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 IPR2017-00701
`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
`
`

`

`IPR2017-00701
`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. 1101). Paper 3 (“Pet.”). The Petition challenges the
`
`patentability of claims 1–10 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 claims 1 and 4–
`
`10 based on Ping, MacKay, Divsalar, and Luby97. However, the instituted
`
`review did not include Petitioner’s obviousness challenge of claims 2 and 3
`
`based on those same references.
`
`
`
`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
`
`

`

`IPR2017-00701
`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 1 and 4–10 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, IPR2017-00700, and
`
`IPR2017-00728. Pet. 3, Paper 7.
`
`3
`
`

`

`IPR2017-00701
`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. 1101, [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
`
`

`

`IPR2017-00701
`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
`
`

`

`IPR2017-00701
`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.
`
`D. Illustrative Claim
`
`
`
`Of the challenged claims of the ’032 patent, claim 1 is the only
`
`independent claim. The remaining challenged claims depend directly or
`
`indirectly from claim 1. Claim 1, reproduced below as corrected by a
`
`Certificate of Correction dated July 27, 2010, is illustrative:
`
`1. A method comprising:
`
`receiving a collection of message bits having a first
`sequence in a source data stream;
`
`generating a sequence of parity bits, wherein each parity
`bit “xj” in the sequence is in accordance with the formula
`
`6
`
`

`

`IPR2017-00701
`Patent 7,421,032 B2
`
`
`where
`“xj-1” is the value of a parity bit “j-1,” and
`
`
`
`
`is the value of a sum of “a” randomly chosen irregular[2] repeats
`of the message bits; and
`
`making the sequence of parity bits available for
`transmission in a transmission data stream.
`
`Ex. 1101, 7:63–8:20; id., Certificate of Correction (July 27, 2010) (replacing
`
`the two formulas).
`
`
`
`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”)
`
`Exhibit
`No.
`Ex. 1102
`
`
`
`2 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. 23–24 (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.”).
`
`7
`
`

`

`IPR2017-00701
`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. 1103
`
`Ex. 1108
`
`Ex. 1117
`
`
`
`Petitioner also relies on the Declaration of Dr. James A. Davis, dated
`
`January 19, 2017 (Ex. 1104), and the Declaration of Brendan Frey, Ph.D.,
`
`dated February 21, 2018 (Ex. 1165) 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. Remaining Asserted Ground of Unpatentability
`
`
`
`The following ground of unpatentability remains at issue in this case
`
`(Pet. 37; Paper 65 (granting joint motion to limit the Petition)):
`
`References
`
`Basis
`
`Claims
`
`Ping, MacKay, Divsalar, and Luby97
`
`§ 103(a)
`
`1 and 4–10
`
`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.
`
`8
`
`

`

`IPR2017-00701
`Patent 7,421,032 B2
`
`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
`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.
`
`
`
`3 Although Patent Owner puts forth evidence of objective indicia of
`non-obviousness (PO Resp. 51–62), we need not reach this evidence based
`on our disposition below.
`
`9
`
`

`

`IPR2017-00701
`Patent 7,421,032 B2
`
`Ex. 1104 ¶ 91; see Pet. 21–22 (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).
`
`
`
`We determine that no terms require explicit construction. See Vivid
`
`Techs., Inc. v. Am. Sci. & Eng’g, Inc., 200 F.3d 795, 803 (Fed. Cir. 1999)
`
`(“[O]nly those terms need be construed that are in controversy, and only to
`
`the extent necessary to resolve the controversy”).
`
`D. The Alleged Obviousness over Ping, MacKay, and Divsalar
`
`
`
`Petitioner alleges that independent claim 1 and dependent claims 4–10
`
`of the ’032 patent would have been obvious over Ping, MacKay, Divsalar,
`
`and Luby97. See Pet. 37–55 (addressing independent claim 1).
`
`
`
`Petitioner asserts that Ping discloses much of the subject matter of
`
`independent claim 1, but maintains that Ping’s outer coder is regular.
`
`10
`
`

