`
`Paper No. ___
`Filed: May 8, 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 IPR2017-00700
`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.Claim Construction ............................................................................................. 5
`
`III.Ground 1 Fails ................................................................................................... 7
`
`A.
`
`
`
`B.
`
`
`
`C.
`
`
`Ping in view of MacKay and Divsalar Fails to Disclose the
`Irregular Repetition of Information Bits Recited in the Tanner
`Graph of Claim 11 .............................................................................. 7
`1. Ping already includes the “irregularity” of MacKay ........................... 9
`2. MacKay fails to teach the modification proposed by Petitioner .........12
`There is no Rationale for Combining Ping with MacKay and
`Divsalar ............................................................................................ 13
`1. There is no reason to modify Ping because it already includes the
`“irregularity” of MacKay ..................................................................14
`2. Petitioner’s remaining arguments provide no motivation to combine 17
`Ping in view of MacKay and Divsalar fails to disclose the
`additional limitations of dependent claim 12 ..................................... 18
`
`IV.Ground 2 Fails ................................................................................................. 22
`
`A.
`
`
`
`Ping fails to teach “a low-density generator matrix (LDGM)
`coder” as recited in claim 13 ............................................................. 22
`
`V.Ground 3 Fails .................................................................................................. 24
`
`A.
`
`
`
`The Petition Fails to Establish That Pfister Qualifies as a Prior
`Art Printed Publication ..................................................................... 24
`
`VI.Conclusion ....................................................................................................... 27
`
`VII.Appendix ........................................................................................................ 29
`
`
`
`
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`
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`-1-
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`

`

`
`
`I.
`
`INTRODUCTION
`
`The Board should not institute inter partes review (IPR) on claims 11-17 of
`
`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 any of its proposed grounds of unpatentability.
`
`The petition fails to establish that the cited references teach or suggest the
`
`irregular repetition and permutation of message bits, as specifically recited in the
`
`claims. They do not. 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 39.
`
`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. 1002 at 1449; Pet at 33. By erroneously focusing on the
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`buzzword “irregular” without adequately addressing substance of the disclosure,
`
`
`1 See, e.g., Pet at 51 (“Ping’s outer LDPC coder 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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`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.
`
`Moreover, Petitioner 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
`
`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
`
`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 the proffered
`
`rationale for combining the references in the first place.
`
`Submitted herewith is a declaration from Dr. R. Michael Tanner, an expert
`
`in graphical analysis of codes and the inventor of the “Tanner graph.” (Ex. 2001,
`
`-3-
`
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`

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`¶¶ 1-6); see also Ex. 2002.2 Dr. Tanner confirms that the “irregularity” of MacKay
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`fails to provide the irregular repetition of information bits required by the
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`challenged claims, and further explains how the code of Ping identified by
`
`Petitioner as a regular code already exhibits irregularity as defined by MacKay,
`
`whether represented as a parity check matrix or a Tanner graph.
`
`As such, the proposed grounds of challenge fail to demonstrate that each
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`feature of claims 11-17 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.
`
`Accordingly, institution of inter partes review should be denied.3
`
`2 Independent claim 11 recites a Tanner graph. Dr. Tanner’s testimony is
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`submitted to explain a deficiency in the petition materials. See e.g., Arris Group,
`
`Inc., et al. v. Mobile Telecomms. Techs., LLC, No. IPR2016-00765, Paper 12
`
`(PTAB September 21, 2016) (crediting testimony explaining the failure of the
`
`petitioner to address or recognize a deficiency in the disclosure of a cited
`
`reference).
`
`3 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
`
`-4-
`
`
`

`

`II. CLAIM CONSTRUCTION
`
`Claim 11 recites a device including an encoder configured to receive a
`
`collection of message bits and encode the message bits to generate a collection of
`
`parity bits in accordance with the following Tanner graph:
`
`
`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 11, 12, and 14-16 as obvious
`
`over Ping, Divsalar, and MacKay ). Concurrent with the present petition, Petitioner
`
`filed two additional IPR petitions (IPR2017-00701 and IPR2017-00729) using
`
`Ping, Divsalar, and MacKay, and Luby97 as the primary references for each
`
`ground.
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`-5-
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`

