Paper 67
`Trials@uspto.gov
`571-272-7822 Entered: August 2, 2018
`
`
`
`
`
`UNITED STATES PATENT AND TRADEMARK OFFICE
`____________
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`____________
`
`APPLE INC.,
`Petitioner,
`
`v.
`
`CALIFORNIA INSTITUTE OF TECHNOLOGY,
`Patent Owner.
`____________
`
`Case IPR2017-00700
`Patent 7,421,032 B2
`____________
`
`
`
`Before KEN B. BARRETT, TREVOR M. JEFFERSON, and
`JOHN A. HUDALLA, Administrative Patent Judges.
`
`BARRETT, Administrative Patent Judge.
`
`
`
`
`FINAL WRITTEN DECISION
`Inter Partes Review
`35 U.S.C. § 318(a) and 37 C.F.R. § 42.73
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`I.
`
`INTRODUCTION
`
`A. Background and Summary
`
`
`
`Apple Inc. (“Petitioner”) filed a Petition requesting inter partes
`
`review of U.S. Patent No. 7,421,032 B2, issued September 2, 2008
`
`(“the ’032 patent,” Ex. 1001). Paper 5 (“Pet.”). The Petition challenges the
`
`patentability of claims 11–17 of the ’032 patent on various grounds of
`
`obviousness under 35 U.S.C. § 103. California Institute of Technology
`
`(“Patent Owner”) filed a Preliminary Response to the Petition. Paper 13
`
`(“Prelim. Resp.”). We instituted inter partes review (Paper 14, “Inst. Dec.”)
`
`of claims 11, 12, and 14–16 based on Ping, MacKay, and Divsalar, and of
`
`claim 13 based on Ping, MacKay, Divsalar, and Luby97. However, the
`
`instituted review did not include Petitioner’s obviousness challenge of
`
`claim 17 based on Ping, MacKay, Divsalar, and Pfister Slides.
`
`
`
`Patent Owner filed a Response to the Petition (Paper 32, “PO Resp.”),
`
`and Petitioner filed a Reply (Paper 45, “Pet. Reply”). Pursuant to our
`
`authorization (Paper 43), Patent Owner filed a Sur-Reply (Paper 55, “PO
`
`Sur-Reply”).
`
`
`
`An oral hearing was held on May 8, 2018, and a transcript of the
`
`hearing is included in the record. Paper 66 (“Tr.”).
`
`As authorized in our Order of February 10, 2018 (Paper 41), Patent
`
`Owner filed a motion for sanctions related to Petitioner’s cross-examination
`
`of Patent Owner’s witnesses, Dr. Mitzenmacher and Dr. Divsalar (Paper 42),
`
`and Petitioner filed an opposition (Paper 47).
`
`
`
`Additionally, Patent Owner filed a Motion to Exclude evidence
`
`(Paper 52), to which Petitioner filed an Opposition (Paper 54), and Patent
`
`Owner filed a Reply (Paper 58).
`
`2
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`
`On April 24, 2018, the Supreme Court held that a decision to institute
`
`under 35 U.S.C. § 314 may not institute on fewer than all claims challenged
`
`in the petition. SAS Inst., Inc. v. Iancu, 138 S. Ct. 1348 (U.S. Apr. 24,
`
`2018). On May 3, 2018, we issued an order modifying our institution
`
`decision to institute on all of the challenged claims and all of the grounds
`
`presented in the Petition. Paper 60. Subsequently, the parties filed a joint
`
`motion to limit the Petition to the claims and grounds that were originally
`
`instituted. Paper 64. We granted the motion. Paper 65. As a result, the
`
`remaining instituted claims and grounds are the same as they had been at the
`
`time of the Institution Decision. See id. at 3.
`
`
`
`We have jurisdiction under 35 U.S.C. § 6. This Final Written
`
`Decision is entered pursuant to 35 U.S.C. § 318(a). After consideration of
`
`the parties’ arguments and evidence, and for the reasons discussed below,
`
`we determine that Petitioner has not shown by a preponderance of the
`
`evidence that claims 11–16 of the ’032 patent are unpatentable.
`
`B. Related Proceedings
`
`
`
`One or both parties identify, as matters involving or related to the
`
`’032 patent, Cal. Inst. of Tech. v. Broadcom Ltd., No. 2:16-cv-03714 (C.D.
