`
`Paper No. ___
`Filed: May 9, 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 IPR2017-00701
`Patent No. 7,421,032
`
`_____________________________
`
`
`
`PATENT OWNER’S PRELIMINARY RESPONSE
`PURSUANT TO 37 C.F.R. § 42.107
`
`
`
`TABLE OF CONTENTS
`
`I.Introduction .......................................................................................................... 2
`
`II.Ground 1 Fails ..................................................................................................... 4
`
`A.
`
`B.
`
`2.
`
`C.
`
`Ping in view of MacKay, Divsalar, and Luby97 fails to disclose
`“irregular repeats of the message bits” as recited in claim 1 ................ 5
`Ping already includes the “irregularity” of MacKay ........................ 7
`1.
`2. MacKay fails to teach the modification proposed by Petitioner ..... 10
`There is no rationale for combining Ping with MacKay,
`Divsalar, and Luby97 ........................................................................ 11
`1. There is no reason to modify Ping because it already includes
`the “irregularity” of MacKay ........................................................ 12
`Petitioner’s remaining arguments provide no motivation to
`combine ........................................................................................ 14
`Ping in view of MacKay, Divsalar, and Luby97 fails to teach
`“wherein the sequence of parity bits is generated is in
`accordance with ‘a’ being constant” as recited in claim 2 ................. 16
`D. MacKay fails to teach “wherein the sequence of parity bits is
`generated is in accordance with ‘a’ varying for different parity
`bits,” as recited in claim 3 ................................................................. 18
`Ping fails to teach “using a low-density generator matrix
`(LDGM) coder” as recited in claim 6 ................................................ 22
`
`E.
`
`III.Conclusion ....................................................................................................... 24
`
`
`
`
`
`
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`-1-
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`
`
`
`I.
`
`INTRODUCTION
`
`The Board should not institute inter partes review (IPR) on claims 1-10 of
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`U.S. Patent No. 7,421,032 (“the ’032 patent”) because petitioner Apple Inc.
`
`(“Petitioner” or “Apple”) has not met its burden of showing that it has a reasonable
`
`likelihood of prevailing on its proposed ground of unpatentability.
`
`The petition fails to establish that the cited references teach or suggest the
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`irregular repetition and permutation of message bits, as specifically recited in the
`
`claims. The cited references do not do so. The petition admits that the primary
`
`reference of Ping fails to disclose irregular repetition of message bits as claimed.1
`
`Petitioner attempts to cure this deficiency with MacKay, alleging one “would have
`
`been motivated to incorporate the irregularity disclosed in MacKay into Ping’s
`
`code.” Pet. at 37.
`
`But Petitioner incorrectly equates the “irregularity” of MacKay and irregular
`
`repetition in the challenged claims. As acknowledged in the petition, MacKay
`
`defines “irregular codes” as codes “whose parity check matrices have nonuniform
`
`weight per column.” Ex. 1102 at 1449; Pet at 32. By erroneously focusing on the
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`buzzword “irregular” without adequately addressing the substance of the
`
`
`1 See, e.g., Pet at 39 (“Ping’s outer LDPC code is regular.”); see also, Pet at 36
`
`(“Divsalar teaches regular repeat-accumulate (RA) codes rather than irregular
`
`repeat-accumulate codes as described and claimed in the ’032 patent.”).
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`-2-
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`
`
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`disclosure, the petition fails to recognize that the “irregularity” disclosed in
`
`MacKay is not the same as the irregular repetition of message bits as specifically
`
`recited in the challenged claims. MacKay’s “parity check matrices [that] have
`
`nonuniform weight per column” are completely different than the irregular
`
`repetition of message bits, as claimed in the ’032 patent.