`

`IPR2017-00701
`Patent 7,421,032 B2
`
`Pet. 39. Petitioner relies on MacKay for the teaching of irregularity, id.
`
`at 37, 39, relies on Divsalar for the teaching of repetition “if Ping alone is
`
`not understood to teach, or render obvious, repeating information bits,” id.
`
`at 42, and relies on Luby97 for the teaching of receiving a source data
`
`stream “to the extent Ping is not understood to teach encoding bits in a
`
`‘stream,’” 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. 1103)
`
`
`
`Ping is an article directed to “[a] semi-random approach to low
`
`density parity check [LDPC] code design.” Ex. 1103, 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:
`
`0
`
`1
`
`)
`
`⋱
`1
`
`1 ⋱
`
`1
`1
`
`0
`
`𝐇𝐩 = (
`
`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
`
`11
`
`

`

`]
`
`
`
`[
`
`IPR2017-00701
`Patent 7,421,032 B2
`
`
`𝐇𝐝 =
`
`𝑑
`ℎ1,1
`𝑑
`ℎ2,1
`𝑑
`ℎ3,1
`
`⋮
`
`𝑑
`ℎ1,2
`𝑑
`ℎ2,2
`𝑑
`ℎ3,2
`
`⋮
`
`𝑑
`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. 1104 ¶ 67.4 For each sub-block of Hd, there is exactly “one element 1
`
`per column and kt/(n-k) 1s per row.” Ex. 1103, 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. 1103, 38 (equation (4)).5
`
`2. MacKay (Ex. 1102)
`
`
`
`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. 1102, 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
`
`
`
`4 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.
`5 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. 1104
`¶ 180.
`
`12
`
`

`

`IPR2017-00701
`Patent 7,421,032 B2
`
`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. 1117)
`
`
`
`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. 1104 ¶ 82 (quoting Ex. 1117, 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. 1117, 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. 1108 )
`
`
`
`Luby97 describes “randomized constructions of linear-time encodable
`
`and decodable codes that can transmit over lossy channels at rates extremely
`
`close to capacity.” Ex. 1108, 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).
`
`13
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`