`
`Cal. filed May 26, 2016) and Cal. Inst. of Tech. v. Hughes Commc’ns, Inc.,
`
`2:13-cv-07245 (C.D. Cal. filed Oct. 1, 2013), and Patent Trial and Appeal
`
`Board cases IPR2015-00059, IPR2015-00060, IPR2015-00061, IPR 2015-
`
`00067, IPR2015-00068, IPR2015-00081, IPR2017-00210, IPR2017-00211,
`
`IPR2017-00219, IPR2017-00297, IPR2017-00423, IPR2017-00701, and
`
`IPR2017-00728. Pet. 3, Paper 7.
`
`3
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`C. The ’032 Patent
`
`
`
`The ’032 patent is titled “Serial Concatenation of Interleaved
`
`Convolutional Codes Forming Turbo-Like Codes.” Ex. 1001, [54]. The
`
`’032 patent explains some of the prior art with reference to its Figure 1,
`
`reproduced below.
`
`Figure 1 is a schematic diagram of a prior “turbo code” system. Id. at 2:16–
`
`17. The ’032 patent specification describes Figure 1 as follows:
`
`
`
`A block of k information bits is input directly to a first
`
`coder 102. A k bit interleaver 106 also receives the k bits and
`interleaves them prior to applying them to a second coder 104.
`The second coder produces an output that has more bits than its
`input, that is, it is a coder with rate that is less than 1. The
`coders 102, 104 are typically recursive convolutional coders.
`
`Three different items are sent over the channel 150: the
`original k bits, first encoded bits 110, and second encoded bits
`112. At the decoding end, two decoders are used: a first
`constituent decoder 160 and a second constituent decoder 162.
`Each receives both the original k bits, and one of the encoded
`portions 110, 112. Each decoder sends likelihood estimates of
`the decoded bits to the other decoders. The estimates are used
`to decode the uncoded information bits as corrupted by the
`noisy channel.
`
`Id. at 1:41–56.
`
`4
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`
`A coder 200, according to a first embodiment of the invention, is
`
`described with reference to Figure 2, reproduced below.
`
`Figure 2 of the ’032 patent is a schematic diagram of coder 200.
`
`
`
`The coder 200 may include an outer coder 202, an
`
`interleaver 204, and inner coder 206. . . . The outer coder 202
`receives the uncoded data. The data may be partitioned into
`blocks of fixed size, say k bits. The outer coder may be an (n,k)
`binary linear block coder, where n>k. The coder accepts as
`input a block u of k data bits and produces an output block v of
`n data bits. The mathematical relationship between u and v is
`v=T0u, where T0 is an n×k matrix, and the rate[1] of the coder is
`k/n.
`The rate of the coder may be irregular, that is, the value
`
`of T0 is not constant, and may differ for sub-blocks of bits in the
`data block. In an embodiment, the outer coder 202 is a repeater
`that repeats the k bits in a block a number of times q to produce
`a block with n bits, where n=qk. Since the repeater has an
`irregular output, different bits in the block may be repeated a
`different number of times. For example, a fraction of the bits in
`the block may be repeated two times, a fraction of bits may be
`repeated three times, and the remainder of bits may be repeated
`four times. These fractions define a degree sequence, or degree
`profile, of the code.
`
`The inner coder 206 may be a linear rate-1 coder, which
`means that the n-bit output block x can be written as x=TIw,
`where TI is a nonsingular n×n matrix. The inner coder 210 can
`
`
`
`1 We understand that the “rate” of an encoder refers to the ratio of the
`number of input bits to the number of resulting encoded output bits related to
`those input bits.
`
`5
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`have a rate that is close to 1, e.g., within 50%, more preferably
`10% and perhaps even more preferably within 1% of 1.
`
`Id. at 2:36–65. In an embodiment, the second (“inner”) coder 206 is an
`
`accumulator. Id. at 2:66–67. “The serial concatenation of the interleaved
`
`irregular repeat code and the accumulate code produces an irregular repeat
`
`and accumulate (IRA) code.” Id. at 3:30–32.
`
`
`
`Figure 4 of the ’032 patent is reproduced below.
`
`
`
`Figure 4 shows an alternative embodiment in which the outer encoder is a
`
`low-density generator matrix (LDGM). Id. at 3:56–59. LDGM codes have a
`
`“sparse” generator matrix. Id. at 3:59–60. The IRA code produced is a
`
`serial concatenation of the LDGM code and the accumulator code. Id.
