`
`correct?
`
`03
`
`204:
`
`46
`
`A.
`
`It is a very particularly hierarchically
`
`03
`
`704:
`
`46
`
`structured code in which some of the nodes have
`
`irregular degrees, yes.
`
`03
`
`204:
`
`al
`
`03
`
`2045
`
`55
`
`Q.
`
`Okay. And that means that when you're
`
`03
`
`204:
`
`57
`
`performing an encoding it's an irregular encoding,
`
`03
`
`SUD:
`
`Ol
`
`right?
`
`03
`
`205
`
`07
`
`
`
`a S
`
`d
`
`2052
`
`03
`
`oUS
`
`03
`
`-05%
`
`03
`
`706s
`
`12
`
`03
`
`206%
`
`15
`
`03
`
`706s
`
`18
`
`03
`
`065
`
`Zi
`
`03
`
`206%
`
`23
`
`03
`
`706
`
`ZS
`
`03
`
`206%
`
`28
`
`03
`
`706%
`
`aL
`
`03
`
`206%
`
`33
`
`03
`
`206s
`
`36
`
`And so in Luby '97 you use a low-density
`
`there are few ls, many 0s?
`
`That is correct.
`
`A.
`
`Os
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`going to read into the record, you have to read it
`
`clearly and slowly.
`
`THE WITNESS:
`
`"As
`
`in many similar applications,
`
`the
`
`graph is chosen to be sparse, which
`
`immediately implies that the encoding and
`
`decoding algorithms are fast."
`
`BY MR. DOWD:
`
`Q.
`
`And that reference to "Sparse," that
`
`refers to what we were talking about earlier about
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`Yes.
`
`03
`
`205:
`
`44
`
`On the right -- oh,
`
`the next sentence.
`
`03
`
`eo
`
`45
`
`"As
`
`in many similar applications."
`
`03
`
`205:
`
`48
`
`Sorry,
`
`I just -- just hold on a second.
`
`03
`
`205%
`
`a1
`
`Oh,
`
`I see: Both are extremely simple
`
`03
`
`20S
`
`56
`
`computing exactly -- okay.
`
`03
`
`euS
`
`39
`
`"As
`
`in many similar applications -- "
`
`03
`
`206:
`
`00
`
`Uh-huh.
`
`03
`
`S063
`
`02
`
`"
`
`-~- the graph is chosen to be sparse,
`
`03
`
`706:
`
`03
`
`which immediately implies that the
`
`03
`
`205%
`
`34
`
`encoding and decoding algorithms are -- "
`
`03
`
`SOS:
`
`ST
`
`THE REPORTER: Wait. Wait.
`
`If you're
`
`03
`
`S053
`
`37
`
`03
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`generator matrix as a part of this code, right?
`
`03
`
`206:
`
`44
`
`A.
`
`Part of these codes can be interpreted as
`
`03
`
`OG
`
`46
`
`a low-density generated.
`
`Okay.
`
`And part would be an LDPC.
`
`03
`
`706:
`
`48
`
`03
`
`OY
`
`50
`
`03
`
`2063
`
`50
`
`And on encoding side, it's the LDGM,
`
`03
`
`O63
`
`52
`
`correct?
`
`03
`
`206:
`
`58
`
`A.
`
`Both are,
`
`in fact, used. Both the LDGM
`
`03
`
`S063
`
`58
`
`and the LDPC.
`
`The reason they still construct codes
`
`03
`
`sOs
`
`02
`
`that have low or linear time encoding complexity is
`
`03
`
`O78
`
`05
`
`that they have so many layers in the hierarchical
`
`03
`
`20s
`
`12
`
`structure.
`
`So imagine that like a pyramid,
`
`that the
`
`03
`
`oO Ts
`
`16
`
`03
`
`20
`
`let -- let's
`
`though this is linear time encoding, it's not
`
`actually a practical way of proceeding.
`
`QO.
`
`Well,
`
`irrespective of that,
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`LDPC, which sits kind of at the very end of the
`
`pyramid at the top, has a size that is, at most,
`
`square root of the total block length.