`
`Petitioner further fails to recognize that the “irregularity” described in
`
`MacKay is already present in Ping, and thus there would be no motivation for a
`
`person of ordinary skill to combine MacKay with Ping and such a combination
`
`would not lead to the invention claimed in the ’032 patent. Ping discloses a code
`
`with a parity check matrix H that is composed of two submatrices, Hp and Hd. But
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`in arguing that Ping would benefit from the “irregularity” of MacKay, the petition
`
`improperly focuses only on submatrix Hd, ignoring Ping’s submatrix Hp and the
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`parity check matrix H as a whole. Ping’s parity check matrix H, however, already
`
`illustrates nonuniform weight per column. As such, Ping’s parity check matrix
`
`already includes the “irregularity” of MacKay, thereby undermining Petitioner’s
`
`proffered rationale for combining the references in the first place.
`
`As such, the proposed grounds of challenge fail to demonstrate that each
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`feature of claims 1-10 of the ’032 patent is found in the cited art. Moreover, the
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`rationale for combining the references is unsupported and is tainted by Petitioner’s
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`misapprehension of the reference disclosures.
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`-3-
`
`
`
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`Accordingly, institution of inter partes review should be denied.2
`
`II. GROUND 1 FAILS
`
`The petition fails to demonstrate that claims 1-10 would have been obvious
`
`over the combination of Ping in view of MacKay, Divsalar, and Luby97 as asserted
`
`in Ground 1 because not every limitation of the challenged claims is found in the
`
`
`2 Petitioner acknowledges that the’032 patent was already “challenged in one
`
`petition for inter partes review.” Pet. at 3. The Board rejected this petition. See
`
`Hughes Network Systems, LLC v. California Institute of Tech., Case No. IPR2015-
`
`00060, Paper 18 (Apr. 27, 2015). The earlier Hughes IPR similarly presented
`
`grounds based on Ping, Divsalar, and the Luby ’909 Patent (U.S. Patent No.
`
`6,081,909), the latter of which is similar in scope to the MacKay paper on which
`
`Petitioner relies in this instance. Compare Hughes Network Sys., Case No.
`
`IPR2015-00060, Paper 4 at 42-56 (challenging claims 1, 8, 10, 18, 19, and 22 as
`
`obvious over combinations including Divsalar and Luby ’909, some of which
`
`include Ping) with Pet. at 39-64 (challenging claims 1-10 as obvious over Ping,
`
`Divsalar, MacKay, and Luby97). Concurrent with the present petition, Petitioner
`
`filed two additional IPR petitions (IPR2017-00700 and IPR2017-00729) using
`
`Ping, Divsalar, and MacKay, and Luby97 as the primary references for each
`
`ground.
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`-4-
`
`
`
`
`prior art.3 In addition, the petition fails to demonstrate that a person of ordinary
`
`skill in the art would have been motivated to combine the references such that the
`
`combination of elements would have been obvious.
`
`A. Ping in view of MacKay, Divsalar, and Luby97 fails to disclose
`“irregular repeats of the message bits” as recited in claim 1
`
`Claim 1 describes an encoding procedure, in which a sequence of parity bits
`
`is generated in accordance with the formula (cid:1)(cid:2)=(cid:1)(cid:2)(cid:4)(cid:5)+∑ (cid:8)((cid:2)(cid:4)(cid:5))((cid:11)(cid:12)(cid:13))
`(cid:11)(cid:13)(cid:14)(cid:5)
`at 7:63-8:20; Ex. 1112. The term ∑ (cid:8)((cid:2)(cid:4)(cid:5))((cid:11)(cid:12)(cid:13))
`(cid:11)(cid:13)(cid:14)(cid:5)
`
`. Ex. 1101
`
` in the above equation is “the
`
`value of a sum of ‘a’ randomly chosen irregular repeats of the message bits.” Id.
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`The petition identifies three requirements arising from this limitation:
`
`(i) computing a parity bit as a sum of the previous parity bit and a set
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`of randomly chosen message bits; (ii) the randomly chosen message
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`bits are “repeats;” and (iii) the repeats of the message bits are
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`“irregular.”
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`Pet. at 48. The petition also notes that the recited “message bits” are “information
`
`bits.” Id. Accordingly, claim 1 describes a method in which information bits are
`
`irregularly repeated, then used to calculate parity bits by setting each parity bit
`
`
`3 Caltech does not concede any of the cited references qualify as prior art for
`
`this proceeding, and specifically notes that the prior art status of the cited Divsalar
`
`reference has not been established. At this stage of the proceeding, the present
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`response focuses on other deficiencies in the petition materials.