`IPR2017-00701
`Patent 7,421,032 B2
`
`
`5. The Alleged Obviousness of Claim 1
`
`
`
`Petitioner, in articulating its obviousness challenge of claim 1, relies
`
`on the testimony of Dr. Davis and maps the teachings of the prior art against
`
`the limitations of the claim. Pet. 45–55.
`
`
`
`Petitioner maintains that Ping, either alone or in light of Luby97,
`
`teaches a method including the step of “receiving a collection of message
`
`bits having a first sequence in a source data stream.” Id. at 45–47 (citing
`
`Ex. 1104 ¶¶ 120–125). Specifically, Petitioner cites the information bits in
`
`Ping denoted by vector d for the “receiving” step. Id. at 46. (citing
`
`Ex. 1103, 38). Petitioner contends that Ping provides equations from which
`
`parity bits p can easily be calculated from information bits d, and that one of
`
`ordinary skill in the art would recognize that “message bits” and
`
`“information bits” are synonymous. Id. at 46–47. Petitioner points to
`
`Luby97’s teaching of receiving data streams and asserts, “[e]ven if Ping is
`
`understood to teach only block encoding, and not encoding bits in [the
`
`claimed] ‘a source data stream,’ it would have been obvious to adapt Ping’s
`
`coder to work with incoming data streams.” Id. at 47; see id. at 44.
`
`Petitioner reasons that it would have been obvious to incorporate the stream
`
`teaching of Luby97 into Ping because coders that receive streams were
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`common, id. at 44, 47, and the resulting incorporation would “make the
`
`encoder [of Ping] capable of receiving and processing ‘streams’ as opposed
`
`to blocks.” Id. at 47; see id. at 44–45.
`
`
`
`Petitioner next addresses the “generating” step (Pet. 48–53), which
`
`provides:
`
`generating a sequence of parity bits, wherein each parity
`
`bit “xj” in the sequence is in accordance with the formula
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`Patent 7,421,032 B2
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`
`where
`“xj-1” is the value of a parity bit “j-1,” and
`
`
`
`
`is the value of a sum of “a” randomly chosen irregular repeats
`of the message bits.
`
`Ex. 1101, 7:66–8:17.
`
`
`
`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 24–25, 49–50. Petitioner points
`
`to Ping’s Equation (4)
`
`𝑑
`𝑝𝑖 = 𝑝𝑖−1 + ∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗
`
`as teaching the calculation of a parity bit as the sum of the prior parity bit
`
`and a summation of message bits. Id. at 49–50. Petitioner argues that Ping
`
`also teaches the “randomly chosen” aspect of the limitation, asserting:
`
`𝑑 equal “1”
`Ping randomly determines which values of ℎ𝑖𝑗
`
`𝑑
`and which values of ℎ𝑖𝑗
` equal “0.” Specifically, Ping teaches
`generating Hd by partitioning it into “t equal sub-blocks,” as
`shown in Equation (3), reproduced below:
`
`
`As Ping explains, “[i]n each sub-block Hdi, i = 1, 2 … t, we
`randomly create exactly one element 1 per column and kt/(n-k)
`1s per row” (Ex. 1103, p. 38, emphasis added.) The positions
`of the 1s in Hd are used to determine which information bits are
`𝑑
`included in each summation ∑ ℎ𝑖𝑗
`𝑑𝑗. By placing the 1s into
`𝑗
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`IPR2017-00701
`Patent 7,421,032 B2
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`
`Hd “randomly,” Ping ensures that the information bits
`𝑑
`contributing to each of the summations ∑ ℎ𝑖𝑗
`𝑑𝑗 are randomly
`𝑗
`chosen. (Ex. 1104, ¶137.)
`
`Pet. 51.
`
`
`
`Petitioner further contends that “it would have been obvious to one of
`
`ordinary skill to implement Ping by repeating every message bit [but] . . . , to
`
`the extent Ping does not itself teach, or render obvious, repeating every
`
`message bit, Divsalar does so explicitly.” Id. at 52; see id. at 42. Petitioner
`
`also argues that the use of a repeater in an outer coder was common in the
`
`art, 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 42–43.
`
`
`
`In addressing the “irregular repeats” aspect of claim 1, Petitioner
`
`contends that, “[i]n Ping’s Hd matrix, every column corresponds to an
`
`𝑑
`information bit (di) and every row corresponds to a 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 the parity bits in
`
`Ping. Id. at 30. 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 39 (quoting Ex. 1103, 38); see id.
`
`at 52–53. 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 40 (quoting Ex. 1102, 1449)
`
`(emphasis in original); see also Pet. Reply 3 (citing Ex. 1165 (Frey Decl.)
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`IPR2017-00701
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`¶¶ 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. 39. 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. 39; Pet. Reply 4. Specifically, Petitioner maintains:
`
`It would have been straightforward for one of ordinary skill to
`change Ping’s generator Hd matrix such that different columns
