Trials@uspto.gov
`571.272.7822
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` Paper No. 16
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`Entered: July 5, 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 IPR2017-00423
`Patent 7,916,781 B2
`____________
`
`
`
`Before KEN B. BARRETT, TREVOR M. JEFFERSON, and
`JOHN A. HUDALLA, Administrative Patent Judges.
`
`HUDALLA, Administrative Patent Judge.
`
`
`
`DECISION
`Institution of Inter Partes Review
`35 U.S.C. § 314(a) and 37 C.F.R. § 42.108
`
`Petitioner, Apple, Inc. (“Apple”), filed a Petition (Paper 5, “Pet.”)
`
`requesting an inter partes review of claims 13–22 of U.S. Patent No.
`
`7,916,781 B2 (Ex. 1101, “the ’781 patent”) pursuant to 35 U.S.C. §§ 311–
`
`319. Apple proffered a Declaration of James A. Davis, Ph.D. (Ex. 1104)
`
`with its Petition. Patent Owner, California Institute of Technology
`
`(“Caltech”), filed a Preliminary Response (Paper 14, “Prelim. Resp.”) to the
`
`Petition.
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`Under 35 U.S.C. § 314(a), the Director may not authorize an inter
`
`partes review unless the information in the petition and preliminary response
`
`“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.” For the
`
`reasons that follow, we institute an inter partes review as to claims 13–16,
`
`18, and 22 of the ’781 patent on certain grounds of unpatentability
`
`presented.
`
`
`
`
`
`A.
`
`Related Proceedings
`
`I. BACKGROUND
`
`
`
`The parties identify the following district court cases related to the
`
`’781 patent (Pet. 1; Paper 7, 1):
`
`Cal. Inst. of Tech. v. Broadcom Ltd., No. 2:16-cv-03714 (C.D. Cal.
`
`filed May 26, 2016);1
`
`Cal. Inst. of Tech. v. Hughes Commc’ns, Inc., No. 2:15-cv-01108
`
`(C.D. Cal. filed Feb. 17, 2015); and
`
`Cal. Inst. of Tech. v. Hughes Commc’ns, Inc., 2:13-cv-07245 (C.D.
`
`Cal. filed Oct. 1, 2013).
`
`The parties also identify co-pending Case IPR2017-00297, in which
`
`Apple has filed a petition for inter partes review of claims 3–12 and 19–21
`
`of the ’781 patent. Pet. 2 n.1; Paper 7, 1. In addition, the ’781 patent was
`
`previously subject to an inter partes review in Case IPR2015-00059
`
`(“059 IPR”). Pet. 19; Ex. 1111; Paper 7, 1. In the Final Written Decision
`
`from the 059 IPR, which Apple filed as Exhibit 1111 in this proceeding, the
`
`
`1 Apple is a defendant in this case. See Pet. 1.
`
`2
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`Board determined that claims 1 and 2 of the ’781 patent are unpatentable as
`
`anticipated by the Divsalar reference, which is one of the asserted references
`
`in this case. See Ex. 1111, 43.
`
`Apple additionally states that patents in the priority chain of the
`
`’781 patent were challenged in Cases IPR2015-00068, IPR2015-00067,
`
`IPR2015-00060, IPR2015-00061, and IPR2015-00081. Pet. 1. We
`
`additionally identify the following cases between the parties:
`
`Cases IPR2017-00210, IPR2017-00211, IPR2017-00219, IPR2017-00700,
`
`IPR2017-00701, IPR2017-00702, IPR2017-00703, and IPR2017-00728.
`
`
`
`B.
`
`The ’781 patent
`
`The ’781 patent describes the serial concatenation of interleaved
`
`convolutional codes forming turbo-like codes. Ex. 1101, Title. It 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 2:20–
`
`21. The ’781 patent specification describes Figure 1 as follows:
`
`
`
`3
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 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 1:44–60.
`
`A coder 200, according to a first embodiment of the invention, is
`
`described with respect to Figure 2, reproduced below.