`
`And so even though that part has a
`
`decoding complexity to which is quite erratic,
`
`the
`
`overall effect it has, since it only have size which
`
`is linear of the overall part, gives you still
`
`something that's linear in the overall block length.
`
`0.
`
`A.
`
`Okay.
`
`But let me -- but also remark that even
`
`207%
`
`03
`
`eis
`
`ps
`
`03
`
`20.7%
`
`27
`
`03
`
`20d
`
`30
`
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`
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`
`33
`
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`
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`
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`
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`
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`
`40
`
`03
`
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`
`43
`
`03
`
`207%
`
`47
`
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`
`20.7%
`
`47
`
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`
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`
`ol
`
`03
`
`Sea
`
`53
`
`03
`
`ds
`
`ad
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`return to the patents for a second.
`
`03
`
`7:08:
`
`02
`
`You've no opinion that the claims of the
`
`03
`
`208:
`
`04
`
`patents require linear or quadratic, right?
`
`03
`
`08:
`
`07
`
`03
`
`308%
`
`11.
`
`No.
`
`A.
`
`Q.
`
`You have no opinion that the claims of the
`
`03
`
`708:
`
`12
`
`patents actually require that it is a commercially
`
`03
`
`UR
`
`14
`
`03
`
`208:
`
`18
`
`03
`
`:06?
`
`19
`
`practicable code, right?
`
`No.
`
`A.
`
`QO:
`
`Okay.
`
`So if we go back to Luby '97, we
`
`03
`
`208:
`
`20
`
`can agree that Luby '97 does disclose an irregular
`
`03
`
`2-08:
`
`34
`
`LDGM;
`
`is that correct?
`
`03
`
`208s
`
`41
`
`A.
`
`It enclose -- it -- it discloses a very
`
`03
`
`SUS:
`
`42
`
`particular irregular and hierarchical LDGM/LDPC
`
`03
`
`:08:
`
`46
`
`combination.
`
`Luby, right?
`
`Q.
`
`Now,
`
`if we turn to Page 930 -- withdrawn.
`
`If we go to Page 943,
`
`the portion that
`
`begins with the heading:
`
`"8."
`
`A.
`
`OQ.
`
`943. Section 8?
`
`Yes.
`
`That first paragraph,
`
`if you could
`
`just read that to yourself for a moment and then let
`
`me know when you've read it.
`
`A.
`
`0.
`
`Yes,
`
`I read it.
`
`Okay.
`
`The matrix MB that they're
`
`describing there,
`
`that is the generator matrix in
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`03
`
`cUe:
`
`51
`
`03
`
`-08%
`
`52
`
`03
`
`2083
`
`56
`
`03
`
`[O93
`
`00
`
`03
`
`209s
`
`04
`
`03
`
`2698
`
`18
`
`03
`
`209:
`
`22
`
`03
`
`209%
`
`25
`
`03
`
`pL
`
`16
`
`03
`
`oO
`
`18
`
`03
`
`LO
`
`22
`
`03%
`
`10:
`
`27
`
`
`
`the resulting matrix MB is sparse."
`
`in the -- these are actually all the bits.
`
`So this
`
`is actually the code word itself in this case.
`
`Q.
`
`So you've got N message bits, right, and
`
`that's multiplied by the beta N times N matrix MB?
`
`Right.
`
`And then that will produce check bits,
`
`A.
`
`Q.
`
`right?
`
`Right.
`
`And those are parity check bits, right?
`
`Yes.
`
`And because it says:
`
`"We choose our graphs B to be sparse,
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`Os
`
`13
`
`03
`
`1 1s
`
`18
`
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`
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`
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`
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`
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`
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`
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`
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`
`34
`
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`
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`
`41
`
`O33
`
`Lis
`
`41
`
`0S
`
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`
`42
`
`03
`
`11%
`
`46
`
`03
`
`el 1s
`
`46
`
`03:
`
`Lk
`
`:48
`
`03%
`
`Lis
`
`a
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`203
`
`A.
`
`Right.