`had different weights – e.g., setting some columns to weight 9
`and others to weight 3, as taught by MacKay. (Ex. 1102,
`p. 1451.) This would result in some information bits
`contributing to more outer LDPC parity bits than others,
`making Ping’s outer LDPC code irregular. This would have
`been an easy way for one of ordinary skill to incorporate the
`irregularity disclosed by MacKay into Ping. Moreover,
`MacKay’s teaching that the best performing LDPC codes are
`irregular would have made this modification obvious (and
`desirable). (Ex. 1102, pp. 1449, 1454, “The excellent
`performance of irregular Gallager codes is the motivation for
`this paper….”) (Ex. 1104, ¶108.)
`
`Pet. 40. 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 10. 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
`
`summarizes its position on this aspect of the claim by asserting that, given
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`IPR2017-00701
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`the teachings of MacKay, “it would have been obvious to one of ordinary
`
`skill to incorporate the non-uniform column weight of MacKay into the
`
`LDPC-accumulate codes of Ping [and] [t]his would result in some
`
`information bits being repeated more than others, satisfying the ‘irregular
`
`repeats’ requirement of claim 1.” Pet. 53 (citing Ex. 1104 ¶ 142).
`
`
`
`The last step of claim 1 recites “making the sequence of parity bits
`
`available for transmission in a transmission data stream.” Ex. 1101, 8:19–
`
`20. Petitioner asserts that Ping, in discussing the performance of the codes,
`
`teaches the transmission of parity bits. Pet. 54. Petitioner again points to
`
`Luby97’s teaching of data streams and argues that one of ordinary skill
`
`would have understood that bits commonly are transmitted in streams and
`
`that “[i]t would also have been obvious to one of ordinary skill that an
`
`encoder receiving bits in a stream would have output bits in a stream, and
`
`that the corresponding decoder would have received encoded bits in a
`
`stream.” Id. (citing Ex. 1108, 150; Ex. 1104, ¶ 146).
`
`
`
`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 eight arguments regarding Petitioner’s Ground), 24. Patent
`
`Owner argues that Ping’s parity check matrix H is already irregular as
`
`defined by MacKay. See id. at 24–29. 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 25 (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
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`have been motivated by MacKay’s teachings that irregular codes are an
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`improvement over regular codes.” PO Resp. 26–27 (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 27–28; 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. 29. 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 27. 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. at 28
`
`(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. 42–47.
`
`Patent Owner argues “the petition does not even attempt to analyze a
`
`reasonable expectation of success, and for that reason, it is incurably
`
`deficient.” Id. at 42. As further evidence of the lack of anticipated success,
`
`Patent Owner emphasizes that constructing error-correction codes “was a
`
`highly unpredictable endeavor” that was subject to “extensive trial-and-error
`
`and experimentation to determine whether new codes led to an
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`improvement.” Id. at 4 (citing Ex. 2004 ¶ 46); see also id. at 42–43 (citing
`
`Ex. 2004 ¶¶ 126–128; Ex. 2033, 256:21–257:12).
`
`
`
`We are persuaded by Patent Owner’s arguments. We agree with
`
`Patent Owner (see PO Resp. 27–28 & n.7) that, although Petitioner may
`
`explain how to modify Ping’s Hd sub-matrix in light of MacKay, it does not
`
`address why such an ordinarily skilled artisan would have done this. Nor
`
`does Petitioner establish that such an artisan reasonably would have
`
`expected success from the modification. Based on the entire trial record, we
`
`determine that Petitioner has not established a persuasive rationale for
`
`modifying Ping in light of MacKay as asserted by Petitioner. Petitioner’s
`
`additional reliance on Divsalar and Luby97 does not remedy this
`
`fundamental flaw in the articulated combination. See Pet. 42, 44–45 (relying
`
`on Divsalar for the teaching of repeating information bits and Luby97 for the
`
`teaching of encoding bits in a stream if Ping is not understood to teach these
`
`aspects).
`
`
`
`Petitioner’s unpatentability contentions presuppose that an ordinarily
`
`skilled artisan would seek to modify a sub-matrix in Ping in light of
`
`MacKay. See Pet. Reply 10 (“Caltech’s comparison of Ping’s H matrix to
`
`MacKay’s is improper. . . . The proper comparison is between Ping’s Hd
`
`matrix . . . and MacKay’s matrix.”). Yet even if MacKay touts
`
`improvements from irregularity in a parity check matrix (e.g., Ping’s matrix
`