`
`at 3:60–62. No interleaver (as in the Figure 2 embodiment) is required in the
`
`Figure 4 arrangement because the LDGM provides scrambling otherwise
`
`provided by the interleaver in the Figure 2 embodiment. Id. at 3:62–64.
`
`
`
`“The set of parity checks may be represented in a bipartite graph,
`
`called the Tanner graph, of the code.” Id. at 3:33–35. Figure 3, shown
`
`below, depicts such a Tanner graph.
`
`6
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`
`
`Figure 3 is described as a “Tanner graph for an irregular repeat and
`
`accumulate (IRA) coder.” Id. at 2:20–21. The left-most column of nodes,
`
`information nodes 302 (the open circles), are variable nodes that receive
`
`information bits. The column of nodes (the filled circles) just to the right of
`
`the “RANDOM PERMUTATION” block are check nodes v indicated by
`
`reference numeral 304. An information bit node connected to two check
`
`nodes represents a repeat of 2. An information node connected to three
`
`check nodes represents a repeat of 3. The nodes (the open circles) in the
`
`right-most column are parity bit nodes x, referenced by 306. As shown by
`
`the edges2 of the Tanner graph, each parity bit is a function of its previous
`
`parity bit and is also a function of information bits (edges connect through
`
`
`
`2 We understand that “edges” are the straight lines that connect one node to
`another node of a Tanner graph. See Ex. 1001, 3:53–54.
`
`7
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`check nodes and random permutation to information bit nodes). Id. at 3:34–
`
`55; see also Ex. 1004 ¶ 110 (discussing the relationship between parity bits
`
`in the context of the claimed Tanner graph and the ’032 patent’s
`
`specification).
`
`D. Illustrative Claim
`
`
`
`Of the challenged claims of the ’032 patent, claim 11 is the only
`
`independent claim. The remaining challenged claims depend directly or
`
`indirectly from claim 11. Claim 11, reproduced below as originally issued
`
`and before issuance of a Certificate of Correction dated February 17, 2009,
`
`is illustrative:
`
`11. A device comprising:
`
`an encoder configured to receive a collection of message
`bits and encode the message bits to generate a collection of
`parity bits in accordance with the following Tanner graph:
`
`
`
`8
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`Ex. 1001, 8:63–9:34. A Certificate of Correction for the ’032 patent
`
`replaced the labels V1, U1, and X1 from the lower portion of the Tanner
`
`graph in claim 11 with Vr, Uk, and Xr, respectively. See id. at Certificate of
`
`Correction (Feb. 17, 2009).
`
`
`
`Petitioner relies on the following art references:
`
`E. Evidence
`
`Reference
`
`D. J. C. MacKay et al., Comparison of Constructions of
`Irregular Gallager Codes, IEEE TRANSACTIONS ON
`COMMUNICATIONS, Vol. 47, No. 10, pp. 1449–54, October
`1999 (“MacKay”)
`
`L. Ping et al., Low Density Parity Check Codes with Semi-
`Random Parity Check Matrix, IEE ELECTRONICS LETTERS,
`Vol. 35, No. 1, pp. 38–39, Jan. 7, 1999 (“Ping”)
`M. Luby et al., Practical Loss-Resilient Codes, PROCEEDINGS
`OF THE TWENTY-NINTH ANNUAL ACM SYMPOSIUM ON THEORY
`OF COMPUTING, May 4–6, 1997, at 150–159 (“Luby97”)
`
`Dariush Divsalar, et al., Coding Theorems for “Turbo-Like”
`Codes, PROCEEDINGS OF THE THIRTY-SIXTH ANNUAL
`ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND
`COMPUTING, Sept. 23–25, 1998, at 201–209 (“Divsalar”)
`
`Exhibit
`No.
`Ex. 1002
`
`Ex. 1003
`
`Ex. 1008
`
`Ex. 1017
`
`
`
`Petitioner also relies on the Declaration of Dr. James A. Davis, dated
`
`January 19, 2017 (Ex. 1004), and the Declaration of Brendan Frey, Ph.D.,
`
`dated February 21, 2018 (Ex. 1065) in support of its arguments. Patent
`
`Owner relies upon the Declaration of Dr. Michael Mitzenmacher, dated
`
`November 21, 2017 (Ex. 2004), and the Declaration of Dr. Dariush Divsalar,
`
`dated November 7, 2017 (Ex. 2031), in support of its arguments in the
`
`Patent Owner Response. The parties rely on other exhibits as discussed
`
`below.