`
`I believe that that's one -- it's
`
`03:
`
`10:
`
`28
`
`1.0%
`
`32
`
`10:
`
`35
`
`3 0
`
`3:
`
`a matrix that corresponds to one of the stages that
`
`they have in their hierarchical description.
`
`Q.
`
`Okay.
`
`So let's just focus on this one
`
`OS's
`
`10%
`
`38
`
`The way this works is that you have a -- a
`
`O33
`
`10°
`
`43
`
`03:
`
`10:
`
`43
`
`vector of N message bits, right?
`
`Yes.
`
`A.
`
`Q.
`
`03:
`
`10:
`
`49
`
`O34
`
`10:
`
`54
`
`That's another way of saying N information
`
`03
`
`Lis
`
`54
`
`bits, Light?
`
`A.
`
`I -- I believe that all the -- I believe
`
`03:
`
`11:
`
`00
`
`03
`
`els
`
`01
`
`that these are actually all the bits that you have
`
`03:
`
`113
`
`10
`
`Lis
`
`
`
`convenient for you.
`
`an element.
`
`Each stage of the first part is an LDGM
`
`or it can be interpreted as an LDGM code.
`
`Q.
`
`Okay.
`
`Now,
`
`I was going to refer you to
`
`Paragraph 139 of your report where you talk about
`
`the cascade issue, but
`
`I think whether you need that
`
`or not.
`
`If we turn to Page 939,
`
`there was the
`
`Figure 2 there.
`
`THE WITNESS:
`
`I would just request a small
`
`bathroom break.
`
`It doesn't have to be this second,
`
`but
`
`I just need one minute. Unfortunately,
`
`I drank
`
`too much Coke.
`
`So could be any time whenever is
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`03
`
`sg
`
`AD
`
`03;
`
`12
`
`“36
`
`O03:
`
`12:
`
`39
`
`03
`
`e123
`
`41
`
`03%
`
`12
`
`44
`
`03:
`
`12%
`
`46
`
`033
`
`12
`
`252
`
`03%
`
`123
`
`53
`
`03
`
`eLuss
`
`55
`
`03
`
`12s
`
`58
`
`03
`
`SLs
`
`02
`
`03%
`
`L133
`
`05
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`204
`
`That's how we know that it's a low-density
`
`03:
`
`14%
`
`54
`
`118
`
`58
`
`59
`
`3g
`
`1 1
`
`4%
`
`3 0
`
`3:
`
`OS's
`
`generator matrix, right?
`
`A.
`
`QO.
`
`Yes.
`
`And we also know that it is an irregular
`
`low-density generator matrix because the paper's
`
`03:
`
`123
`
`03
`
`already told us that it's irregular, right?
`
`O33
`
`12?
`
`06
`
`A.
`
`Each component of that can be interpreted
`
`03:
`
`LZ:
`
`08
`
`that the overall graph, of course, has some
`
`additional structure.
`
`O34
`
`12%
`
`id
`
`OS
`
`12:
`
`14
`
`Q.
`
`Okay. But I'm just focusing on the LDGM
`
`03:
`
`12:
`
`14
`
`piece,
`
`that would be an irregular LDGM?
`
`03
`
`212:
`
`18
`
`A.
`
`Right.
`
`Each stage of the LDGM is,
`
`itself,
`
`03:
`
`12:3
`
`13
`
`Os
`
`12
`
`23
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`MR. DOWD: Why don't we just finish this
`
`205
`
`one issue --
`
`THE WITNESS: Okay.
`
`MR. DOWD:
`
`-- then we can break.
`
`THE WITNESS:
`
`Sure.
`
`DOWD:
`
`that at least part of the output
`
`03:
`
`13:
`
`07
`
`03?