`

`
`Ex. 1001 at 9:1-34; see also id. at Certificate of Correction (replacing the bottom
`
`V1, U1, and X1 with Vr, Uk, and Xr, respectively). Although Petitioner provides a
`
`construction for the Tanner graph of claim 11 including three elements, in the
`
`present case no construction is necessary beyond observing that in the above
`
`Tanner graph, different subsets of message bits are repeated a different number of
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`times. See Pet. at 48 (stating in element (i) that “at least two different subsets of
`
`message bits are repeated a different number of times”); see also id. at 25-26. This
`
`is the referenced “irregularity” of claim 11, which stands in contrast to the so
`
`called “irregularity” of MacKay. As discussed further below, the petition defines
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`-6-
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`

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`the “irregularity” of MacKay as nonuniform weight per column in a parity check
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`matrix. Pet. at 41. Petitioner suggests adding the irregularity of MacKay to Ping,
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`but fails to address that (1) Ping’s parity check matrix already includes nonuniform
`
`weight per column; and (2) the “irregularity” of MacKay is distinct from the
`
`irregular repetition of claim 11. The latter aspect can only be provided by
`
`conjecture and improper hindsight.
`
`III. GROUND 1 FAILS
`
`The petition fails to demonstrate that claims 11, 12, and 14-16 would have
`
`been obvious over the combination of Ping in view of MacKay and Divsalar as
`
`asserted in Ground 1 because not every limitation of the challenged claims is found
`
`in the prior art. 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 and Divsalar Fails to Disclose the
`Irregular Repetition of Information Bits Recited in the Tanner
`Graph of Claim 11
`
`Petitioner asserts that Ping in view of MacKay teaches the irregular
`
`repetition of the Tanner graph in claim 11 (i.e., “at least two different subsets of
`
`message bits are repeated a different number of times”). Pet. at 48; see also id. at
`
`51. However, neither Ping nor MacKay, alone or in any combination, provide the
`
`requisite disclosure.
`
`-7-
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`

`

`The Petition admits that Ping does not teach irregular repetition, and relies
`
`on MacKay for its disclosure of “irregular” coding—i.e., nonuniform weight per
`
`column. See Pet. at 51 (“Ping’s outer LDPC coder is regular. … [O]ne of ordinary
`
`skill would have been motivated to use MacKay’s irregularity in Ping, thus making
`
`Ping’s outer LDPC encoder irregular”); see also id. at 42-43 (discussing the
`
`proposed modification).
`
`But the petition errs in equating the “irregularity” claimed (“at least two
`
`different subsets of message bits are repeated a different number of times”) with
`
`the “irregularity” of MacKay (“codes whose parity check matrices have
`
`nonuniform weight per column”). Id. at 41; see also id. at 33. Those 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,
`
`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 at
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`least two different subsets of message bits repeated a different number of times in a
`
`coding operation (or, more pertinently, in a Tanner graph per claim 11). While
`
`Petitioner cites generically to MacKay as teaching “nonuniform weight per
`
`column,” the petition identifies no instance of nonuniform weight per column
`
`among information bits. See, e.g., Pet at 33-34. The petition further cites to an
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`-8-
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`

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`example of a parity check matrix (presumably the example in Table I of MacKay)
`
`having columns of weight 9 and others of weight 3. Pet at 42. But Petitioner
`
`identifies nothing in MacKay, and is unable to do so, 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 11.
`
`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. See also Ex. 2001 ¶¶27-32.
`
`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).
`
`Id. at 39; 42-43. 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
`
`overlooks the fact that Ping’s parity check matrix H already includes nonuniform
`
`weight per column—i.e., the “irregularity” of MacKay.
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`-9-
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`

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`Ping’s parity check matrix H is composed of two submatrices, Hp and Hd. H
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`has the following form:
`
`Ex. 1003 at 38; see also Pet. at 29.
`
`(cid:1)=(cid:3)(cid:1)(cid:4) (cid:1)(cid:5)(cid:6).
`
`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
`
`information bits and n-k is the number of parity bits. Ex. 1003 at 38. Because Hd
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`has t ones per column, it is said to have a “column weight of t.” Ex. 1003 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. See also Ex. 2001 ¶28.
`
`Ping further discloses that Hp has a specific, deterministic structure with 1s
`
`on the diagonal and immediately below the diagonal, as follows:
`
`0
`
`
`(cid:1)(cid:4)=(cid:8)1
`
`
`1 1
`1 1(cid:13).
` ⋱ ⋱
`0
`
`
`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
`
`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:
`
`-10-
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`

