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`Paper No. ___
`Filed: November 21, 2017
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`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 RESPONSE
`PURSUANT TO 37 C.F.R. § 42.120
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`

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`TABLE OF CONTENTS
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`Dr. Davis’s evasiveness during his deposition undermines his
`
`STATEMENT OF PRECISE RELIEF REQUESTED .................................. 1
`I.
`INTRODUCTION AND OVERVIEW OF ARGUMENT ............................ 1
`II.
`III. OVERVIEW OF THE ART AND CITED REFERENCES .......................... 4
`A. MacKay (EX1102) .............................................................................. 6
`B.
`Ping (EX1103) .................................................................................... 7
`C.
`Divsalar (EX1117) .............................................................................. 9
`IV. WEIGHT TO BE GIVEN RESPECTIVE EXPERT TESTIMONY ............ 10
`A. Dr. Davis’s testimony includes basic errors demonstrating a
`lack of credibility .............................................................................. 10
`B.
`Dr. Davis’s testimony is not independent .......................................... 12
`C.
`credibility.......................................................................................... 12
`V.
`CLAIM CONSTRUCTION ........................................................................ 14
`“irregular” ......................................................................................... 14
`A.
`VI. GROUND 1: PING IN VIEW OF MACKAY IN FURTHER VIEW
`AND 4-10 OBVIOUS ................................................................................. 15
`A.
`Legal Principles ................................................................................ 16
`B.
`irregular repetition ............................................................................ 18
`C.
`generator matrix as required by claim 6 ............................................ 22
`D.
`non-systematic code as required by claim 9 ...................................... 22
`E.
`MacKay ............................................................................................ 24
`1. Ping is already irregular as defined by MacKay ............................. 24
`2. The proposed modification would eliminate Ping’s stated
`improvement ................................................................................. 29
`3. Petitioner’s additional arguments regarding motivation to
`combine fail .................................................................................. 32
`
`OF DIVSALAR AND LUBY 97 DOES NOT RENDER CLAIMS 1
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`Petitioner fails to establish that either Ping or MacKay discloses
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`Petitioner fails to establish that Ping discloses a low-density
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`Petitioner fails to explain how Ping could be modified to be a
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`A POSA would not be motivated to modify Ping in view of
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`-i-
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`Petitioner fails to Provide a Rationale to Further Modify Ping
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`4. Dr. Davis’s claim that MacKay’s irregularity is ill-defined
`indicates a lack of motivation to combine ..................................... 36
`F.
`Petitioner inadequately defines its proposed modification ................. 38
`G. Modifying Ping in view of MacKay would not be expected to
`succeed. ............................................................................................ 42
`H.
`and MacKay in view of Divsalar ....................................................... 47
`VII. OBJECTIVE INDICIA OF NON-OBVIOUSNESS.................................... 51
`A. Nexus between the Objective Evidence and the Claims .................... 52
`Long-felt need and failure of others .................................................. 55
`B.
`C.
`Industry Praise .................................................................................. 57
`D. Unexpected Results........................................................................... 59
`E.
`Commercial Success ......................................................................... 60
`VIII. CONCLUSION .......................................................................................... 62
`IX. APPENDIX ................................................................................................ 65
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`-ii-
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`

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`I.
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`STATEMENT OF PRECISE RELIEF REQUESTED
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`Apple, Inc. (“Petitioner”) filed a petition for inter partes review of various
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`claims of U.S. Patent No. 7,421,032 (the “’032 patent”, EX1101). The patent
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`owner (“Caltech”) hereby requests that the Board now issue a final written
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`decision rejecting confirming that claims 1 and 4-10 are not unpatentable.
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`II.
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`INTRODUCTION AND OVERVIEW OF ARGUMENT
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`The ’032 patent is one of four Caltech patents that resulted from research
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`performed by the inventors, Dr. Jin, Dr. Khandekar, and Dr. McEliece, in 1999-
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`2000. The patents claim inventions directed to a revolutionary class of error-
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`correction codes, dubbed “irregular repeat and accumulate codes,” or “IRA codes,”
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`which surpassed the performance of the best known codes at that time. One of the
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`features that made IRA codes superior to other known codes, however, was their
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`capability of being encoded and decoded with linear complexity, a critical
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`requirement for most practical applications. No other code known at the time
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`could boast linear encoding, linear decoding, and performance near the theoretical
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`Shannon limit.
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`In arguing that the instituted claims are unpatentable, Petitioner relies chiefly
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`on three prior art references: the MacKay reference, which discloses randomly
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`generated parity-check matrices (which are “irregular” in the sense that 11 of 12
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`columns are weight 3 and 1 of 12 columns are weight 9), the Ping reference, which
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`-1-
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`describes a method of improving random parity-check matrices of the type
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`described by MacKay by imposing certain structural constraints to the matrix, and
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`the Divsalar reference, which describes an altogether different kind of code: a
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`simple “turbo-like” code created for the purpose of proving a mathematical
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`conjecture.