`
`L133
`
`id
`
`03
`
`0 Rie
`
`Ls
`
`03:
`
`ist
`
`15
`
`03
`
`Las
`
`17
`
`03:
`
`13%
`
`22
`
`Os
`
`13s
`
`22
`
`03
`
`e133
`
`22
`
`03;
`
`13%
`
`25
`
`O03:
`
`Loe
`
`29
`
`03
`
`f13%
`
`31
`
`Ose
`
`Los
`
`36
`
`03
`
`O33
`
`42
`
`46
`
`i L
`
`ae
`
`0S
`
`135
`
`47
`
`03
`
`PLS
`
`49
`
`03
`
`13s
`
`52
`
`03:
`
`LSi
`
`54
`
`03%
`
`L133
`
`5g
`
`If we go to Page 939 in Figure 2 where it
`
`"The code levels"?
`
`939, Figure 2, yes.
`
`And that's what you're pointing to when
`
`you're saying that there's a cascade of graphs,
`
`right?
`
`A.
`
`Os
`
`Exactly.
`
`And what that means is that you've got a
`
`graph of one code whose output is the input
`
`to the
`
`next code, right?
`
`A.
`
`Q.
`
`Yes.
`
`Now,
`
`in a serial concatenated code,
`
`the
`
`output of the first code is the input
`
`to the second
`
`code, right?
`
`A.
`
`Q.
`
`Yes,
`
`that is correct.
`
`So that's also how serial concatenated
`
`codes work, right?
`
`A.
`
`A standard definition of how serial
`
`concatenated works,
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`
`
`a Tanner graph representation, right?
`
`Os
`
`So let's stick with Luby '97 and go to
`
`Page 3 -- I'm sorry, 938. And I'm looking at the
`
`Section 2,
`
`the codes.
`
`Do you see that there's a statement there,
`
`second sentence:
`
`"We begin by defining a code C(B)
`
`within message bits and beta end check
`
`bits by associating these bits with a
`
`bipartite graph B"?
`
`Yes.
`
`What they're talking about there are -- is
`
`A.
`
`Q.
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`220:
`
`03
`
`cas
`
`36
`
`03;
`
`20:
`
`41
`
`03
`
`320%
`
`48
`
`03
`
`S203
`
`49
`
`03
`
`e202
`
`a2
`
`03
`
`[208
`
`53
`
`03
`
`2Z0:
`
`58
`
`03
`
`tes
`
`02
`
`03
`
`o21%
`
`06
`
`03
`
`“21%
`
`07
`
`03:
`
`21
`
`:07
`
`03
`
`Ls
`
`09
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`206
`
`of some code might be the input of something else.
`
`03:
`
`14:
`
`00
`
`14:
`
`04
`
`14:
`
`05
`
`3 0
`
`3:
`
`OS's
`
`14:
`
`09
`
`Q.
`
`And the RA code in Divsalar that we've
`
`been focused on is a type of serial concatenated
`
`code, right?
`
`A.
`
`You can interpret them as a serial code.
`
`03:
`
`14:
`
`i
`
`MR. DOWD: Okay. Why don't we take the
`
`O33
`
`14:
`
`1 1
`
`8
`
`THE VIDEOGRAPHER: Going off the record.
`
`O34
`
`14:
`
`03:
`
`14:
`
`The time is 3:14 p.m.
`
`(Recess taken at 3:14 p.m.)
`
`THE VIDEOGRAPHER: We are back on the
`
`record.
`
`The time is 3:20 p.m.
`
`BY MR. DOWD:
`
`OS
`
`14
`
`220
`
`03:
`
`14:
`
`22
`
`03
`
`220s
`
`fe
`
`03
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`
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`
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`
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`
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`
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`
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`
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`
`They're describing exactly the picture
`
`when we submitted it to be -- to the journal, we
`
`actually do not cite it. And I believe I was at
`
`that point actually not aware of the paper.
`
`It is
`
`in the final 2001 published version.
`
`And I don't remember now who alerted me to
`
`that paper. But at least in the '99 somehow April
`
`time frame,
`
`I must have not been aware of that
`
`paper.
`
`Q.
`
`Okay. Well, setting aside what -- what
`
`you were or were not aware of,
`
`in Luby '97 they're
`
`describing a bipartite graph that has message nodes
`
`on the left and check bit nodes on the right?
`
`Right?
`
`A.
`
`PLANET DEPOS
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`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`207
`
`A.
