Paper: 63
`Trials@uspto.gov
`571-272-7822 Mailed August 20, 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 IPR2017-00728
`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
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`INTRODUCTION
`I.
`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. 1201). Paper 5 (“Pet.”). The Petition challenges the
`patentability of claims 18–23 of the ’032 patent on the ground 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 all the challenged claims based on Ping, MacKay, Divsalar, and Luby97.
`
`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 62 (“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).
`
`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,
`
`2
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`we determine that Petitioner has not shown by a preponderance of the
`evidence that claims 18–23 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, IPR2015-
`00067, IPR2015-00068, IPR2015-00081, IPR2017-00210, IPR2017-00211,
`IPR2017-00219, IPR2017-00297, IPR2017-00423, IPR2017-00700, and
`IPR2017-00701. Pet. 3, Paper 7.
`
`C. The ’032 Patent
`The ’032 patent is titled “Serial Concatenation of Interleaved
`
`Convolutional Codes Forming Turbo-Like Codes.” Ex. 1201, [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:
`
`3
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`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.
`
`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
`
`4
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`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
`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
`
`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
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`“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.
`
`
`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
`
`6
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`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
`check nodes and random permutation to information bit nodes). Id. at 3:34–
`55; see also Ex. 1204 ¶ 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 18 is the only
`
`independent claim. The remaining challenged claims depend directly from
`claim 18. Claim 18, reproduced below as originally issued and before
`issuance of a Certificate of Correction dated February 17, 2009, and with
`paragraphing added, is illustrative:
`18. A device comprising:
`
`a message passing decoder configured to decode a
`received data stream that includes a collection of parity bits,
`
`the message passing decoder comprising two or more
`check/variable nodes operating in parallel to receive messages
`from neighboring check/variable nodes and send updated
`messages to the neighboring variable/check nodes,
`
`wherein the message passing decoder is configured to
`decode the received data stream that has been encoded in
`accordance with the following Tanner graph:
`
`
`2 We understand that “edges” are the straight lines that connect one node to
`another node of a Tanner graph. See Ex. 1201, 3:53–54.
`7
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`
`Ex. 1201, 9:57–10:42. 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 18 with Vr, Uk, and Xr, respectively. See id. at Certificate of
`Correction (Feb. 17, 2009).
`
`
`
`E. Evidence
`Petitioner relies on the following art references:
`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”)
`
`Exhibit
`No.
`Ex. 1202
`
`8
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`Reference
`
`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. 1203
`
`Ex. 1208
`
`Ex. 1217
`
`Petitioner also relies on the Declaration of Dr. James A. Davis, dated
`
`January 19, 2017 (Ex. 1204), and the Declaration of Brendan Frey, Ph.D.,
`dated February 21, 2018 (Ex. 1265) 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.
`
`F. The Asserted Ground of Unpatentability
`The following ground of unpatentability remains at issue in this case
`
`(Pet. 41; Inst. Dec. 9, 22 (instituting a trial on all of the challenged claims
`and on the sole ground presented in the Petition)):
`References
`Basis
`Ping, MacKay, Divsalar, and Luby97
`§ 103(a)
`
`Claim(s)
`18–23
`
`9
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`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) 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
`
`
`3 Although Patent Owner puts forth evidence of objective indicia of
`non-obviousness (PO Resp. 55–66), we need not reach this evidence based
`on our disposition below.
`
`10
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`
`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. 1204 ¶ 98; see Pet. 26 (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
`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
`
`11
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`construction in the present case. Inst. Dec. 10–11 (quoting IPR2015-00060,
`Paper 18, 12–14; citing Pet. 28–294). 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
`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. 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
`
`
`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. 29 (citing Ex. 1213).
`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. 27–28 (advocating the adoption of that construction in this case);
`IPR2017-00700, Paper 32, 14 (Patent Owner, in a related case, 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
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`how to encode bits according to the Tanner graph in the claims and in view
`of the specification.” PO Resp. 15; 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.