`
`Figure 2 of the ’781 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 [that] may be partitioned into blocks of fixed size,
`[e.g.] 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.
`
`4
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`The mathematical relationship between u and v is v=T0u, where
`T0 is an n×k matrix, and the rate[2] 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 2:40–3:2 (footnote added). Codes characterized by a regular repeat of
`
`message bits into a resulting codeword are referred to as “regular repeat,”
`
`whereas codes characterized by irregular repeat of message bits into a
`
`resulting codeword are referred to as “irregular repeat.” The second
`
`(“inner”) encoder 206 performs an “accumulate” function. Thus, the two
`
`step encoding process illustrated in Figure 2, including a first encoding
`
`(“outer encoding”) followed by a second encoding (“inner encoding”),
`
`results in either a “regular repeat accumulate” (“RRA”) code or an “irregular
`
`repeat accumulate” (“IRA”) code, depending upon whether the repetition in
`
`the first encoding is regular or irregular.
`
`
`2 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
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`Figure 4 of the ’781 patent is reproduced below.
`
`
`
`Figure 4 shows an alternative embodiment in which the first encoding is
`
`carried out by a low density generator matrix. Low density generator matrix
`
`(LDGM)3 codes are a special class of low density parity check codes that
`
`allow for less encoding and decoding complexity. LDGM codes are
`
`systematic linear codes generated by a “sparse” generator matrix. 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.
`
`Apple notes (Pet. 3) that the ’781 patent claims priority to a
`
`provisional application filed on May 18, 2000. Ex. 1101, at [60]. As
`
`discussed below, we determine for purposes of this Decision that Apple’s
`
`asserted references qualify as prior art even when assuming that May 18,
`
`2000, is the effective filing date for the challenged claims of the ’781 patent.
`
`
`
`
`3 We understand that a “generator” matrix (typically referred to by “G”) is
`used to create (generate) codewords. A parity check matrix (typically
`referred to by “H”) is used to decode a received message.
`6
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`C.
`
`Illustrative Claim
`
`Claims 13 and 19–21 of the ’781 patent are independent. Claims 14–
`
`18 depend directly or indirectly from claim 13, and claim 22 depends from
`
`claim 21. Claim 13 is illustrative of the challenged claims and recites:
`
`13. A method of encoding a signal, comprising:
`
`receiving a block of data in the signal to be encoded, the
`block of data including information bits; and
`
`performing an encoding operation using the information
`bits as an input, the encoding operation including an
`accumulation of mod-2 or exclusive-OR sums of bits in subsets
`of the information bits, the encoding operation generating at
`least a portion of a codeword,
`
`wherein the information bits appear in a variable number
`of subsets.
`
`Id. at 8:7–17.
`
`
`
`D.
`
`The Prior Art
`
`Apple relies on the following prior art:
`
`MacKay et al., “Comparison of Constructions of Irregular
`Gallager Codes,” IEEE TRANSACTIONS ON COMMUNICATIONS,
`Vol. 47, No. 10, pp. 1449–54, October 1999 (Ex. 1102,
`“MacKay”);
`
`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 (Ex. 1103, “Ping”); and
`
`Coombes et al., U.S. Patent No. 4,271,520, filed June 25,
`1979, issued June 2, 1981 (Ex. 1118, “Coombes”).
`
`
`
`E.
`
`The Asserted Grounds
`
`Apple challenges claims 13–22 of the ’781 patent on the following
`
`grounds (Pet. 31–32, 48):
`
`7
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`References
`
`Basis
`
`Claims Challenged
`
`Ping and MacKay
`
`35 U.S.C. § 103(a) 13–15 and 17–22
`
`Ping, MacKay, and
`Coombes
`
`
`
`35 U.S.C. § 103(a) 16
`
`F.
`
`Claim Interpretation
`
`In an inter partes review, we construe claims by applying the broadest
`
`reasonable interpretation in light of the specification. 37 C.F.R. § 42.100(b);
`
`see Cuozzo Speed Techs., LLC v. Lee, 136 S. Ct. 2131, 2144–46 (2016).