`
`In hindsight, or in 2015, you might call
`
`03:
`
`21:
`
`12
`
`this a Tanner graph representation, yes.
`
`03
`
`e213
`
`15
`
`Q.
`
`And the graph that they're talking about
`
`03
`
`tol
`
`we
`
`is shown in Figure 1, right?
`
`03
`
`edi
`
`19
`
`A.
`
`Q.
`
`Yes, it's shown in Figure 1A,
`
`I believe.
`
`03:
`
`21s
`
`23
`
`Right.
`
`Now, Tanner graphs existed before
`
`03
`
`7215
`
`28
`
`1997, right?
`
`03
`
`ea Le
`
`al
`
`A.
`
`So Tanner's paper was published,
`
`I
`
`03?
`
`21
`
`234
`
`believe, sometimes in the '80s.
`
`But, you know,
`
`just from my own
`
`03:
`
`21
`
`238
`
`03
`
`221%
`
`41
`
`experience,
`
`in the -- in our own '99 paper in April,
`
`03
`
`2Z12
`
`45
`
`03:
`
`Z1s
`
`49
`
`
`
`208
`
`that was given in terms in -- gathered during his
`
`60s thesis.
`
`Q.
`
`And what
`
`they say is that the graph B has
`
`N left nodes and beta N right nodes corresponding to
`
`the message bits and the check bits respectively,
`
`right?
`
`A,
`
`Q.
`
`That is correct.
`
`Now,
`
`to make the code irregular, you can
`
`have two different degrees for the message nodes on
`
`the left? Right?
`
`A.
`
`To make it irregular what you have to do
`
`is to choose, let's say, either variable or check
`
`nodes and -- or both and decide that some of these
`
`nodes within the same group would have different
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`nodes that has a certain degree. And there's
`
`degrees.
`
`QO.
`
`A.
`
`And that's what Luby '97 does, right?
`
`Yes. Within the structure of these
`
`cascaded or hierarchical LDGM/LDPC codes,
`
`they
`
`introduce a notion of irregularity.
`
`QO.
`
`Now,
`
`in Luby '97,
`
`the information bit
`
`variable nodes have different degree profiles,
`
`right?
`
`A.
`
`In the -- yes,
`
`in this picture they have
`
`different degrees.
`
`So there's a certain fraction of
`
`PLANET DEPOS
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`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`209
`
`something which is called a "degree profile" that
`
`03
`
`2:24:
`
`42
`
`describes what fraction of the nodes has what
`
`degree.
`
`03
`
`e24as
`
`46
`
`03
`
`224:
`
`48
`
`QO.
`
`Okay.
`
`So there's some fraction of
`
`03
`
`324%
`
`48
`
`information bit nodes that has one degree and
`
`03
`
`224s
`
`53
`
`another fraction of information bit nodes that has a
`
`03
`
`285
`
`56
`
`different degree, right?
`
`03
`
`set
`
`00
`
`A.
`
`That is correct. There is a degree
`
`03
`
`S2o%
`
`03
`
`profile that describes what fraction of the various
`
`03
`
`225s
`
`05
`
`nodes has what degree.
`
`03
`
`25%
`
`08
`
`Os
`
`And what that means is that the first
`
`03
`
`225
`
`10
`
`fraction -- withdrawn.
`
`That what it means is that
`
`What that means is that the information
`
`bits of the first fraction will be repeated a
`
`different number of times than the information bits
`
`of the second fraction?
`
`A.
`
`What it means is that the degrees,
`
`the
`
`edges -- the number of edges that one such variable
`
`node would have is that that, call it degree, would
`
`vary --
`
`THE REPORTER:
`
`Sorry.
`
`"That that..."
`
`THE WITNESS:
`
`Let me restart it.
`
`THE REPORTER:
`
`Thank you.
`
`THE WITNESS:
`
`PLANET DEPOS
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`
`03
`
`$203
`
`24
`
`03
`
`225%
`
`25
`
`03
`
`oaexs
`
`28
`
`03;
`
`25%
`
`03
`
`220%
`
`03
`
`S209
`
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`
`T25%
`
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`
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`
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`
`e252
`
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`
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`
`03
`
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`
`03
`
`ahs
`
`03
`
`S258
`
`03
`
`raat
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`for different variables the number of edges that
`
`03
`
`225%
`
`52
`
`such a variable would have would depend on to which
`
`03
`
`S25
`
`56
`
`group this bit belongs to.