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`-5-
`
`
`
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`equal to the sum of the previous parity bit (if any) and a random set of “a”
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`irregularly repeated information bits. As the ’032 patent describes, this “is in effect
`
`the encoding algorithm” represented by the Tanner graph of Fig. 3. Ex. 1101 at
`
`3:65-4:19, Fig. 3.
`
`The Petition admits that Divsalar and Ping do not teach the claimed irregular
`
`repetition, and relies on MacKay for its disclosure of irregular coding—i.e.
`
`nonuniform weight per column. See Pet. at 52 (“implementing Ping’s encoding
`
`methods using Divsalar’s technique … [involves] ‘regular,’ rather than ‘irregular’
`
`[repetition]. However, incorporating the nonuniform column weights of MacKay
`
`into Ping would yield the claimed “irregular repeats.”).
`
`But the petition errs in equating the “irregularity” claimed (“irregular repeats
`
`of the message bits”) with the “irregularity” of MacKay (“codes whose parity
`
`check matrices have nonuniform weight per column”). Id. at 39-40; see also id. at
`
`32-33. These are two distinct concepts. As discussed in further detail below, there
`
`are many examples of codes whose parity check matrices have nonuniform weight
`
`per column yet which, nonetheless, fail to provide irregular repetition of message
`
`bits. Indeed, the codes of Ping and Divsalar provide just such examples.
`
`As for MacKay, Petitioner has identified nothing in MacKay teaching
`
`irregular repeats of message bits. While Petitioner cites generically to MacKay as
`
`teaching “nonuniform weight per column,” the petition identifies no instance of
`
`-6-
`
`
`
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`nonuniform weight per column among information bits. See, e.g., Pet at 32-33.
`
`The petition further cites to an example of a parity check matrix (presumably the
`
`example in Table I of MacKay) having columns of weight 9 and others of weight
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`3. Pet at 40. But Petitioner identifies nothing in MacKay, and is unable to do so,
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`describing any disclosure or example having nonuniform weight per column
`
`among information bits in a parity check matrix such that information bits are
`
`repeated a different number of times in a coding operation.
`
`The cited references fail to disclose at least this aspect of claim 1.
`
`1. Ping already includes the “irregularity” of MacKay
`
`As indicated above, Ping provides an example of a code whose parity check
`
`matrix has nonuniform weight per column yet, nonetheless, fails to provide
`
`irregular repetition of message bits.
`
`Petitioner argues that MacKay’s “irregularity”—the nonuniform weight per
`
`column—could be added to Ping’s parity check matrix (identified in Ping as H).
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`Id. at 37-38; 40-41. The parity check matrix of Ping, however, already includes
`
`nonuniform weight per column, which would have been apparent had the petition
`
`not focused on only a subset of Ping’s matrix.
`
`In particular, the petition incorrectly addresses only a portion of Ping’s
`
`parity check matrix Hd, rather than the parity check matrix H. As such, the petition
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`-7-
`
`
`
`
`overlooks the fact that Ping’s parity check matrix H already includes nonuniform
`
`weight per column—i.e., the “irregularity” of MacKay.
`
`Ping’s parity check matrix H is composed of two submatrices, Hp and Hd. H
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`has the following form:
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`Ex. 1103 at 38; see also Pet. at 27.
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`(cid:15)=((cid:15)(cid:16) (cid:15)(cid:17)).
`
`Hd is a randomly generated matrix of ones and zeros in which each column
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`has exactly t ones and each row has exactly kt/(n-k) ones, where k is the number of
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`information bits and n-k is the number of parity bits. Ex. 1103 at 38. Because Hd
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`has t ones per column, it is said to have a “column weight of t.” Ex. 1103 at 38.
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`The only value of t disclosed by Ping is 4 (see id. at 39); accordingly, Ping
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`discloses that Hd has a uniform column weight of 4.
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`Ping further discloses that Hp has a specific, deterministic structure with 1s
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`on the diagonal and immediately below the diagonal, as follows:
`
`0
`
`
`(cid:15)(cid:16)=(cid:19)1
`
`
`1 1
`1 1(cid:24).