`
`Under the broadest reasonable interpretation standard, and absent any
`
`special definitions, 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 disclosure. See In re Translogic Tech. Inc., 504 F.3d
`
`1249, 1257 (Fed. Cir. 2007). Any special definitions for claim terms or
`
`phrases must be set forth “with reasonable clarity, deliberateness, and
`
`precision.” In re Paulsen, 30 F.3d 1475, 1480 (Fed. Cir. 1994).
`
`Based on the current record, we determine that no terms require
`
`explicit construction at this time. 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”).
`
`
`
`II. ANALYSIS
`
`We now consider Apple’s asserted grounds and Caltech’s arguments
`
`in the Preliminary Response to determine whether Apple has met the
`
`8
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`“reasonable likelihood” threshold standard for institution under 35 U.S.C.
`
`§ 314(a).
`
`
`
`A.
`
`Obviousness Ground Based on Ping and MacKay
`
`Apple contends claims 3, 5–8, 10, and 12 are would have been
`
`obvious over Ping and MacKay. Pet. 31–48. Caltech disputes Apple’s
`
`contention. Prelim. Resp. 8–26.
`
`
`
`1.
`
`Ping
`
`Ping is an article directed to “[a] semi-random approach to low
`
`density parity check [LDPC] code design.” Ex. 1103, 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],
`
`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
`1
`
`𝐇𝐩 = (
`
`⋱
`1
`1
`0
`Id. Hd is created such that it “has a column weight of t and a row weight of
`
`0
`
`)
`
`1 ⋱
`
`kt/(n–k) (the weight of a vector is the number of 1s among its elements)”
`
`such that
`
`9
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`Id.; Ex. 1104 ¶ 67.4
`
`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
`
`Apple contends Ping “was published in January 1999” and “is thus
`
`prior art to the ’781 patent under 35 U.S.C. § 102(a) and (b).” Pet. 24. Ping
`
`appears to be included in a publication from the Institution of Electrical
`
`Engineers bearing a “7th January 1999” date and a “JAN 25 1999” date
`
`stamp from “LINDA HALL LIBRARY.” Ex. 1103. Caltech does not
`
`dispute the prior art status of Ping. For purposes of this Decision, we
`
`
`4 This particular representation of Hd is taken from Dr. Davis’s testimony.
`Caltech does not dispute this representation. Cf. Prelim. Resp. 10–11 &
`n.10.
`
`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: 1⊕1=0, 1⊕0=1, 0⊕1=1, and 0⊕0=0. See Pet. 11–12 &
`n.2.
`
`10
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`determine that Ping qualifies as prior art under 35 U.S.C. § 102(b)6 because
`
`the January 7, 1999, edition date and the January 25, 1999, date stamp
`
`provide some evidence of publication more than one year before the earliest
`
`possible effective filing date for the challenged claims of the ’781 patent,
`
`which is May 18, 2000. See Ex. 1101, at [60]; Ex. 1103.
`
`
`
`2. MacKay
`
`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
`
`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.
`
`Apple contends MacKay “was published in October 1999” and
`
`therefore “qualifies as prior art under 35 U.S.C. § 102(a) and (b).” Pet. 29,
`
`32. MacKay appears to be taken from a publication of the Institute of
`
`Electrical and Electronics Engineers bearing an “October 1999” date and a
`
`
`6 The Leahy-Smith America Invents Act, Pub. L. No. 112-29, 125 Stat. 284
`(2011) (“AIA”), amended 35 U.S.C. §§ 102 and 103. Because the priority
`date of the ’781 patent is before the effective date of the applicable AIA
`amendments, the pre-AIA versions of 35 U.S.C. §§ 102 and 103 apply.