`
`So there might be some
`
`03
`
`Lao
`
`O01
`
`fraction of bits that perhaps has two edges
`
`03
`
`EZ26%
`
`05
`
`outgoing,
`
`there's some edges that perhaps has
`
`03
`
`2263
`
`10
`
`bit -- four edges going out, and there's some
`
`03
`
`2263
`
`13
`
`that perhaps has five edges going out.
`
`BY MR. DOWD:
`
`03
`
`726°
`
`15
`
`03
`
`S200
`
`Li
`
`Q.
`
`Okay. And the number of edges that are
`
`03
`
`7263
`
`going out from an information node,
`
`that determines
`
`03
`
`26:
`
`21
`
`how many times the bit of that node is repeated,
`
`03
`
`2265
`
`28
`
`03
`
`$263
`
`o1
`
`degree profile.
`
`the testimony.
`
`THE WITNESS:
`
`"Repeat" can have many, many
`
`different meanings.
`
`I don't see, you know,
`
`in this
`
`paper that the word "repeat" is being used, being
`
`used as an edge degree profile or as a variable node
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`right?
`
`A.
`
`"Repeat," unless you give me an exact
`
`definition, which I don't think is in this paper
`
`here,
`
`it simply means that in a graph the number of
`
`edges that go out
`
`from such a bit is different.
`
`That's what it means.
`
`Q.
`
`So you don't know what "repeat" means?
`
`MR. GLASS: Objection. Mischaracterizes
`
`03
`
`226%
`
`a1
`
`03
`
`c265
`
`34
`
`03
`
`726%
`
`03
`
`726%
`
`03
`
`SEOs
`
`03
`
`726
`
`03
`
`25%
`
`03
`
`EZo8
`
`03
`
`266
`
`03
`
`126%
`
`03
`
`126s
`
`03
`
`226%
`
`03
`
`rads
`
`
`
`there's some certain edges going out. And these
`
`respect to patents,
`
`Os
`
`Okay. Let's for the sake of this question
`
`assume that "repeat" means "duplicate," okay?
`
`Do
`
`you have that in mind?
`
`A.
`
`Ox
`
`A.
`
`What does "duplicate" mean?
`
`It means create a copy of.
`
`Does an irregular LDPC code repeat bits?
`
`"Copy of," meaning in exactly what way?
`
`What do you mean with making a copy?
`
`Q.
`
`A.
`
`I mean create duplicate bits.
`
`No,
`
`it simply means that there's a node
`
`and the value of this node is stored somewhere, and
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`03
`
`om as
`
`39
`
`03;
`
`27%
`
`42
`
`03
`
`220%
`
`47
`
`03
`
`Sees
`
`47
`
`03
`
`ts
`
`49
`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
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`
`08
`
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`
`120%
`
`10
`
`03
`
`226%
`
`12
`
`03
`
`r2B¢
`
`Md
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`So I would like to characterize it in
`
`exactly the same way as they do it.
`
`BY MR. DOWD:
`
`03
`
`e27:
`
`02
`
`03
`
`e203
`
`04
`
`03
`
`teat
`
`07
`
`QO.
`
`Well, yes, no, or I don't know;
`
`the degree
`
`03
`
`S22
`
`07
`
`profile of an information node in an irregular LDPC
`
`03
`
`ees
`
`Ls
`
`code corresponds to the number of repeats of the
`
`03
`
`e205
`
`24
`
`information bit that will occur?
`
`03
`
`21%
`
`24
`
`A.
`
`Unless you give me an exact definition of
`
`03
`
`So 2%
`
`25
`
`what "repeat" means,
`
`I cannot answer that question.