` ⋱ ⋱
`0
`
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`Id. at 38. Counting the number of ‘1s’ in each column of Hp gives two ‘1s’ for
`
`each column (n-k-1 in total) except the last, which has one ‘1’ (each column has
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`one ‘1’ on the diagonal and one ‘1’ below the diagonal; the last column does not
`
`have an entry below the diagonal, so it has just one ‘1’). This is illustrated below:
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`-8-
`
`
`
`
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`Putting Hp together with Hd gives a parity check matrix H that has k
`
`columns with weight 4, one column with weight 1, and (n-k-1) columns with
`
`weight 2, as shown below:
`
`
`In other words, Ping discloses a parity check matrix with different numbers
`
`of ones per column—i.e., different column weights. These variable column
`
`weights, however, indicate that there is variability between parity bits and message
`
`bits, not that there is irregular repetition of the message bits themselves.
`
`Accordingly, as MacKay’s disclosure of “nonuniform … column weight”
`
`describes a property that Ping’s parity check matrix already has, and which
`
`Petitioner admits does not satisfy claim 1.
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`-9-
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`
`
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`2. MacKay fails to teach the modification proposed by
`Petitioner
`
`To the extent Petitioner proposes modifying only Ping’s submatrix Hd in
`
`view of MacKay (see Pet. at 39), nothing in the reference teaches such a specific
`
`modification. MacKay says nothing about modifying a specific portion of a parity
`
`check matrix to provide that subset of columns with nonuniform column weights,
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`let alone doing so for a portion specifically corresponding to information bits. As
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`such, MacKay provides no disclosure that would be applicable to submatrix Hd as
`
`opposed to parity check matrix H (which already includes nonuniform weight per
`
`column). Moreover, Petitioner provides no explanation as to how MacKay’s
`
`teachings would result in a modification directed to Ping’s submatrix Hd,
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`particularly when Ping already satisfies the definition of irregularity provided by
`
`MacKay. At best, MacKay’s teachings relate only to the overall parity check
`
`matrix, not a subset of the parity check matrix selectively modified, and therefore
`
`do not teach or suggest the modification to Ping’s submatrix Hd that Petitioner
`
`alleges.
`
`Divsalar does not remedy this deficiency, as Divsalar admittedly teaches
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`only regular repetition, and at any rate is not relied on for this claim element. See
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`Pet. at 52-53. Luby97 is also not relied on in relation to this claim element, and in
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`any event does not remedy the deficiencies of Ping, MacKay, and Divsalar.
`
`Accordingly, Petitioner has failed to show that Ping in view of MacKay, Divsalar,
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`-10-
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`
`
`
`and Luby97 discloses “irregular repeats of the message bits,” as required by claim
`
`1, and as included in dependent claims 2-10.
`
`B. There is no rationale for combining Ping with MacKay, Divsalar,
`and Luby97
`
`The proposed combination of Ping and MacKay fails because the petition
`
`fails to reasonably describe how these two references would be combined and why
`
`one of ordinary skill in the art would have been motivated to do so. As explained
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`below, the petition fails to provide the requisite “articulated reasoning with some
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`rational underpinning” to support the asserted conclusion of obviousness. KSR Int’l
`
`v. Teleflex, Inc., 550 U.S. 398, 419 (2007) (citing In re Kahn, 441 F.3d 977, 988
`
`(Fed. Cir. 2006)). The stated justifications for combining the references, which are
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`repeated in both the petition and Dr. Davis’s declaration, do not withstand scrutiny
`
`for several reasons.4
`
`
`4 While Petitioner submitted the expert declaration of Dr. James A. Davis. (Ex.