`
`11
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`“NOV 02 1999” date stamp from “LINDA HALL LIBRARY.” Ex. 1102,
`
`1449. Caltech does not dispute the prior art status of MacKay. For purposes
`
`of this Decision, we determine that MacKay qualifies as prior art under
`
`35 U.S.C. § 102(a) because the October 1999 edition date and the
`
`November 2, 1999, date stamp provide some evidence of publication before
`
`the earliest possible effective filing date for the challenged claims of the
`
`’781 patent, which is May 18, 2000. See Ex. 1101, at [60]; Ex. 1102, 1449.
`
`
`
`3.
`
`Claims 13–15 and 18
`
`A 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. See 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) where in evidence, so-called secondary
`
`considerations. See Graham v. John Deere Co., 383 U.S. 1, 17–18 (1966).
`
`We also recognize that prior art references must be “considered together
`
`with the knowledge of one of ordinary skill in the pertinent art.” In re
`
`Paulsen, 30 F.3d at 1480 (citing In re Samour, 571 F.2d 559, 562 (CCPA
`
`1978)). We analyze Apple’s obviousness grounds with the principles
`
`identified above in mind.
`
`In its obviousness analysis for claim 13, Apple cites the information
`
`bits in Ping denoted by vector d for the step of “receiving a block of data in
`
`12
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`the signal to be encoded.” Pet. 38 (citing Ex. 1103, 38). Apple contends
`
`“Ping receives the information bits d and computes from them an encoded
`
`codeword c.” Id. (citing Ex. 1104 ¶ 100). For the limitation “performing an
`
`encoding operation using the information bits as an input, the encoding
`
`operation including an accumulation of mod-2 or exclusive-OR sums of bits
`
`in subsets of the information bits,” Apple cites the modulo-2 summation
`
`𝑑
`∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗 and contends that these summations are sums of bits in a subset of
`
`the information bits, because each dj is an information bit. Id. at 38–39
`
`(citing Ex. 1103, 38; Ex. 1104 ¶ 102). Apple contends “Ping’s encoding
`
`operation also generates a codeword, so it must generate ‘at least a portion
`
`of a codeword’ as claimed.” Id. at 39 (citing Ex. 1103, 38; Ex. 1104 ¶ 103).
`
`Regarding “the information bits appear in a variable number of
`
`subsets,” Apple cites Ping in view of MacKay. See id. at 39–40. As
`
`background for its analysis of this limitation, Apple states the following
`
`regarding Ping:
`
`Ping’s outer code is regular because, in Ping, each information
`𝑑
`bit contributes to the same number of summations ∑ ℎ𝑖𝑗
`𝑑𝑗.
`𝑗
`Those summations are the “parity bits,” produced by Ping’s
`outer coder (and are distinct from the “parity bits” subsequently
`produced by Ping’s inner coder, the accumulator). The number
`of outer coder parity bits to which each information bit
`contributes is determined by Ping’s generator matrix Hd (which
`is, as explained above, also a portion of Ping’s parity-check
`matrix H). (Ex. 1103, Equations (1), (3) and (4), p. 38.) Each
`column in matrix Hd corresponds to a single information bit,
`and the number of 1s in a column determines the number of
`summations, or outer coder parity bits, to which the
`corresponding information bit contributes. (Id.) Ping refers to
`the number of 1s per column as the “column weight” of matrix
`Hd, and uses the variable “t” to set this number for every
`column. (Ex. 1103, p. 38.) (Ex. 1104, ¶87.)
`
`13
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`Id. at 32.
`
`Apple contends “[e]ach column of Ping’s matrix Hd corresponds to an
`
`information bit, and each row of the matrix Hd corresponds to a subset of
`
`information bits that are added together to form Ping’s outer coder parity
`
`𝑑
`bits, the summations (∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗).” Id. at 39 (citing Ex. 1104 ¶ 104).
`
`According to Apple, “[t]he number of subsets in which an information bit
`
`appears is given by the number of 1s in the column of Hd corresponding to
`
`that information bit,” which Ping teaches is “exactly ‘t’ 1s.” Id. at 34, 39.
`
`Apple further 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).