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`Petitioner’s obviousness challenges are lacking in many respects. In
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`ascribing motivation to combine the asserted references, Petitioner attempts to take
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`MacKay’s teachings about nonuniform column weights in a full parity-check
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`matrix and apply it to only a part of Ping’s parity-check matrix. Yet nothing in
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`MacKay teaches the propriety of applying a general aspect of a full matrix to
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`merely a part of a matrix in a different code. Indeed, Ping’s parity-check matrix as
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`a whole is already “irregular” (in fact, more “irregular”) according to MacKay’s
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`teachings, and neither reference provides any motivation to add more irregularity
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`to part of the matrix, as Petition proposes. To the contrary, Petitioner’s proposed
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`combination ignores and destroys fundamental constraints of Ping’s codes imposed
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`explicitly for performance reasons. Ping’s code is presented as an improvement
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`over random parity-check matrices like those in MacKay, and modifying it in light
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`of MacKay would have been viewed as a step backwards. There would simply be
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`no motivation to modify Ping in light of the fact it already achieves what MacKay
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`-2-
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`teaches, and the proposed modification would eliminate the very improvements
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`Ping proposes.
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`The petition is further flawed in its proposal to modify Ping’s Hd submatrix
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`by “setting some columns to weight 9 and others to weight 3.” Pet. 40. Aside
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`from the fact that MacKay does not teach such a modification, Petitioner fails to
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`specifically describe how such a modification would be accomplished for
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`generating a workable code. Among other things, Petitioner provides no guidance
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`as to which columns should be modified, how many should be modified, and how
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`such a modification would maintain the constraints taught by Ping and MacKay.
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`Petitioner’s failure to provide any meaningful detail regarding its proposed
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`modification underscores the lack of any plausible motivation to combine with a
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`reasonable expectation of success. A POSA would have known that error-
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`correcting codes were an unpredictable field of endeavor and that merely
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`combining elements from different codes could not be expected to succeed, yet
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`nowhere in the petition is expectation of success addressed. Petitioner ignores this
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`critical requirement of an obviousness inquiry under Graham v. John Deere, and
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`the challenge can be rejected for this reason alone.
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`Furthermore, objective indicia of nonobviousness weigh heavily in favor of
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`nonobviousness. The IRA encoding and decoding methods and systems described
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`and claimed in the ’032 patent were a groundbreaking development in the field of
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`-3-
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`coding theory. The invention overcame longstanding issues with previously
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`known error correcting codes in a way that was unexpected, has been widely
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`praised since its introduction, and has experienced commercial success by others
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`through adoption in numerous information transmission standards.
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`For these reasons, all of the remaining grounds of challenge must be denied.
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`III. OVERVIEW OF THE ART AND CITED REFERENCES
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`Modifying or constructing error-correction codes was a highly unpredictable
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`endeavor. Since it was effectively impossible to mathematically prove the
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`performance of a code, researchers were forced to engage in extensive trial-and-
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`error and experimentation to determine whether new codes led to an improvement.
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`Even when improvements occurred, the reasons for improved performance were
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`typically not well-understood. EX2004, ¶46. As Petitioner’s expert conceded
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`during cross-examination:
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`What you would really like to be able to do is a formal
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`mathematical analysis of the strength of the codes that
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`you are working with, but that’s often really hard. So
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`often what the engineers in particular would do is … take
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`a variety of different [codes], run simulations and … then
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`I will get a general sense of what the [mathematical]
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`analysis would have shown me. … [I]t might even be
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`impossible to do the mathematical analysis.
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`-4-
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`EX2033 at 256:21-257:12 (emphasis added). Caltech’s expert, Dr. Mitzenmacher,
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`likewise explains that discoveries had to be made via guesswork and
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`experimentation. EX2004, ¶46. As a result, it was rarely the case that a researcher
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`could reasonably predict that a particular modification would result in an
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`improvement in the performance of a code. Id.
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`Experiments showed that the performance of a code was highly dependent
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`on the specific properties and constraints of the code. These codes did not have
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`interchangeable parts, where a property of a performant code could simply be
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`incorporated into other codes to improve them. Instead, such chimeras could end
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`up being nonfunctioning. Id.