`
`1104), Dr. Davis’s declaration should be given little to no weight, as it merely
`
`repeats the Petition’s arguments while adding essentially no independent facts,
`
`data, or analysis. Dr. Davis’s testimony is frequently a near-verbatim recitation of
`
`the conclusory arguments included within the Petition. E.g., compare Pet. at 39-40,
`
`with Ex. 1104, ¶¶ 106-07; compare Pet. at 25, with Ex. 1104, ¶ 64; compare Pet. at
`
`41-42, with Ex. 1104 ¶¶ 109-11); see Kinetic Techs., Inc. v. Skyworks Solutions,
`
`-11-
`
`
`
`
`1. There is no reason to modify Ping because it already
`includes the “irregularity” of MacKay
`
`Petitioner’s motivation to combine is premised on the idea that a “person of
`
`ordinary skill would have been motivated to incorporate the irregularity disclosed
`
`in MacKay into Ping’s code.” Pet at 37. But as demonstrated above (see Section
`
`II.A.1), Ping’s parity check matrix includes the “irregularity” provided in MacKay
`
`and relied upon by Petitioner (i.e., a parity check matrix with nonuniform weight
`
`per column). No modification of Ping is necessary to achieve the stated objective.
`
`As such, there is no rationale to combine the cited references.
`
`Petitioner admits that Ping’s equation is “regular” in the context of the ’032
`
`patent and does not satisfy claim 1. See, e.g., Pet. at 52-53 (“Ping’s encoding
`
`methods using Divsalar’s technique [has] ‘regular,’ rather than ‘irregular’”
`
`repeats.), 39 (“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.”). Thus, Ping
`
`
`Inc., Case No. IPR2014-00529, Paper 8 at 15 (P.T.A.B. Sept. 23, 2014) (“Merely
`
`repeating an argument from the Petition in the declaration of a proposed expert
`
`does not give that argument enhanced probative value.”); Corning Inc. v. DSM IP
`
`Assets B.V., Case No. IPR2013-00048, Paper 94 at 33 (P.T.A.B. May 9, 2014)
`
`(finding that an expert’s verbatim repeating of attorney argument warrants “little
`
`weight in the absence of objective evidentiary support”).
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`-12-
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`
`
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`already discloses an “irregular” code as MacKay uses the term, yet Petitioner
`
`concedes this does not satisfy the “irregularity” recited in the claims.
`
`As described in Section II.A.1, Ping’s parity check matrix (reproduced
`
`below) is an “irregular” parity check matrix as MacKay uses the term:
`
`
`In other words, Ping discloses a parity check matrix with different numbers of ones
`
`per column—i.e., different column weights.
`
`Because Ping’s parity check matrix H has different column weights (weight
`
`2, weight 1, and weight t = 4), Ping’s parity check matrix is already irregular as
`
`defined by Petitioner and MacKay. Petitioner’s failure to recognize that Ping
`
`already incorporates the irregularity of MacKay fatally undercuts the proposed
`
`rationale to combine: if there is no irregularity to add, there can be no reason to
`
`combine MacKay with Ping.
`
`To the extent the petition proposes modifications to only a portion of Ping’s
`
`parity check matrix, such partial modifications are entirely unexplained and wholly
`
`unsupported in the cited references. The petition proposes modifying Ping’s code
`
`by varying the column weights in Ping’s parity check matrix, but addresses only a
`
`-13-
`
`
`
`
`portion of the parity check matrix H. Pet. at 42-43. As explained above, Ping’s Hd
`
`matrix is not a parity check matrix; it is only a portion of the parity check matrix
`
`H. See id. (“Ping’s Hd matrix is also part of Ping’s ‘parity check’ matrix H”).
`
`Ping’s parity check matrix H already includes nonuniform weight per column, i.e.,
`
`the “irregularity” of MacKay.
`
`Moreover, other than the ’032 patent itself, the cited references, including
`
`MacKay, are devoid of any teaching of modifying only a specific portion of a
`
`parity check matrix, including why or how it would be attempted. Petitioner does
`
`not explain why varying the column weights of only a portion of Ping’s parity
`
`check matrix, rather than the entire parity check matrix as described in MacKay,
`
`would have resulted in a functional encoder, let alone one which would have
`
`predictably produced improved code performance. The Petition asserts that it
`
`“would have been straightforward” to change the column weights and it “would
`
`have been an easy way for one of ordinary skill to incorporate the irregularity
`
`disclosed by MacKay into Ping” (Pet. at 40), but these conclusory statements do
`
`not provide a reason why Ping would be particularly modified in a way no cited
`
`reference suggests, or otherwise provide a rationale to combine.