`
`D. The Alleged Obviousness over Ping, MacKay, Divsalar, and Luby97
`Petitioner alleges that independent claim 18 and dependent claims 19–
`
`23 of the ’032 patent would have been obvious over Ping, MacKay,
`Divsalar, and Luby97. See Pet. 41–64 (addressing independent claim 18).
`
`Petitioner asserts that Ping discloses much of the subject matter of
`independent claim 18, but maintains that Ping’s outer coder is regular.
`Pet. 41–42; see also id. at 58. Petitioner relies on MacKay for teaching
`irregularity, id. at 41, 43, relies on Divsalar for teaching repetition “if Ping
`standing alone is not understood to teach, or render obvious, repeating
`information bits,” id. at 46, and relies on Luby97 for teaching receiving a
`source data stream, id. at 48. Additionally, Petitioner relies on Divsalar,
`MacKay, and Luby97 for teaching that message passing decoders were
`
`13
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`well-known in the art. See Pet. 20, 51–52. 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. 1203)
`Ping is an article directed to “[a] semi-random approach to low
`
`density parity check [LDPC] code design.” Ex. 1203, 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:
`
`1⋱
`
`0
`1�
`ℎ1,𝑘𝑘𝑑𝑑
`…
`ℎ2,𝑘𝑘𝑑𝑑
`…
`ℎ3,𝑘𝑘𝑑𝑑
`…
`⋮
`⋮
`… ℎ𝑛𝑛−𝑘𝑘,𝑘𝑘
`𝑑𝑑
`
`⋱
`1
`ℎ1,3𝑑𝑑
`ℎ2,3𝑑𝑑
`ℎ3,3𝑑𝑑
`⋮
`ℎ𝑛𝑛−𝑘𝑘,3
`𝑑𝑑
`
`
`
`⎦⎥⎥⎥⎥⎥⎤
`
`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
`
`𝐇𝐇𝐩𝐩=�1
`1
`0
`ℎ1,2𝑑𝑑
`⎣⎢⎢⎢⎢⎢⎡ℎ1,1𝑑𝑑
`ℎ2,2𝑑𝑑
`ℎ3,2𝑑𝑑
`⋮
`ℎ𝑛𝑛−𝑘𝑘,2
`𝑑𝑑
`
`ℎ2,1𝑑𝑑
`ℎ3,1𝑑𝑑
`⋮
`ℎ𝑛𝑛−𝑘𝑘,1
`𝑑𝑑
`
`𝐇𝐇𝐝𝐝=
`
`14
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`Ex. 1204 ¶ 74.6 For each sub-block of Hd, there is exactly “one element 1
`per column and kt/(n-k) 1s per row.” Ex. 1203, 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:
`
`𝑝𝑝1=�ℎ1𝑗𝑗𝑑𝑑
`𝑗𝑗
`
`𝑑𝑑𝑗𝑗 and 𝑝𝑝𝑖𝑖=𝑝𝑝𝑖𝑖−1+�ℎ𝑖𝑖𝑗𝑗𝑑𝑑
`𝑗𝑗
`
`𝑑𝑑𝑗𝑗 (mod 2)
`
`Ex. 1203, 38 (equation (4)).7
`2. MacKay (Ex. 1202)
`MacKay is a paper related to Gallager codes based on irregular
`
`graphs, which are “low-density parity check codes whose performance is
`closest to the Shannon limit.” Ex. 1202, 1449. According to MacKay,
`“[t]he best known binary Gallager codes are irregular codes whose parity
`check matrices have nonuniform weight per column.” Id. A parity check
`matrix that “can be viewed as defining a bipartite graph with ‘bit’ vertices
`corresponding to the columns and ‘check’ vertices corresponding to the
`rows” where “[e]ach nonzero entry in the matrix corresponds to an edge
`connecting a bit to a check.” Id. at 1450. As an example of an irregular
`
`
`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
`defined as follows: 0⊕0=0, 0⊕1=1, 1⊕0=1, and 1⊕1=0. See Ex. 1204
`
`¶ 185.
