Paper 14
`Trials@uspto.gov
`571-272-7822 Entered: August 21, 2017
`
`
`
`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.
`
`
`
`
`DECISION
`Institution of Inter Partes Review
`37 C.F.R. § 42.108
`
`
`Trials@uspto.gov
`571-272-7822 Entered: August 21, 2017
`
`
`
`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.
`
`
`
`
`DECISION
`Institution of Inter Partes Review
`37 C.F.R. § 42.108
`
`
`
`IPR2017-00728
`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. 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.”).
`An inter partes review may not be instituted “unless . . . the
`
`information presented in the petition . . . shows that there is a reasonable
`likelihood that the petitioner would prevail with respect to at least 1 of the
`claims challenged in the petition.” 35 U.S.C. § 314(a). Having considered
`the arguments and evidence presented by Petitioner and Patent Owner, we
`determine that Petitioner has demonstrated a reasonable likelihood that it
`would prevail in establishing the unpatentability of challenged claims 18–23
`of the ’032 patent.
`
`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, IPR2017-00700, and
`IPR2017-00701. Pet. 3, Paper 7.
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`Patent 7,421,032 B2
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`
`C. The ’032 Patent
`The ’032 patent is titled “Serial Concatenation of Interleaved
`
`Convolutional Codes Forming Turbo-Like Codes.” 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. Ex. 1201,
`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.
`
`3
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`IPR2017-00728
`Patent 7,421,032 B2
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`A coder 200, according to a first embodiment of the invention, is
`
`described with respect 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.
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`IPR2017-00728
`Patent 7,421,032 B2
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`
`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”) encoder 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.
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`Patent 7,421,032 B2
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`
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`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. 1201, 3:53–54.
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`Patent 7,421,032 B2
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`check nodes and random permutation to information bit nodes). Ex. 1201,
`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 the Certificate of Correction 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:
`
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`Patent 7,421,032 B2
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`
`
`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.
`
`E. Applied 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”)
`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”)
`
`Exhibit No.
`Ex. 1202
`
`Ex. 1203
`
`8
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`Patent 7,421,032 B2
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`
`Reference
`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”)
`D. 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. 1208
`
`Ex. 1217
`
`Petitioner also relies on the Declaration of Dr. James A. Davis, dated
`
`January 19, 2017 (Ex. 1204), in support of its arguments. Patent Owner
`relies upon the Declaration of Dr. R. Michael Tanner, dated May 8, 2017
`(Ex. 2001), in support of its arguments.
`
`
`
`F. Asserted Ground of Unpatentability
`Petitioner asserts the following ground of unpatentability:
`References
`Basis
`Claims
`Ping, MacKay, Divsalar, and Luby97
`§ 103(a)
`18–23
`
`II. ANALYSIS
`A. 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
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`Patent 7,421,032 B2
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`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
`In a prior decision regarding the ’032 patent, the Board construed the
`
`Tanner graph of claim 18 as follows:
`[1] a graph representing an [irregular3 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.
`IPR2015-00060, Paper 18, 12–14 (numbering and paragraphing added for
`clarity).
`
`Petitioner supports the application of the same construction here.
`Pet. 28–29. Patent Owner contends “no construction is necessary beyond
`observing that in the above Tanner graph, different subsets of message bits
`are repeated a different number of times.” Prelim. Resp. 5. Patent Owner’s
`position corresponds to only the first of the three requirements in the
`
`
`3 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);
`Prelim. Resp. 5–6 (asserting that the “irregularity” of the Tanner graph of
`claim 18 means “different subsets of message bits are repeated a different
`number of times”).
`
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`Board’s prior construction. Patent Owner’s proposed construction does not
`go far enough as it does not address the other limitations apparent from the
`Tanner Graph.
`
`We adopt our prior construction for purposes of this decision.
`
`B. The Alleged Obviousness of
`Claims 18–23 Over Ping, MacKay, Divsalar, and Luby97
`Petitioner alleges that claims 18–23 of the ’032 patent would have
`
`been obvious over Ping, MacKay, Divsalar, and Luby97. Pet. 41–73. Patent
`Owner opposes. Prelim. Resp. 6–21.
`
`Petitioner asserts that Ping discloses much of the subject matter of
`independent claim 18, but maintains that Ping’s outer coder is regular. See
`Pet. 41–42; see also id. at 58. Petitioner relies on MacKay for the teaching
`of irregularity, id. at 41, 43, 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 46, and relies on Luby97 for the teaching
`of receiving a source data stream, id. at 48. Additionally, Petitioner relies on
`Divsalar, MacKay, and Luby97 for the teaching that message passing
`decoders were well-known in the art. See Pet. 20, 51–52.
`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,
`“[a]n LDPC code is defined from a randomly generated parity check matrix
`H.” 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.
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`Patent 7,421,032 B2
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`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:
`
`
`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
`
`
`
`Ex. 1204 ¶ 74.