`
`2. Petitioner’s remaining arguments provide no motivation to
`combine
`
`Petitioner further argues that one of ordinary skill would have been
`
`motivated to combine Ping and MacKay because the two references use similar
`
`-14-
`
`
`
`
`terminology. Pet. at 41. The petition cites no legal authority supporting the notion
`
`that the mere usage of similar terms in two references permits a reformulation of
`
`technical aspects in a manner suggested nowhere in the prior art. Moreover, the
`
`key similarity between MacKay and Ping’s discussion of matrices is the one thing
`
`Petitioner ignores: each reference already discloses a parity check matrix with
`
`nonuniform weight per column, neither of which teaches the irregular repetition of
`
`message bits in the manner recited in claim 1.
`
`Petitioner’s remaining arguments essentially amount to assertions that the
`
`cited references are analogous art. For example, the petition argues a person of
`
`ordinary skill would have been motivated to combine Ping and MacKay because
`
`the references are “directed to the same field of endeavor.” Pet. at 37-38. However,
`
`whether prior art references are in the same field of endeavor is an inquiry best
`
`suited for determining analogous art; it is insufficient to show a rationale for
`
`combining one reference with another. See Microsoft Corp., Case No. IPR2014-
`
`00745, Paper 12 at 14 (“Petitioner’s contention that the references solve the same
`
`need is better characterized as a contention that the references are analogous art
`
`than as a rational underpinning for the proposed combination.”); TRW Auto. US
`
`LLC v. Magna Elecs. Inc., Case No. IPR2014-00263, Paper 15 at 14 (P.T.A.B.
`
`June 26, 2014) (“The mere fact that the two references are ‘in the same field of
`
`endeavor’ is not persuasive.”).
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`-15-
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`
`
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`The further combination of Divsalar and Luby97 with Ping and MacKay
`
`does not remedy the deficiencies in Ping and MacKay, either with regard to the
`
`references’ teachings or with regard to the proffered motivation to combine.
`
`Divsalar discloses a code that Petitioner admits to have only regular repetition. See
`
`Pet. at 36 (“Divsalar teaches regular repeat-accumulate (RA) codes rather than
`
`irregular repeat-accumulate codes as described and claimed in the ’032 patent.”).
`
`Divsalar is relied on only to teach the repeating of bits (Pet. at 44-45), not to
`
`supply irregularity. Luby97 is relied on only to teach a “stream of bits” (Pet. at 44-
`
`45, 47, 55), and thus is irrelevant to the “irregular repetition” of the claims.
`
`Accordingly, Divsalar and Luby97 do not remedy the deficiencies of Ping and
`
`MacKay.
`
`For the foregoing reasons, Petitioner’s rationale to combine is insufficient,
`
`based on numerous false assumptions and improper hindsight, and does not
`
`support Petitioner’s Ground 1. Thus, Ground 1 is not supportable and should be
`
`rejected.
`
`C. Ping in view of MacKay, Divsalar, and Luby97 fails to teach
`“wherein the sequence of parity bits is generated is in accordance
`with ‘a’ being constant” as recited in claim 2
`
`Petitioner asserts that Ping teaches this limitation because Ping teaches a
`
`matrix Hd with a constant number of ones per row. Pet. at 55-56. However, claim 2
`
`depends from claim 1 and necessarily incorporates all elements of claim 1.
`
`-16-
`
`
`
`
`Petitioner’s discussions for claim 2 and claim 1 are inconsistent, as explained
`
`further below.
`
`According to Petitioner’s discussion for claim 1, Ping’s matrix Hd must be
`
`modified to incorporate non-uniform column weights in order to disclose claim 1.
`
`See Pet. at. 53 (suggesting modifying Ping’s Hd by “incorporating the nonuniform
`
`column weights”).
`
`For claim 2, however, Petitioner relies on an unmodified matrix Hd of Ping.