`
`9
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`F. Remaining Asserted Grounds of Unpatentability
`
`
`
`The following grounds of unpatentability remain at issue in this case
`
`(Pet. 39, 64, 71; Paper 65 (granting joint motion to limit the Petition)):
`
`References
`
`Basis
`
`Claim(s)
`
`Ping, MacKay, and Divsalar
`
`§ 103(a)
`
`11, 12, and 14–16
`
`Ping, MacKay, Divsalar, and Luby97
`
`§ 103(a)
`
`13
`
`II. ANALYSIS
`
`A. Principles of Law
`
`
`
`Petitioner bears the burden of proving unpatentability of the claims
`
`challenged in the Petition, and that burden never shifts to Patent Owner.
`
`Dynamic Drinkware, LLC v. Nat’l Graphics, Inc., 800 F.3d 1375, 1378
`
`(Fed. Cir. 2015). To prevail, Petitioner must establish the facts supporting
`
`its challenge by a preponderance of the evidence. 35 U.S.C. § 316(e);
`
`37 C.F.R. § 42.1(d).
`
`
`
`A patent claim is unpatentable under 35 U.S.C. § 103(a) if the
`
`differences between the claimed subject matter and the prior art are such that
`
`the subject matter, as a whole, would have been obvious at the time the
`
`invention was made to a person having ordinary skill in the art to which said
`
`subject matter pertains. KSR Int’l Co. v. Teleflex Inc., 550 U.S. 398, 406
`
`(2007). The question of obviousness is resolved on the basis of underlying
`
`factual determinations including: (1) the scope and content of the prior art;
`
`(2) any differences between the claimed subject matter and the prior art; (3)
`
`10
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`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`the level of skill in the art; and (4) any objective evidence of
`
`non-obviousness.3 Graham v. John Deere Co., 383 U.S. 1, 17–18 (1966).
`
`B. The Level of Ordinary Skill in the Art
`
`
`
`Petitioner’s declarant, Dr. Davis, opines that:
`
`A person of ordinary skill in the art at the time of the
`
`alleged invention of the ’032 patent would have had a Ph.D. in
`mathematics, electrical or computer engineering, or computer
`science with emphasis in signal processing, communications, or
`coding, or a master’s degree in the above area with at least three
`years of work experience in this field at the time of the alleged
`invention.
`
`Ex. 1004 ¶ 98; see Pet. 23 (citing the same). Patent Owner’s declarant,
`
`Dr. Mitzenmacher, applies the same definition offered by Dr. Davis.
`
`Ex. 2004 ¶ 66.
`
`
`
`We determine that the definition offered by Dr. Davis comports with
`
`the qualifications a person would have needed to understand and implement
`
`the teachings of the ’032 patent and the prior art of record. Accordingly, we
`
`apply Dr. Davis’s definition of the level of ordinary skill in the art.
`
`C. Claim Construction
`
`In an inter partes review, claim terms in an unexpired patent are given
`
`their broadest reasonable construction in light of the specification of the
`
`patent in which they appear. 37 C.F.R. § 42.100(b); see also Cuozzo
`
`Speed Techs. LLC v. Lee, 136 S. Ct. 2131, 2144–46 (2016). Under the
`
`broadest reasonable construction standard, claim terms are given their
`
`ordinary and customary meaning, as would be understood by one of ordinary
`
`
`
`3 Although Patent Owner puts forth evidence of objective indicia of
`non-obviousness (PO Resp. 54–66), we need not reach this evidence based
`on our disposition below.
`
`11
`
`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`skill in the art in the context of the entire patent disclosure. In re Translogic
`
`Tech., Inc., 504 F.3d 1249, 1257 (Fed. Cir. 2007).
`
`Tanner Graph
`
`
`
`For purposes of our Institution Decision, we adopted the construction
`
`for “Tanner graph” set forth in a prior Board decision concerning the
`
`’032 patent and for which Petitioner supports the application of the same
`
`construction in the present case. Inst. Dec. 9–10 (quoting IPR2015-00060,
`
`Paper 18, 12–14; citing Pet. 264). The prior construction was specifically
`
`addressing the Tanner graph of claim 18, but is equally applicable to claim
`
`11, at issue in this case, because the Tanner graph is the same in both claims.