`Parity bits “p = {pi} can easily be calculated from a given d = {di}”
`
`using the following expressions:
`
`(cid:1856)(cid:3037) (cid:4666)mod 2(cid:4667)
`
`(cid:1868)(cid:2869)(cid:3404)(cid:3533)(cid:1860)(cid:2869)(cid:3037)(cid:3031)
`(cid:3037)
`
`(cid:1856)(cid:3037) and (cid:1868)(cid:3036)(cid:3404)(cid:1868)(cid:3036)(cid:2879)(cid:2869)(cid:3397)(cid:3533)(cid:1860)(cid:3036)(cid:3037)(cid:3031)
`(cid:3037)
`
`Ex. 1203, 38 (equation (4)).4
`
`
`4 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.
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`
`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
`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.
`
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`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 Independent Claim 18
`For reasons discussed below, Petitioner has shown a reasonable
`
`likelihood that it would prevail in establishing unpatentability of
`independent claim 18 as obvious over Ping, MacKay, Divsalar, and Luby97.
`
`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
`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)
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`(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, inter alia, on the testimony of
`Dr. Davis, Petitioner contends that such a parallel operation would have
`been obvious because message passing decoding works by passing messages
`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 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 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).
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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
`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
`” 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
`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).
`
`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.” Id. at 43. Petitioner
`maintains:
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`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.)
`Pet. 44. Petitioner notes that Ping credits a reference written by the author
`of MacKay as having creating “revived interest in the low density parity
`check (LDPC) codes originally introduced in 1962 by Gallager.” Id. at 42
`(quoting Ex. 1203, 38).
`
`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.” Id. at 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
`
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`IPR2017-00728
`Patent 7,421,032 B2
`
`message bits, [which] enforce constraints that determine the parity bits.” Id.
`at 61–63. Petitioner points to Ping’s Equation (4)
`
`
`as teaching check nodes constraining the relationship between information
`bits and parity bits. Id. at 61–63. Petitioner further maintains that Ping,
`using Divsalar’s repetition, teaches that the check nodes are randomly
`connected to repeated message bits. Id. at 63–64.
`
`We now turn to Patent Owner’s arguments. Patent Owner first argues
`that MacKay fails to disclose the irregularity of claim 18, namely
`irregularity in the number of message (information) bits repeated in a coding
`operation. See Prelim. Resp. 7–8. Specifically, Patent Owner asserts that
`Petitioner fails to identify any “instance of nonuniform weight per column
`among information bits.” Id. at 8. Petitioner’s articulated ground, however,
`is based at least on the application of MacKay’s irregularity into Ping’s
`generator Hd matrix making the outer LDPC code irregular. Pet. 43–44
`(citing, inter alia, Ex. 1204 ¶¶ 114–116); see also id. at 37 (Petitioner
`arguing “MacKay’s nonuniform weight per column ensures that some
`information bits contribute to more parity bits than others.”). Patent
`Owner’s argument that MacKay standing alone lacks the irregularity of
`claim 18 does not persuade us that Petitioner incorrectly asserts that the
`combination of references would result in that subject matter.
`
`Patent Owner also argues “the petition incorrectly addresses only a
`portion of Ping’s parity check matrix Hd, rather than the parity check matrix
`H.” Prelim. Resp. 9. Accordingly, Patent Owner argues “Ping’s parity
`check matrix H already includes nonuniform weight per column—i.e., the
`
`18
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`IPR2017-00728
`Patent 7,421,032 B2
`
`‘irregularity’ of MacKay.” Id. Based on Patent Owner’s interpretation of
`the structure of parity check matrix H as being [Hp, Hd], and Patent Owner’s
`allegation regarding Hd that “[t]he only value of t disclosed by Ping is 4”
`(Prelim. Resp. 9–10), Patent Owner contends that matrix H has column
`weights as shown in a diagram from page 11 of the Preliminary Response,
`which is reproduced below.
`
`
`Id. at 11, 14. Patent Owner concludes “Ping discloses a parity check matrix
`with different numbers of ones per column—i.e., different column weights
`[weight 2, weight 1, and weight t = 4].” Id. at 11. Thus, Patent Owner
`argues that there would be no reason to modify Ping to include “irregularity”
`when Ping “already incorporates the irregularity of MacKay.” Id. at 15.
`
`Patent Owner’s argument does not address directly Petitioner’s
`articulation of the ground. Petitioner does not utilize Ping’s entire parity
`check matrix H in its analysis; rather, Petitioner notes that the Hd matrix is
`part of Ping’s “parity check” matrix H. Pet. 45. Petitioner maintains that,
`“[b]ecause Ping’s Equation (4) uses the Hd matrix to produce parity bits
`from information bits, it is a ‘generator matrix.’” Id. (citing Ex. 1203, 38).