`
`03:
`
`27
`
`2:28
`
`Ow
`
`You're aware that the word "repeat" has
`
`03
`
`ers
`
`30
`
`03
`
`P2432
`
`ao
`
`34
`
`37
`
`a 2
`
`27%
`
`03
`
`03
`
`been construed in this case?
`
`A.
`
`I have no legal opinion to what's in
`
`I don't know.
`
`
`
`implementation.
`
`what
`
`the paper talks about.
`
`Os
`
`Okay. Let's set this paper aside for one
`
`second and just talk about --
`
`(Overlapping speakers.)
`
`THE REPORTER: Wait. Wait. One at a --
`
`hold on.
`
`I didn't -- you guys overlapped,
`
`so can I
`
`get a clean question, please.
`
`BY MR. DOWD:
`
`Let's set the paper aside for one second,
`
`My expertise and my particular question
`
`was regarding this paper and was not about any
`
`hypothetical
`
`PLANET DEPOS
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`220
`
`03
`
`c2B:
`
`59
`
`03;
`
`29
`
`:06
`
`03
`
`229%
`
`06
`
`03
`
`S293
`
`06
`
`03
`
`123s
`
`06
`
`03
`
`2298
`
`07
`
`03
`
`229%
`
`07
`
`03
`
`29%
`
`07
`
`03
`
`229%
`
`10
`
`03
`
`129%
`
`10
`
`03
`
`eo
`
`12
`
`03
`
`roo
`
`16
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
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`212
`
`edges, you know, go to the check nodes. And this
`
`03
`
`228:
`
`21
`
`number of edges that go from a particular variable
`
`03
`
`228%
`
`25
`
`node differs from variable node to variable node.
`
`That's what it means to me.
`
`03
`
`228%
`
`29
`
`03
`
`oe
`
`32
`
`Q.
`
`Okay.
`
`So I can implement an irregular
`
`03
`
`228s
`
`34
`
`S 4
`
`1
`
`03
`
`e283
`
`03
`
`226°
`
`03
`
`[28%
`
`44
`
`code in the sense that there is a different number
`
`of edges from the information node to the check
`
`node? Are you with me so far?
`
`A.
`
`I don't think that this paper talks about
`
`03:
`
`28
`
`245
`
`the implementation of how this is done.
`
`It simply
`
`03
`
`228%
`
`48
`
`talks about a mathematical concept of a bipartite
`
`03
`
`2202
`
`50
`
`graph in which nodes have different degrees. That's
`
`03
`
`$285
`
`5S
`
`03
`
`58
`
`
`
`VIDEOTAPED DEPOSITION OF RUDIGER L. URBANKE
`CONDUCTED ON WEDNESDAY, FEBRUARY25, 2015
`
`ZLS
`
`Q.
`
`I'm asking you,
`
`just set the paper aside
`
`03
`
`229%
`
`Li
`
`for one second; are you capable of doing that?
`
`03
`
`ooo
`
`21
`
`A.
`
`QO.
`
`sure,
`
`03
`
`Lao
`
`26
`
`And I'd like you to have in mind an
`
`03
`
`S28
`
`28
`
`irregular graph where the number of edges from one
`
`03
`
`229s
`
`35
`
`fraction of information nodes is different than the
`
`03
`
`y29%
`
`39
`
`number of edges from another fraction of information
`
`03
`
`sao
`
`44
`
`nodes.
`
`A.
`
`Q.
`
`Do you have that?
`
`Sure.
`
`03
`
`Sane
`
`49
`
`03:
`
`29
`
`249
`
`03
`
`229%
`
`Bt
`
`Okay.
`
`Now,
`
`that could be implemented
`
`03
`
`2202
`
`54
`
`without repeating any of the information bits,
`
`03
`
`S29
`
`56
`
`am I correct that the information
`
`back to our irregular graph.
`
`In the case where you
`
`have some fraction of information nodes with one
`
`number of edges, another fraction with a different
`
`number of edges,
`
`PLANET DEPOS
`888.433.3767 | WWW.PLANETDEPOS.COM
`
`right?
`
`A.
`
`I -- you know,
`
`this paper doesn't talk
`
`about
`
`implementation.
`
`I have not
`
`though