`
`See Ex. 1004 ¶ 99 (Dr. Davis); Ex. 2001 ¶ 20 (Dr. Tanner); Tr. 49:18–21,
`
`62:10–13. That construction is as follows:
`
`[1] a graph representing an [irregular5 repeat accumulate] IRA
`code as a set of parity checks where every message bit is
`
`
`
`4 Petitioner contends that this construction is the broadest reasonable
`interpretation, yet is narrower than that adopted by the District Court in
`Caltech v. Hughes Communications Inc., No. 2:13-cv-07245 (C.D. Cal.)
`because the court’s construction did not include the constraint regarding
`parity bit determination (constraint [3]). Pet. 26 (citing Ex. 1013).
`Petitioner contends that the difference has no substantive effect on the issues
`before us. See Tr. 34:16–35:2.
`5 The Board, in the prior decision regarding the ’032 patent, adopted a
`construction where, “[i]n the context of the ’032 patent specification, . . .
`‘irregular’ refers to the notion that different message bits or groups of
`message bits contribute to different numbers of parity bits.”
`IPR2015-00060, Paper 18, 12 (Decision denying institution); see also
`Pet. 24 (advocating the adoption of that construction in this case); PO
`Resp. 14 (citing Ex. 2004 ¶ 69 and asserting: “Caltech does not believe the
`term needs to be construed, as the plain and ordinary meaning of irregular
`repetition is clear. That message bits contribute in differing numbers to
`parity bits is made clear in the claim language.”).
`
`12
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`

`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`repeated, at least two different subsets of message bits are
`repeated a different number of times, and
`
`[2] check nodes, randomly connected to the repeated message
`bits, enforce constraints that determine the parity bits[, and] . . .
`
`[3] a parity bit is determined as a function of both information
`bits and other parity bits as shown by the configuration of nodes
`and edges of the Tanner graph.
`
`Inst. Dec. 9–10.
`
`
`
`
`
`Patent Owner does not express disagreement with the construction but
`
`contends that the term “Tanner graph” need not be construed because, inter
`
`alia, a person of ordinary skill in the art “would have readily understood
`
`how to encode bits according to the Tanner graph in the claims and in view
`
`of the specification.” PO Resp. 16; see also Ex. 2004 ¶ 73 (Dr.
`
`Mitzenmacher not disagreeing with any aspect of the construction but
`
`opining that: “[T]here is no need to ‘construe’ the graph. Any person of
`
`ordinary skill could readily comprehend what the graph requires in terms of
`
`an encoder or a decoder.”).
`
`
`
`Regardless as to whether the person of ordinary skill in the art—e.g., a
`
`person with a doctorate in mathematics—would understand the claim, we
`
`find a verbal description of the graph to be helpful. Accordingly, we again
`
`adopt that prior construction for purposes of analyzing Petitioner’s
`
`challenges before us in this case.
`
`
`
`On this record and for purposes of deciding the dispositive issues
`
`before us, we determine that no other claim terms require express
`
`construction.
`
`13
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`

`IPR2017-00700
`Patent 7,421,032 B2
`
`
`D. The Alleged Obviousness over Ping, MacKay, and Divsalar
`
`
`
`Petitioner alleges that independent claim 11 and dependent claims 12,
`
`and 14–16 of the ’032 patent would have been obvious over Ping, MacKay,
`
`and Divsalar. See Pet. 39–57 (addressing independent claim 11).
`
`
`
`Petitioner asserts that Ping discloses much of the subject matter of
`
`independent claim 11, but maintains that Ping’s outer coder is regular.
`
`Pet. 41; see also id. at 51. Petitioner relies on MacKay for the teaching of
`
`irregularity, id. at 39, 41, and relies on Divsalar for the teaching of repetition
`
`“if Ping standing alone is not understood to teach, or render obvious,
`
`repeating information bits,” id. at 44. Patent Owner argues, inter alia, that
`
`the Petition presents a flawed reason to modify Ping in light of MacKay. PO
`
`Resp. 2–3.
`
`1. Ping (Ex. 1003)
`
`
`
`Ping is an article directed to “[a] semi-random approach to low
`
`density parity check [LDPC] code design.” Ex. 1003, 38. In this approach,
`
`“only part of [parity check matrix] H is generated randomly, and the
`
`remaining part is deterministic,” which “achieve[s] essentially the same
`
`performance as the standard LDPC encoding method with significantly
`
`reduced complexity.” Id. The size of matrix H is (n–k) × n where k is the
`
`information length and n is the coded length. Id. A codeword c is
`
`decomposed “as c = [p, d]t, where p and d contain the parity and
`
`information bits, respectively.” Id. Parity check matrix H can be
`
`decomposed into two parts corresponding to p and d as “H = [Hp, Hd].” Id.