`
`Petitioner argues that the unmodified matrix of Ping teaches uniform row weights,
`
`thereby teaching the element “wherein the sequence of parity bits is generated is in
`
`accordance with ‘a’ being constant” in claim 2. Pivoting back to the unmodified
`
`matrix Hd of Ping undermines Petitioner’s theory as to independent claim 1, from
`
`which claim 2 depends. In other words, the matrix cannot be both modified and
`
`unmodified. If Hd is unmodified, Petitioner’s challenge to claim 1 fails, and the
`
`challenge to dependent claim 2 fails along with it. If Hd is modified, then
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`Petitioner’s argument with respect to claim 2 fails as it rests on false assumptions.
`
`As such, Petitioner’s theories of unpatentability of independent claim 1 and
`
`dependent claim 2 are different and incompatible.
`
`Illustrating the inconsistent and incompatible theories, arbitrarily changing
`
`column weights changes row weights as well. For example, one way to change a
`
`column’s weight is to add a ‘1’ to a column. However, such an addition also adds a
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`-17-
`
`
`
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`‘1’ to a row, so both weights change. For example, the 3×3 identity matrix below
`
`has row and column weights of 1. Adding a ‘1’ to the upper right entry changes the
`
`last column’s weight to 2, but also changes the first row’s weight to 2, while the
`
`remaining rows have weights of 1.
`
`(cid:25)1 0 0
`0 0 1(cid:26)(cid:11)(cid:17)(cid:17) (cid:5)(cid:27)(cid:28)(cid:28)(cid:29)(cid:25)1 0 1
`0 0 1(cid:26)
`0 1 0
`0 1 0
`
`Accordingly, Petitioner has failed to show how to modify the Hd matrix (as
`
`required to meet the limitations of claim 1) in a way that would also meet the
`
`limitations of claim 2. Thus, Petitioner fails to demonstrate that Ping in view of
`
`MacKay, Divsalar, and Luby97 teaches “wherein the sequence of parity bits is
`
`generated is in accordance with ‘a’ being constant” as recited in claim 2.
`
`D. MacKay fails to teach “wherein the sequence of parity bits is
`generated is in accordance with ‘a’ varying for different parity
`bits,” as recited in claim 3
`
`Claim 3 recites “wherein the sequence of parity bits is generated is in
`
`accordance with ‘a’ varying for different parity bits.” Petitioner asserts that
`
`“MacKay teaches the further limitation of claim 3” (Pet. at 57); however, MacKay
`
`fails to teach this limitation, because MacKay’s “nonuniform row weights”
`
`describe the row weights of the whole parity check matrix, whereas Petitioner
`
`attempts to apply the concept to only the Hd portion of the parity check matrix.
`
`-18-
`
`
`
`
`The petition asserts that this claim element is equivalent to requiring
`
`nonuniform row weight in the Hd matrix of Ping, and admits that Ping does not
`
`teach this limitation. The petition admits that Ping only teaches a parity check
`
`matrix H for which the submatrix Hd has uniform weight per row. Pet. at 56
`
`(quoting Ping as teaching a fixed number (kt/(n-k)) of 1s per row); see also id. at
`
`60-61 (suggesting a modification of Ping to arrive at the recited claim elements).
`
`The petition further states that “varying the row weight of Ping’s Hd matrix would
`
`make the number of inputs into the check nodes variable, as required by claim 3.”
`
`Id. at 59. Accordingly, the Petition turns to MacKay for this limitation.
`
`Because Petitioner again misinterprets the teachings of MacKay, Petitioner
`
`mistakenly concludes that the “nonuniform row weight” for a parity check matrix
`
`mentioned by MacKay corresponds to a “nonuniform row weight” of Hd, which is
`
`only a portion of a parity check matrix. Because MacKay only discusses a parity
`
`check matrix as a whole, it provides no teaching or suggestion of modifying the Hd
`
`portion of Ping’s parity check matrix.
`
`As with the nonuniform column weight discussed above in regard to claim 1,
`
`the difference between nonuniform row weight of Hd and nonuniform row weight
`
`of H is illustrated by the fact that although Hd has uniform row weight, H does not.