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`See also Ex. 2001 ¶29.
`
`
`
`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. See Ex. 2001 ¶30;
`
`see also id. ¶31 (explaining that a Tanner graph representation of Ping would be an
`
`“irregular” graph as defined by MacKay, despite lacking irregular repetition of
`
`information bits).
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`-11-
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`

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`Accordingly, 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 11.
`
`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 42), nothing in the references teach such a specific
`
`modification. MacKay says nothing about modifying a specific portion of a parity
`
`check matrix to provide a subset of columns with nonuniform column weights, let
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`alone doing so for a portion specifically corresponding to information bits. As
`
`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 only 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
`
`only regular repetition, and at any rate is not relied on for this claim element. See
`
`-12-
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`

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`Pet. at 51. Accordingly, Petitioner has failed to show that Ping in view of MacKay
`
`and Divsalar discloses “at least two different subsets of message bits are repeated a
`
`different number of times,” as required by claim 11, and as included in dependent
`
`claims 12 and 14-16.
`
` There is no Rationale for Combining Ping with MacKay and
`B.
`Divsalar
`
`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
`
`below, the petition fails to provide the requisite “articulated reasoning with some
`
`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
`
`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.
`
`1004), 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 41-42,
`
`-13-
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`

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`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 “person of
`
`ordinary skill would have been motivated to incorporate the irregularity disclosed
`
`in MacKay into Ping’s code.” Pet at 39. But as demonstrated above (see Section
`
`III.A.1), Ping’s parity check matrix already 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 11. See, e.g., Pet. at 51 (“Ping’s outer LDPC
`
`coder is regular.”), 41 (“Ping’s outer LDPC code is regular because each column in
`
`
`with Ex. 1004, ¶¶ 114-15; compare Pet. at 27-28, with Ex. 1004, ¶ 71; compare
`
`Pet. at 42-43, with Ex. 1004, ¶¶ 117-19); see Kinetic Techs., Inc. v. Skyworks
`
`Solutions, 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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`-14-
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`

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`Ping’s generator matrix Hd contains the same number of 1s—exactly ‘t’ 1s.”).
`
`Thus, Ping 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 III.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
`
`-15-
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`

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`by varying the column weights in Ping’s parity check matrix, but addresses only a
`
`portion of the parity check matrix H. Pet. at 42. 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 42), 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.
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`-16-
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`

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`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
`
`terminology. Pet. at 42. 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 11.
`
`The 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 39. 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
`
`-17-
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`
`

`

`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.”).
`
`The further combination of Divsalar 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. Accordingly, Divsalar does 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 and Divsalar fails to disclose the
`additional limitations of dependent claim 12
`
`Claim 12 recites “wherein the encoder is configured to generate the
`
`collection of parity bits as if a number of inputs into nodes vi was not constant.”
`
`Petitioner asserts that “MacKay teaches claim 12’s additional ‘not constant’
`
`-18-
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`

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`limitation” (Pet. at 58); 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.
`
`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 57
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`(quoting Ping as teaching a fixed number (kt/(n-k)) of 1s per row); see also id. at
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`62 (suggesting a modification of Ping to arrive at the recited claim elements). The
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`petition further states that “varying the row weight of Ping’s Hd matrix would
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`make the number of inputs into the check nodes variable, as required by claim 3.”
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`Id. at 61. Accordingly, the Petition turns to MacKay for this limitation.
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`Because Petitioner again misinterprets the teachings of MacKay, Petitioner
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`mistakenly concludes that the “nonuniform row weight” for a parity check matrix
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`mentioned by MacKay corresponds to a “nonuniform row weight” of Hd, which is
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`only a portion of a parity check matrix. Because MacKay only discusses a parity
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`check matrix as a whole, it provides no teaching or suggestion of modifying the Hd
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`portion of Ping’s parity check matrix.
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`-19-
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`

`

`As with the nonuniform column weight discussed above in regard to claim
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`11, the difference between nonuniform row weight of Hd and nonuniform row
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`weight of H is illustrated by the fact that although Hd has uniform row weight, H
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`does not. See also Ex. 2001 ¶¶32-36.
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`Ping discloses that Hd has a constant column weight of t and row weight of
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`kt/(n-k). Ex. 1003 at 38. The row weight of Hd is thus constant, and determined by
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`the code’s rate (i.e, the ratio of the number of information bits to the number of
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`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
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`total weight of each row indicated:
`
`
`In other words, Ping discloses a parity check matrix with different numbers of ones
`
`per row—i.e., different row weights. In particular, the first row has weight
`
`
`(cid:14)(cid:15)
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`(cid:3)(cid:16)(cid:17)(cid:14)(cid:6)(cid:18)1 and the remaining rows have weight (cid:14)(cid:15)(cid:3)(cid:16)(cid:17)(cid:14)(cid:6)(cid:18)2. The variable row
`
`-20-
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`
`