`
`Hp is defined as follows:
`
`14
`
`

`

`0
`
`1
`
`)
`
`⋱
`1
`
`1 ⋱
`
`1
`1
`
`0
`
`𝐇𝐩 = (
`
`IPR2017-00700
`Patent 7,421,032 B2
`
`
`Id. Hd is created such that it “has a column weight of t and a row weight of
`
`kt/(n–k) (the weight of a vector is the number of 1s among its elements),” id.,
`
`]
`
`
`
`[
`
`such that
`
`𝐇𝐝 =
`
`𝑑
`ℎ1,1
`𝑑
`ℎ2,1
`𝑑
`ℎ3,1
`
`⋮
`
`𝑑
`ℎ1,2
`𝑑
`ℎ2,2
`𝑑
`ℎ3,2
`
`⋮
`
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`ℎ1,3
`𝑑
`ℎ2,3
`𝑑
`ℎ3,3
`
`⋮
`
`…
`
`…
`
`…
`
`⋮
`
`𝑑
`ℎ1,𝑘
`𝑑
`ℎ2,𝑘
`𝑑
`ℎ3,𝑘
`⋮
`
`𝑑
`ℎ𝑛−𝑘,1
`
`𝑑
`ℎ𝑛−𝑘,2
`
`𝑑
`ℎ𝑛−𝑘,3
`
`𝑑
`… ℎ𝑛−𝑘,𝑘
`
`
`
`Ex. 1004 ¶ 74.6 For each sub-block of Hd, there is exactly “one element 1
`
`per column and kt/(n-k) 1s per row.” Ex. 1003, 38. This construction
`
`“increase[s] the recurrence distance of each bit in the encoding chain” and
`
`“reduces the correlation during the decoding process.” Id.
`
`
`
`Parity bits “p = {pi} can easily be calculated from a given d = {di}”
`
`using the following expressions:
`
`𝑑
`𝑝1 = ∑ ℎ1𝑗
`𝑗
`
`𝑑
`𝑑𝑗 and 𝑝𝑖 = 𝑝𝑖−1 + ∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗 (mod 2)
`
`Ex. 1003, 38 (equation (4)).7
`
`
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`6 This particular representation of Hd is taken from Dr. Davis’s testimony.
`Patent Owner’s description of Hd is found at page 8 of its Response.
`7 The reference to “mod 2” refers to modulo-2 addition. Modulo-2 addition
`corresponds to the exclusive-OR (XOR or ⊕) logical operation, which is
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`Patent 7,421,032 B2
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`2. MacKay (Ex. 1002)
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`
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`MacKay is a paper related to Gallager codes based on irregular
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`graphs, which are “low-density parity check codes whose performance is
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`closest to the Shannon limit.” Ex. 1002, 1449. According to MacKay,
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`“[t]he best known binary Gallager codes are irregular codes whose parity
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`check matrices have nonuniform weight per column.” Id. A parity check
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`matrix that “can be viewed as defining a bipartite graph with ‘bit’ vertices
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`corresponding to the columns and ‘check’ vertices corresponding to the
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`rows” where “[e]ach nonzero entry in the matrix corresponds to an edge
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`connecting a bit to a check.” Id. at 1450. As an example of an irregular
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`code in a parity check matrix, MacKay describes a matrix that “has columns
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`of weight 9 and of weight 3 [and] all rows hav[ing] weight 7.” Id. at 1451.
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`3. Divsalar (Ex. 1017)
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`
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`Divsalar teaches “repeat and accumulate” codes, described as “a
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`simple class of rate 1/q serially concatenated codes where the outer code is a
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`q-fold repetition code and the inner code is a rate 1 convolutional code with
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`transfer function 1/(1 + D).” Ex. 1004 ¶ 89 (quoting Ex. 1017, 1 (Abstr.)).
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`Petitioner relies on Divsalar’s Figure 3, reproduced below.
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`Figure 3 of Divsalar describes an encoder for a (qN, N) repeat and
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`accumulate code. Ex. 1017, 5. The numbers above the input-output lines
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`
`
`
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`defined as follows: 0⊕0=0, 0⊕1=1, 1⊕0=1, and 1⊕1=0. See Ex. 1004
`¶ 185.
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`indicate the length of the corresponding block, and those below the lines
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`indicate the weight of the block. Id.