`
`15
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`code in a parity check matrix, MacKay describes a matrix that “has columns
`of weight 9 and of weight 3 [and] all rows hav[ing] weight 7.” Id. at 1451.
`3. Divsalar (Ex. 1217)
`Divsalar teaches “repeat and accumulate” codes, described as “a
`
`simple class of rate 1/q serially concatenated codes where the outer code is a
`q-fold repetition code and the inner code is a rate 1 convolutional code with
`transfer function 1/(1 + D).” Ex. 1204 ¶ 89 (quoting Ex. 1217, 1 (Abstr.)).
`Petitioner relies on Divsalar’s Figure 3, reproduced below.
`
`
`
`Figure 3 of Divsalar describes an encoder for a (qN, N) repeat and
`accumulate code. Ex. 1217, 5. The numbers above the input-output lines
`indicate the length of the corresponding block, and those below the lines
`indicate the weight of the block. Id.
`4. Luby97 (Ex. 1208 )
`Luby97 describes “randomized constructions of linear-time encodable
`
`and decodable codes that can transmit over lossy channels at rates extremely
`close to capacity.” Ex. 1208, 150 (Abstr.). Luby97 describes receiving data
`to be encoded in a stream of data symbols, such as bits, where the “stream of
`data symbols [] is partitioned and transmitted in logical units of blocks.” Id.
`(emphasis added, footnote omitted).
`5. The Alleged Obviousness of Claims 18–23
`As discussed above in the context of claim construction, independent
`
`claim 18 contains a Tanner graph having at least three elements. Petitioner,
`in articulating its obviousness challenge of claim 18, relies on the testimony
`
`16
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`of Dr. Davis and maps the teachings of the prior art against those three
`elements as well as the express recitations of the claim. Pet. 50–64.
`
`Claim 18 recites “a message passing decoder configured to decode a
`received data stream that includes a collection of parity bits.” Petitioner
`maintains that Divsalar teaches an encoding device and teaches message
`passing decoding. Id. at 51. Petitioner maintains that MacKay and Luby97
`also teach forms of message passing decoding. Id. at 51–52. Petitioner
`reasons that, in light of these teachings and “the fact that one of ordinary
`skill would understand message passing algorithms to be a standard
`technique for decoding linear error-correcting codes,” it would have been
`obvious to use a message passing decoder to decode the codes of Ping. Id.
`at 52 (citing Ex. 1204 ¶ 194); see also id. at 20 (citing Ex. 1204 ¶ 62)
`(Petitioner asserting that a message passing decoder was a well-known type
`of decoder). Petitioner points to Luby97’s teaching of receiving, in streams,
`data to be encoded and asserts that the sequence of blocks of symbols
`transmitted by the encoder of Luby97 constitutes a stream. Id. at 48–49.
`Petitioner asserts that it would have been obvious to use, for Ping’s codes, a
`decoder that can receive encoded bits in a stream where the encoder that
`encoded those bits outputs them in a stream. Id. at 49–50, 52–53; see
`Ex. 1204 ¶¶ 195–200.
`
`Claim 18 next recites “the message passing decoder comprising two
`or more check/variable nodes operating in parallel to receive messages from
`neighboring check/variable nodes and send updated messages to the
`neighboring variable/check nodes.” Relying on, inter alia, the testimony of
`Dr. Davis, Petitioner contends that such a parallel operation would have
`been obvious because message passing decoding works by passing messages
`
`17
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`back and forth between variable nodes and check nodes according to a
`Tanner graph. Pet. 23–24, 53–54; Ex. 1204 ¶¶ 68, 201–203.
`
`As for the Tanner graph of claim 18, Petitioner addresses the three
`elements of our construction 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 information bits and other parity bits as
`shown by the configuration of nodes and edges of the Tanner graph,”
`Petitioner asserts that Ping teaches a two-stage, low-density parity-check
`(LDPC)-accumulate code where the value of one parity bit is used in the
`calculation of the next parity bit. Pet. at 30, 55–57; see also id. at 58
`(maintaining that Ping’s inner coder is an accumulator).