`
`Apple contends it would have been obvious to an ordinarily skilled
`
`artisan “to incorporate the non-uniform column weight of MacKay into the
`
`LDPC-accumulate codes of Ping, thus making Ping’s information bits
`
`𝑑
`contribute to different numbers of summations (∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗).” Id. at 40 (citing
`
`Ex. 1104 ¶ 105). Apple states that this would result in “some information
`
`𝑑
`bits . . . contribut[ing] to more summations (∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗) than others, such that
`
`the information bits would appear in a variable number of subsets.” Id.
`
`Based on MacKay’s teaching that “irregular codes perform better than
`
`regular codes,” Apple contends an ordinarily skilled artisan would have been
`
`motivated to incorporate irregularity into Ping’s “generator” matrix Hd. Id.
`
`at 34–36. Apple 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 33 (quoting
`
`Ex. 1103, 38).
`
`14
`
`
`

`

`IPR2017-00423
`Patent 7,916,781 B2
`
`Considering Apple’s analysis and submitted evidence, and the
`
`arguments presented in Caltech’s Preliminary Response, we are satisfied
`
`there is a reasonable likelihood that Apple would prevail in showing
`
`claim 13 would have been obvious over the combination of Ping and
`
`MacKay. We add the following for additional explanation.
`
`Caltech argues “Ping does not provide any disclosure of receiving
`
`data in a signal to be encoded, let alone receiving the data in a block
`
`format.” Prelim. Resp. 24. Caltech contends Ping’s “codeword c” is already
`
`encoded, and vector d “is merely a mathematical representation of the
`
`information bits in the codeword c . . . and provides no indication as whether
`
`information bits were ever received at all.” Id. In this instance, however,
`
`we understand the received “block of data to be encoded” to be
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`commensurate with the information bits in vector d that are encoded in
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`Ping’s described process. The Specification of the ’781 patent does not
`
`describe any particular form of the input “signal” or particular process for
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`“receiving” a block of data. Thus, we are satisfied on the current record
`
`with Apple’s mapping of Ping’s inputted information bits from vector d to
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`the recited “receiving a block of data in a signal to be encoded.”
`
`Caltech also argues Apple’s “analysis is flawed in that it incorrectly
`
`addresses only a portion of Ping’s parity check matrix Hd, rather than the
`
`parity check matrix H.” Prelim. Resp. 9. Accordingly, Caltech argues
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`“Ping’s parity check matrix H already includes nonuniform weight per
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`column—i.e., the ‘irregularity’ of MacKay.” Id. Based on Caltech’s
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`interpretation of the “particular structure” of parity check matrix H as being
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`[Hp, Hd], and Caltech’s allegation regarding Hd that “[t]he only value of t
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`disclosed by Ping is 4” (Prelim. Resp. 10–12), Caltech contends that matrix
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`Patent 7,916,781 B2
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`H has column weights as shown in a diagram from page 12 of the
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`Preliminary Response, which is reproduced below.
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`
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`Id. at 12, 18. Caltech concludes “Ping discloses a parity check matrix with
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`different numbers of ones per column—i.e., different column weights . . .
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`(weight 2, weight 1, and weight t = 4).” Id. at 12, 19. Thus, Caltech argues
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`that there would be no motivation to modify Ping to include “irregularity”
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`when Ping “already includes the aspects identified in MacKay.” Id. at 14,
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`17–20. For similar reasons, Caltech argues Apple “has failed to show that
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`Ping in view of MacKay discloses ‘wherein the information bits appear in a
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`variable number of subsets.’” Id. at 20.
`
`Yet Caltech misapprehends Apple’s mapping of the teachings from
`
`Ping to the language of claim 13. Apple does not utilize Ping’s entire parity
`
`check matrix H in its analysis; rather, Apple maps Ping’s “series of
`
`𝑑
`summations ∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗” to the recited “encoding operation” of claim 13.