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`4. The Alleged Obviousness of Claim 11
`
`
`
`As discussed above in the context of claim construction, independent
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`claim 11 contains a Tanner graph having at least three elements. Petitioner,
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`in articulating its obviousness challenge of claim 11, relies on the testimony
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`of Dr. Davis and maps the teachings of the prior art against those three
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`elements as well as the express recitations of the claim. Pet. 46–57.
`
`
`
`Petitioner maintains that Ping teaches the recited “encoder configured
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`to receive a collection of message bits and encode the message bits to
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`generate a collection of parity bits.” Id. at 46–47 (citing Ex. 1004 ¶¶ 127–
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`128). Specifically, Petitioner contends that Ping provides equations from
`
`which parity bits p can easily be calculated from information bits d, and that
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`one of ordinary skill in the art would recognize that “message bits” and
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`“information bits” are synonymous. Id.
`
`
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`As for the Tanner graph, Petitioner addresses the three elements but in
`
`an order different than that listed above in the claim construction section.
`
`For the element “[3] a parity bit is determined as a function of both
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`information bits and other parity bits as shown by the configuration of nodes
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`and edges of the Tanner graph,” Petitioner asserts that Ping teaches a two-
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`stage, low-density parity-check (LDPC)-accumulate code where the value of
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`one parity bit is used in the calculation of the next parity bit. Id. at 27, 48–
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`50; see also id. at 51–52 (maintaining that Ping’s inner coder is an
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`accumulator).
`
`
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`The next element of the Tanner graph addressed by Petitioner is “[1] a
`
`graph representing an [irregular repeat accumulate] IRA code as a set of
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`parity checks where every message bit is repeated, at least two different
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`subsets of message bits are repeated a different number of times.” Pet. 50–
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`54. Petitioner asserts that a particular code may be represented as matrices
`
`or as a Tanner graph, with those being two ways of describing the same
`
`thing, and contends that the proposed combination would have been
`
`understood by one of ordinary skill in the art to correspond to the claimed
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`Tanner graph. Id. at 52–54.
`
`
`
`Petitioner contends that, “[i]n Ping’s Hd matrix, every column
`
`corresponds to an information bit (di) and every row corresponds to a
`
`𝑑
`summation (∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗)” and that one of ordinary skill in the art would have
`
`understood that the summations are computed as the first stage of computing
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`the parity bits in Ping. Id. at 31, 32. According to Petitioner, “Ping’s outer
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`LDPC code is regular because each column in Ping’s generator matrix Hd
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`contains the same number of 1s – exactly ‘t’ 1s,” and notes that “Ping thus
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`states that matrix ‘Hd has a column weight of t . . . .’” Id. at 41 (quoting
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`Ex. 1003, 38). Petitioner cites MacKay for teaching that “[t]he best known
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`binary Gallager codes are irregular codes whose parity check matrices have
`
`nonuniform weight per column.” Id. at 41 (quoting Ex. 1102, 1449)
`
`(emphasis in original); see also Pet. Reply 3 (citing Ex. 1065 (Frey Decl.)
`
`¶¶ 20–24) (“MacKay also teaches that codes with such parity check
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`matrices, i.e., matrices with uneven column weights, can outperform their
`
`regular counterparts.”).
`
`
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`Petitioner reasons that, “[b]ecause MacKay teaches that irregular
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`codes perform better than regular codes, one of ordinary skill would have
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`been motivated to incorporate irregularity into Ping.” Pet. at 41. Petitioner
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`proposes modifying Ping’s Hd matrix (or outer coder), which Petitioner
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`characterizes as regular, and contends that one of ordinary skill in the art
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`would have made this modification to improve the performance of Ping’s
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`code. Pet. 41; Pet. Reply 4. Specifically, Petitioner maintains:
`
`It would have been straightforward for a person of ordinary
`skill to change Ping’s generator Hd matrix such that not all
`columns had the same weight – e.g., setting some columns to
`weight 9 and others to weight 3, as taught by MacKay.
`(Ex. 1002, p. 1451.) This change would result in some
`information bits contributing to more outer LDPC parity bits
`than others, and would have made Ping’s outer LDPC code
`irregular. . . . Moreover, MacKay’s teaching that the best
`performing LDPC codes are irregular would also have made
`this modification obvious (and desirable) to try. (Ex. 1002,
`pp. 1449, 1454, “The excellent performance of irregular
`Gallager codes is the motivation for this paper….”) (Ex. 1004,
`¶116.)