`Petitioner asserts that “Ping’s outer LDPC code is regular because each
`column in Ping’s generator matrix Hd 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). As such, we do not
`
`19
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`IPR2017-00728
`Patent 7,421,032 B2
`
`agree that matrix Hd from Ping, as cited by Petitioner and as forming the
`basis of the articulated ground, already includes “irregularity” in the manner
`suggested by Patent Owner. We understand Petitioner’s combination as
`relating to the specific application of MacKay’s “non-uniform column
`weight” to Ping’s matrix Hd (see Pet. 44–46), not a generic application of
`“irregularity” to Ping’s teachings as a whole. Accordingly, Patent Owner’s
`arguments do not undermine Petitioner’s stated reason to combine MacKay
`with Ping.
`
`Patent Owner additionally argues “nothing in the reference [MacKay]
`teaches such a specific modification” of only Ping’s “submatrix Hd” and that
`“MacKay says nothing about modifying a specific portion of a parity check
`matrix to provide a subset of columns with nonuniform column weights, let
`alone doing so for a portion specifically corresponding to information bits.”
`Prelim. Resp. 11; see also id. 14–15. Nevertheless, Petitioner shows
`persuasively, on this record, that MacKay “teaches how to make LDPC
`matrices ‘irregular’ by implementing a ‘nonuniform weight per column.’”
`Pet. 44 (quoting Ex. 1202, 1449). Petitioner cites a specific example in
`MacKay where a matrix “has columns of weight 9 and of weight 3.” Id. at
`43–44 (quoting Ex. 1202, 1451 and citing Ex. 1204 ¶ 115). In light of this
`evidence, we agree that an ordinarily skilled artisan would have known how
`to add nonuniform column weights from MacKay to the uniform column
`weights in Ping’s matrix Hd.
`
`Having considered Petitioner’s and Patent Owner’s arguments and
`evidence, we determine Petitioner has established sufficiently at this stage
`that Ping, MacKay, Divsalar, and Luby97 teach every limitation of claim 18.
`Petitioner also has provided, on the current record, a sufficient rationale for
`
`20
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`Patent 7,421,032 B2
`
`its proposed combination. Thus, for the foregoing reasons, Petitioner
`demonstrates a reasonable likelihood of prevailing in showing that claim 18
`would have been obvious over Ping, MacKay, Divsalar, and Luby97.
`6. The Alleged Obviousness of Dependent Claims 19–23
`Over Ping, MacKay, Divsalar, and Luby97
`The remaining claims subject to Petitioner’s ground, claims 19–23,
`
`each depend directly from independent claim 18.
`
`Patent Owner specifically addresses dependent claim 20, Prelim.
`Resp. 18–21, which recites “the message passing decoder is configured to
`decode the received data stream as if a number of inputs into nodes vi was
`not constant,” Ex. 1201, 10:46–48. Petitioner relies on MacKay for the
`teaching of this limitation, equating nonuniform row weight with the “not
`constant” aspect of the claim. Pet. 66–70. Petitioner’s analysis, including
`the reasoning to combine the references’ teachings, is similar to that
`regarding claim 18 and the application of MacKay’s teaching of
`“nonuniform column weight” in the combination of Ping, MacKay, and
`Divsalar and specifically to make Ping’s matrix Hd nonuniform. See id.
`at 68. Patent Owner again argues that Petitioner’s reference to only Ping’s
`matrix Hd, rather than H, is flawed. Prelim. Resp. 20 (“Petitioner’s attempt
`to apply MacKay’s ‘nonuniform row weights’ to Hd (see Pet. at 68-70)
`repeats the errors discussed above in Section III.A.2, and so should be
`disregarded for similar reasons.”). Patent Owner also argues that Petitioner
`fails to provide a reason to modify the references with regard to this claim
`but Patent Owner does not address adequately Petitioner’s statements on
`pages 68–69 of the Petition. Prelim. Resp. 21. We again do not find Patent
`Owner’s arguments persuasive, and determine, on the record before us, that
`
`21
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`IPR2017-00728
`Patent 7,421,032 B2
`
`Petitioner has demonstrated a reasonable likelihood of prevailing in showing
`that claim 20 would have been obvious over Ping, MacKay, Divsalar, and
`Luby97.
`
`Patent Owner does not address separately Petitioner’s explanations
`and supporting evidence regarding claims 19 and 21–23. See Prelim.
`Resp. 21. Based on the record before us, Petitioner has demonstrated a
`reasonable likelihood that it would prevail on its assertion that claims 19 and
`21–23 would have been unpatentable over Ping, MacKay, Divsalar, and
`Luby97. See Pet. 64–65, 70–73.
`
`III. CONCLUSION
`Petitioner has demonstrated that there is a reasonable likelihood of
`
`establishing the unpatentability of claims 18–23 of the ’032 patent.
`
`IV. ORDER
`For the foregoing reasons, it is
`
`ORDERED that, pursuant to 35 U.S.C. § 314, inter partes review is
`
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