`
`Ping discloses that Hd has a constant column weight of t and row weight of
`
`kt/(n-k). Ex. 1103 at 38. The row weight of Hd is thus constant, and determined by
`
`-19-
`
`
`
`
`the code’s rate (i.e., the ratio of the number of information bits to the number of
`
`codeword bits). If Hd has a uniform row weight of kt/(n-k), then the row weights of
`
`each row of Ping’s parity check matrix H is given by the row weight of Hd (kt/(n-
`
`k)) plus the row weight of Hp for that row (1 or 2). H is reproduced below, with the
`
`total weight of each row indicated:
`
`
`In other words, Ping discloses a parity check matrix having different numbers of
`
`ones per row—i.e., different row weights. In particular, the first row has weight
`
`
`(cid:30)(cid:31)
`
`( (cid:4)(cid:30))+1 and the remaining rows have weight (cid:30)(cid:31)( (cid:4)(cid:30))+2. The variable row
`
`weights, however, reflects variability in the row weights of Hp, not that there is
`
`variability of the row weights of Hd.
`
`Accordingly, as illustrated above, Ping’s parity check matrix H has different
`
`row weights. Thus, MacKay’s discussion of “nonuniform row weights” describes a
`
`property that Ping’s parity check matrix already has, and which Petitioner admits
`
`does not satisfy claim 3.
`
`-20-
`
`
`
`
`Petitioner’s attempt to apply MacKay’s “nonuniform row weights” to Hd
`
`(see Pet. at 59-61) repeats the errors discussed above in Section II.A.2, and so
`
`should be disregarded for similar reasons.
`
`Furthermore, the petition fails to establish a motivation to combine MacKay
`
`and Ping with regard to this limitation. The only motivation asserted by the petition
`
`is as follows:
`
`Specifically, one of ordinary skill would have been motivated to
`
`implement MacKay’s uneven row weight in Ping’s matrix to
`
`determine whether this improved the code’s bit error rate (BER) as
`
`MacKay suggests (when reporting on the teachings of Luby et al.).
`
`Pet. at 59. This contradicts the teachings of MacKay.
`
`What MacKay actually states regarding nonuniform column and row
`
`weights is the following:
`
`The irregular codes of [Luby et al.] have parity check matrices with
`
`nonuniform weights per row and nonuniform weights per column. It
`
`has not yet been established whether both of these nonuniformities are
`
`desirable. In our experience with codes for noisy channels,
`
`performance is more sensitive to the distribution of column weights.
`
`In this paper, we concentrate on irregular codes with the weight per
`
`row as uniform as possible.
`
`Ex. 1102 at 1449. Contrary to the petition’s assertions, MacKay never suggests that
`
`an “improved bit error rate” would result from adding row weight nonuniformities.
`
`MacKay states that the desirability of nonuniform row weights “has not yet been
`
`-21-
`
`
`
`
`established” and that “performance is more sensitive to the distribution of column
`
`weights.” For this reason, MacKay concentrates “on irregular codes with the
`
`weight per row as uniform as possible.” A teaching that a proposed modification
`
`lacks predictability and has no established benefits cannot serve as a motivation to
`
`combine. Accordingly, the petition has not established a motivation to combine
`
`Ping and MacKay to arrive at the invention recited in claim 3.
`
`Accordingly, Petitioner has failed to show that MacKay teaches “wherein
`
`the encoder is configured to generate the collection of parity bits as if a number of
`
`inputs into nodes vi was not constant,” as recited in claim 3.
`
`E. Ping fails to teach “using a low-density generator matrix (LDGM)
`coder” as recited in claim 6
`
`Claim 6 recites “wherein generating the random sequence of bits comprises
`
`coding the collection of message bits using a low-density generator matrix
`
`(LDGM) coder.” Petitioner asserts that Ping discloses this limitation, stating that
`
`the Hd portion of Ping’s parity check matrix “corresponds to a generator matrix.”
`
`Pet. at 68. Petitioner further argues that Ping’s Hd submatrix is a low-density
`
`generator matrix on the basis that Hd is “a very low density matrix.” Id.
`
`
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