`
`Pet. 38–39. Apple correctly notes that Ping’s matrix Hd, rather than entire
`
`parity check matrix H, is utilized in forming these summations. See id. at
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`32, 34, 36–40. Because each “subset” of claim 13 is a column of the matrix
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`(see id. at 32, 34–36, 39–40; Prelim. Resp. 9–12), Apple’s mapping results
`
`in a “regular” number of 1s, denoted by the variable t, in each subset. See
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`Pet. 33–34. As such, we do not agree that matrix Hd from Ping, as cited by
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`Apple, already includes “irregularity” in the manner suggested by Caltech.
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`We understand Apple’s combination as relating to the specific application of
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`MacKay’s “non-uniform column weight” to Ping’s matrix Hd (see Pet. 40),
`
`not a generic application of “irregularity” (which is not a limitation in
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`claim 13) to Ping’s teachings as a whole. As established by Apple, such a
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`modification would result in “some information bits would contribute to
`
`𝑑
`more summations (∑ ℎ𝑖𝑗
`𝑗
`
`𝑑𝑗) than others, such that the information bits
`
`would appear in a variable number of subsets, as required by claim 13.” Id.
`
`Accordingly, Caltech’s arguments do not undermine Apple’s stated
`
`motivation to combine MacKay with Ping. Nor do they undermine Apple’s
`
`analysis of the “variable number of subsets” limitation in claim 13.
`
`Caltech additionally argues MacKay is “devoid of any teaching of
`
`modifying only a specific portion of a parity check matrix [i.e., Hd],
`
`including why or how it would be attempted.” Prelim. Resp. 15.
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`Nevertheless, Apple shows persuasively that MacKay “teaches how to make
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`LDPC matrices ‘irregular’ by implementing a ‘nonuniform weight per
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`column.’” Pet. 35, 40 (both quoting Ex. 1102, 1449). Apple cites a specific
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`example in MacKay where a matrix “has columns of weight 9 and of weight
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`3.” Id. (quoting Ex. 1102, 1451). 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.
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`Finally, Caltech argues that we should deny institution under 35
`
`U.S.C. § 325(d) based on certain alleged similarities between the instant
`
`ground and the challenge of claims 13–15 in the 059 IPR based on Ping and
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`another reference called Luby (U.S. Patent No. 6,081,909), among other
`
`things. See Prelim. Resp. 2–8. We note that MacKay was not asserted in the
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`059 IPR, so we decline to exercise our authority under § 325(d) as to claims
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`13–15.7
`
`Having considered Apple’s evidence and Caltech’s arguments in its
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`Preliminary Response, we determine Apple has established sufficiently at
`
`this stage that Ping and MacKay teach every limitation of claim 13. Apple
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`has also provided a sufficient rationale for its proposed combination. Thus,
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`for the foregoing reasons, Apple demonstrates a reasonable likelihood of
`
`prevailing in showing that claim 13 would have been obvious over Ping and
`
`MacKay. Caltech does not address separately Apple’s explanations and
`
`supporting evidence regarding claims 14, 15, and 18. Based on the record
`
`before us, Apple has demonstrated a reasonable likelihood that it would
`
`prevail on its assertion that claims 14, 15, and 18 would have been
`
`unpatentable over Ping and MacKay. See Pet. 40–41, 42–43.
`
`
`
`
`
`4.
`
`Claim 17
`
`Claim 17 depends from claim 13 and recites “each of the subsets of
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`the information bits includes a constant number of the information bits.”
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`Apple cites Ping for teaching that “‘Hd has … a row weight of kt/(n-k),’
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`meaning that every row of Hd contains exactly kt/(n-k) 1s.” Id. at 41
`
`(quoting Ex. 1103, 38). Relative to the language of claim 17, Apple explains
`
`that “[t]he number of information bits in a subset is given by the number of
`
`1s in the row of Hd corresponding to that subset” meaning that “there are
`
`
`7 For similar reasons, we decline to deny institution of the Ping-MacKay-
`Coombes obviousness ground based on § 325(d).
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`kt/(n-k) information bits in each and every subset.” Id. (citing Ex. 1104
`
`¶ 111).
`
`Caltech notes that Apple’s analysis for claim 13 depends on Ping’s
`
`matrix Hd as modified by MacKay’s non-uniform column weights. Prelim.