`

`weights, however, reflects variability in the row weights of Hp, not that there is
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`variability of the row weights of Hd.
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`Accordingly, as illustrated above, Ping’s parity check matrix H has different
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`row weights. Thus, MacKay’s discussion of “nonuniform row weights” describes a
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`property that Ping’s parity check matrix already has, and which Petitioner admits
`
`does not satisfy claim 3.
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`Petitioner’s attempt to apply MacKay’s “nonuniform row weights” to Hd
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`(see Pet. at 61-62) repeats the errors discussed above in Section III.A.2, and so
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`should be disregarded for similar reasons.
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`Furthermore, the petition fails to establish a motivation to combine MacKay
`
`and Ping with regard to this limitation. While Petitioner asserts that introducing
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`nonuniform row weights in Hd “would have been straightforward for a person of
`
`ordinary skill” (Pet. at 61), Petitioner does not give any reason that a person of
`
`ordinary skill would have been motivated to make such a change. Because the
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`petition has not provided any reason why a person of ordinary skill would have
`
`implemented the modification proposed, it has failed to demonstrate the alleged
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`obviousness of claim 12.
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`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 12.
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`-21-
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`

`

`IV. GROUND 2 FAILS
`
`The petition fails to demonstrate that claim 13 would have been obvious
`
`over the combination of Ping in view of MacKay, Divsalar, and Luby97 as asserted
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`in Ground 2. The Board should reject Ground 2 at least on the basis that Ping,
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`MacKay, and Divsalar fail to disclose all of the elements of claim 11, from which
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`claim 13 depends, and Petitioner fails to present sufficient motivation to combine
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`Ping and MacKay, as explained above for Ground 1. Petitioner presents Luby97 in
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`this ground only for the limitation in claim 13 relating to a “data stream.” Pet. at
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`65-66, 69. Petitioner does not assert that Luby97 cures the deficiencies of Ping,
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`MacKay, and Divsalar discussed above in Ground 1. Accordingly, Petitioner’s
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`Ground 2 fails.
`
`A.
`
` Ping fails to teach “a low-density generator matrix (LDGM)
`coder” as recited in claim 13
`
`Ground 2 additionally fails for failure to demonstrate that Ping discloses
`
`encoding with a low-density generator matrix, as recited in claim 13. Petitioner
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`argues that Ping’s Hd submatrix is a low-density generator matrix on the basis that
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`Hd is “a very low density matrix.” Pet. at 68.
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`Regardless of whether Hd is low-density, Ping never identifes Hd as a
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`generator matrix. Ping only ever identifies Hd as a portion of a “parity check
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`matrix H.” Ex. 1003 at 38. Petitioner simply assumes, without sufficient
`
`explanation or support, that Hd is a generator matrix because one of its rows
`
`-22-
`
`
`

`

`appears in Ping’s Equation (4). See Pet. at 42 (asserting that “[b]ecause Ping’s
`
`Equation (4) uses the Hd matrix to produce parity bits from information bits, it is a
`
`‘generator matrix.’”). Petitioner cites to Ping as allegedly supporting the assertion,
`
`but Ping only discloses using Hd as part of a calculation involving parity bits, not
`
`using Hd as a “generator matrix.” See Ex. 1003 at 38. The mere fact that part of Hd
`
`is used when calculating parity bit values does not make Hd a generator matrix.5
`
`Furthermore, the petition’s own discussion of generator matrices adds
`
`confusion as it contradicts Petitioner’s identification of Hd as a generator matrix.
`
`The petition defines a generator matrix as a matrix that generates a codeword x
`
`from a set of information bits. See Pet. at 13-14. However, the Hd portion of the
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`parity check matrix of Ping fails to generate a codeword x from a set of
`
`information bits. No codeword at all is generated by the Hd portion of the parity
`
`check matrix of Ping; it instead “generates” a vector of length n-k (i.e., the number
`
`of parity bits). For instance, for a code such as Ping’s with n codeword bits
`
`generated from k information bits, a generator matrix G (as defined by Petiti