`
`Pet. 42. According to Petitioner, a person of ordinary skill would not have
`
`been motivated to modify Hp because “it has only a single form and because
`
`doing so would have complicated a simple encoder.” Pet. Reply 8. Thus,
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`Petitioner contends that the person of ordinary skill “who wanted to obtain
`
`the benefit of MacKay’s irregularity in Ping would have had only one
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`option—to incorporate MacKay’s irregularity into Hd.” Id.
`
`
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`Petitioner further contends that, “even if Ping standing alone is not
`
`understood to teach, or render obvious, repeating information bits, doing so
`
`would have been obvious in view of Divsalar’s explicit teaching of repeating
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`bits.” Pet. 44. Petitioner also argues that “[o]ne of ordinary skill would
`
`have been further motivated to implement Ping using the repeater of
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`Divsalar because this implementation would be both cost-effective and easy
`
`to build,” and that the similarities between Ping and Divsalar provide
`
`additional motivation to combine the references teachings. Id. at 44–45.
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`Thus, argues Petitioner, the combination of Ping, MacKay, and
`
`Divsalar teaches an irregular repeat accumulate code where message bits are
`
`repeated and at least two different subsets of message bits are repeated a
`
`different number of times. Id. at 52 (citing Ex. 1004 ¶ 139).
`
`
`
`Lastly, Petitioner contends that Ping teaches the Tanner graph
`
`requirement of “[2] check nodes, randomly connected to the repeated
`
`message bits, [which] enforce constraints that determine the parity bits.” Id.
`
`at 54–57. Petitioner points to Ping’s Equation (4)
`
`𝑑
`𝑝𝑖 = 𝑝𝑖−1 + ∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗
`
`as teaching check nodes constraining the relationship between information
`
`bits and parity bits. Id. at 54–56. Petitioner further maintains that Ping,
`
`using Divsalar’s repetition, teaches that the check nodes are randomly
`
`connected to repeated message bits. Id. at 56–57.
`
`
`
`Patent Owner disputes, inter alia, Petitioner’s rationale for combining
`
`Ping and MacKay—which underlies the overall combination of Ping,
`
`MacKay, and Divsalar—on a number of bases. See PO Resp. 17–18
`
`(summarizing eight arguments regarding Petitioner’s Ground 1), 26. Patent
`
`Owner argues that Ping’s parity check matrix H is already irregular as
`
`defined by MacKay. See id. at 26–30. According to Patent Owner, “Ping’s
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`parity-check matrix has three different column weights (t, 2, and 1), and two
`
`different row weights (kt/(n-k)+1 and kt/(n-k)+2).” Id. at 28 (citing
`
`Ex. 2033, 231:11–14); see also Ex. 2004 ¶ 92 (same). As such, Patent
`
`Owner argues “Ping’s parity-check matrix is actually even more ‘irregular’
`
`than MacKay’s irregular codes,” so ordinarily skilled artisans “would not
`
`have been motivated by MacKay’s teachings that irregular codes are an
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`improvement over regular codes.” PO Resp. 28–29 (citing Ex. 2004 ¶¶ 94,
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`95, and 97–99).
`
`
`
`Patent Owner also highlights that Petitioner’s proposed modifications
`
`relate only to a portion of Ping’s parity check matrix H, namely, sub-matrix
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`Hd. See id. at 29–30; see also Ex. 2004 ¶ 96. Patent Owner argues
`
`“MacKay does not even consider modifying submatrices, much less teach
`
`that there may be benefits to try.” PO Resp. 31. According to Patent
`
`Owner, “MacKay teaches that irregular parity-check matrices as a whole
`
`may define better codes than regular parity-check matrices as a whole—it
`
`does not teach any improvement from making a submatrix within a parity-
`
`check matrix irregular, or from using any other type of irregular matrix (e.g.,
`
`irregular generator matrices).” Id. at 30. Patent Owner argues MacKay does
`
`not “suggest that additional irregularity should be applied to individual
`
`portions when the overall parity-check matrix is already irregular.” Id.
`
`(citing Ex. 2004 ¶¶ 96–99) (footnote omitted).
`
`
`
`Patent Owner further argues that Petitioner has not established that an
`
`ordinarily skilled artisan would have reasonably expected success from the
`
`proposed modification of Ping in light of MacKay. See PO Resp. 44–49.
`
`Patent