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`Resp. 21. Caltech argues that, in an apparent contradiction, Apple relies on
`
`an unmodified version of Ping’s Hd for teaching the “constant number of
`
`information bits” limitation in claim 17. Id. Caltech provides an example of
`
`how a matrix having constant row weights (like Hd) would no longer have
`
`constant weights after modification of the column weights to introduce non-
`
`uniformity. Id. at 22.
`
`We are persuaded by Caltech’s arguments. Apple’s analysis for
`
`claim 17 is inconsistent with its analysis for claim 13, which relies on a
`
`version of Ping’s Hd that has been modified according to the teachings of
`
`MacKay. See Pet. 39–40. Apple has not persuasively shown that this
`
`modified version of Hd would still have constant row weights of kt/(n-k) as
`
`in the unmodified version of Hd. Indeed, Apple’s analysis for claim 17
`
`makes no mention of MacKay or its teachings. Accordingly, Apple has not
`
`shown a reasonable likelihood that it would prevail with respect to claim 17
`
`as obvious over Ping and MacKay.
`
`
`
`5.
`
`Claims 19–21
`
`Apple’s analysis for each of claims 19–21 states:
`
`Petitioner does not contend that [this claim] requires
`irregularity, as the Board decided in IPR2015-00059. In the
`event that the Board now finds that [this claim] requires
`irregularity, the combination of Ping and MacKay teaches every
`limitation of [this claim].
`
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`Pet. 43–45. The analysis for each claim then cites Ping exclusively except
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`that “MacKay teaches irregularity if the Board finds that irregularity is
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`required.” Id. at 44–45, 47.
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`Apple’s generalized allegations about the concept of “irregularity” in
`
`claims 19–21 do not fulfill Apple’s requirement to “identif[y], in writing and
`
`with particularity . . . the grounds on which the challenge to each claim is
`
`based. 35 U.S.C. § 312(a)(3) (emphasis added). Instead of citing MacKay
`
`for teaching particular claim limitations in each of claims 19–21, Apple
`
`would have us use MacKay to fill potential breaches in Apple’s analysis
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`“[i]n the event that the Board now finds that [claims 19–21] require[]
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`irregularity.” See Pet. 43–45. We agree with Caltech (Prelim. Resp. 5 n.1)
`
`that this general invocation of MacKay fails to “specify where each element
`
`of the claim is found in the prior art patents or printed publications.”
`
`37 C.F.R. § 42.104(a)(4) (emphasis added). We have considered the entirety
`
`of Apple’s analysis for claims 19–21, including its many references to the
`
`analysis for limitations appearing in earlier claims. See Pet. 43–47. Apple’s
`
`analysis fails to map precisely MacKay’s teachings to the particular
`
`language of claims 19–21. In the absence of such a particularized showing,
`
`we determine Apple has failed to demonstrate a reasonable likelihood that it
`
`would prevail on its assertion that claims 19–21 would have been
`
`unpatentable over Ping and MacKay.
`
`
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`6.
`
`Claim 22
`
`Claim 22 depends from claim 21.8 For the reasons that follow, we
`
`determine that Apple’s analysis for claim 22 cures the deficiencies
`
`mentioned above regarding claim 21. In discussing claim 22, we incorporate
`
`Apple’s analysis for claim 21.
`
`Apple cites the information bits in Ping denoted by vector d for the
`
`step of “receiving a block of data in the signal to be encoded.” Pet. 38, 46
`
`(citing Ex. 1103, 38). Apple contends “Ping receives the information bits d
`
`and computes from them an encoded codeword c.” Id. at 38 (citing Ex. 1104
`
`¶ 100). Apple additionally maps the calculation of Ping’s first parity bit 𝑝1
`
`𝑑
`according to the summation ∑ ℎ1𝑗
`𝑗
`
`𝑑𝑗 for the “first parity bit” limitation. Id.
`
`at 42–43, 46. Regarding the “second parity bit” limitation, Apple maps the
`
`calculation of Ping’s second