`
`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
`parity checks where every message bit is repeated, at least two different
`subsets of message bits are repeated a different number of times.” Pet. 57–
`61. 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
`Tanner graph. Id. at 59–61.
`Petitioner contends that, “[i]n Ping’s Hd matrix, every column
`
`corresponds to an information bit (di) and every row corresponds to a
`
`summation (∑ℎ𝑖𝑖𝑗𝑗𝑑𝑑𝑗𝑗
`
`𝑑𝑑𝑗𝑗)” and that one of ordinary skill in the art would have
`
`understood that the summations are computed as the first stage of computing
`the parity bits in Ping. Id. at 34, 35. According to Petitioner, “Ping’s outer
`LDPC code is regular because each column in Ping’s generator matrix Hd
`
`18
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`contains the same number of 1s – exactly ‘t’ 1s,” and notes that “Ping thus
`states that matrix ‘Hd has a column weight of t . . . .’” Id. at 43 (quoting
`Ex. 1203, 38). Petitioner cites MacKay for teaching that “[t]he best known
`binary Gallager codes are irregular codes whose parity check matrices have
`nonuniform weight per column.” Id. at 44 (quoting Ex. 1202, 1449)
`(emphasis in original); see also Pet. Reply 3 (citing Ex. 1265 (Frey Decl.)
`¶¶ 20–24) (“MacKay also teaches that codes with such parity check
`matrices, i.e., matrices with uneven column weights, can outperform their
`regular counterparts.”).
`
`Petitioner reasons that, “[b]ecause MacKay teaches that irregular
`codes perform better than regular codes, one of ordinary skill would have
`been motivated to incorporate irregularity into Ping.” Pet. 43. Petitioner
`proposes modifying Ping’s Hd matrix (or outer coder), which Petitioner
`characterizes as regular, and contends that one of ordinary skill in the art
`would have made this modification to improve the performance of Ping’s
`code. Pet. 43; Pet. Reply 4. 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. 1202, 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. 1202,
`pp. 1449, 1454, “The excellent performance of irregular
`Gallager codes is the motivation for this paper….”) (Ex. 1204,
`¶116.)
`
`19
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`Pet. 44. 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,
`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
`option—to incorporate MacKay’s irregularity into Hd.” Id.
`
`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
`bits.” Pet. 46. Petitioner also argues that “[o]ne of ordinary skill would
`have been further motivated to implement Ping using the repeater of
`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 47–48.
`
`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 59 (citing Ex. 1204 ¶ 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 61–63. Petitioner points to Ping’s Equation (4)
`
`𝑝𝑝𝑖𝑖=𝑝𝑝𝑖𝑖−1+�ℎ𝑖𝑖𝑗𝑗𝑑𝑑
`𝑗𝑗
`
`𝑑𝑑𝑗𝑗
`
`as teaching check nodes constraining the relationship between information
`bits and parity bits. Id. at 61–63. Petitioner further maintains that Ping,
`
`20
`
`

`

`IPR2017-00728
`Patent 7,421,032 B2
`
`using Divsalar’s repetition, teaches that the check nodes are randomly
`connected to repeated message bits. Id. at 63–64.
`
`Patent Owner disputes, inter alia, Petitioner’s rationale for combining
`Ping and MacKay—which underlies the overall combination of Ping,
`MacKay, Divsalar, and Luby97—on a number of bases. See PO Resp. 15–
`16 (summarizing ten arguments regarding Petitioner’s ground), 27–28.
`Patent Owner argues that Ping’s parity check matrix H is already irregular as
`defined by MacKay. See id. at 28–33. According to Patent Owner, “Ping’s
`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 29 (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
`improvement over regular codes.” PO Resp. 30–31 (citing Ex. 2004 ¶¶ 94,
`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
`Hd. See id. at 31–32; 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. 33. According to Paten