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`One example of this unpredictability is illustrated in the discovery of the
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`classes of codes found in the cited prior art references: turbo codes and low-density
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`parity-check codes. Turbo codes were discovered by Claude Berrou in 1993, and
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`his discovery was met with skepticism because he could not explain why his code
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`performed. Many believed he had made an error in his initial experiments. Yet
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`after his results were independently confirmed, research and use of his turbo codes
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`became widespread. (EX2004, ¶¶47-51)
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`LDPC codes, which are often viewed as a competitor to turbo codes, also
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`had a modest beginning. LDPC codes were first discovered by Dr. Robert
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`Gallager in 1963, but largely remained ignored for over 35 years. That such codes
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`-5-
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`performed well was surprising to those skilled in the art. Dr. Gallager himself
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`explains the unpredictability of this field with regard to his code, “I had a little bit
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`of an inkling [they could be good], but I also had a suspicion that they well might
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`not be. And I spent a long time trying to resolve whether they were or not.”
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`(EX2004, ¶¶52-56)
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`A. MacKay (EX1102)
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`MacKay highlights the unpredictability in the field at the time and the
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`corresponding need for experimentation to
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`identify functioning codes. MacKay
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`investigated performance of irregular Gallager
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`codes, a class of codes defined by randomly
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`generating low-density parity-check matrices that were “irregular,” which
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`according to MacKay meant that the columns of the parity-check matrices had
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`nonuniform weights. EX1102, p. 1449. Specifically, MacKay’s irregular codes
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`had 1/12 of the columns had a weight of nine, and the remaining 11/12 columns
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`had weight of 3. EX1102, Table 1; see also Fig. 2 (excerpt shown). MacKay
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`randomly generated several parity-check matrices using patterns with the above
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`constraints and according to a generalized Poisson distribution. See e.g., EX1102,
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`p. 1451 (“The edges are placed ‘completely at random’.”). MacKay then ran
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`simulations to test performance of the constructions. Such experimentation was
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`-6-
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`

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`necessary because mathematical analysis would not have been able to predict
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`whether the constructions improved performance. (EX2004, ¶57)
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`MacKay’s codes were divided into sub-classes (i.e., Poisson, sub-Poisson,
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`super-Poisson patterns) and MacKay, based on its testing, reported that “super-
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`Poisson” patterns performed better than the other patterns. MacKay noted that a
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`number of the randomly generated codes exhibited high error floors and had to be
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`discarded. EX1102, p. 1452 (“We discard the two codes with error floors…”).
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`MacKay explains that such error floors were the result of “cycles of length 4,”
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`whose avoidance “is not so easy to enforce in irregular Gallager codes with high
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`weight columns.” Id., p. 1454; see also, id. p. 1449 (acknowledging that
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`performance is “sensitive to the distribution of column weights.”). MacKay did
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`not provide any of the actual codes used in its evaluation of Poisson patterns.
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`(EX2004, ¶58)
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`B.
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`Ping (EX1103)
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`Ping describes a method of improving Gallager codes with random parity-
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`check matrices, such as those described by MacKay, by introducing specific non-
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`random structural constraints to the parity-check matrix, because encoding codes
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`with random matrices was “costly in terms of both memory and the operations
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`involved.” EX1103, p. 38. (EX2004, ¶59)
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`-7-
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`Ping instructs that, first, the columns of the parity-check matrix H be
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`constructed as two submatrices: submatrix Hp and submatrix Hd, each of which
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`have a specifically defined structure. Id. With regard to Hp, Ping teaches it is a
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`deterministic square matrix populated as follows:
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`
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`With regard to Hd, Ping instructs that it be subdivided into “t equal sub-blocks,”
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`where t is “a preset integer constrained by (i) t divides n-k and (ii) n-k divides kt”
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`(n is the length of the codeword and k is the number of information bits). Id. Hd
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`appears as follows:
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`
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`For each of these sub-blocks, there is exactly “one element 1 per column and kt/(n-
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`k) 1s per row.” Id. This means that the submatrix Hd has both uniform column
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`and row weight, and the 1s are evenly distributed within the submatrix. Ping
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`explains that these constraints for Hd are necessary because they “best increase the
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`recurrence distance of each bit in the encoding chain … and, intuitively, reduce[]
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`the correlation during the decoding process.” Id. In other words, Ping specifically
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`identifies its uniform distribution of Hd as an improvement over random parity-
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`-8-
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`

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`check matrices like those found in MacKay. See also, id., p. 39 (“Conclusion: It
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`has been shown that a semi-random approach to LDPC code design can achieve
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`essentially the same performance as the existing method with considerably reduced
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`complexity.”) (EX2004, ¶¶60-63)
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`C. Divsalar (EX1117)
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`The Divsalar reference describes the work of Dr. Dariush Divsalar, along
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`with two of the inventors of the ’032 patent (Dr. McEliece and Dr. Jin), in
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`developing a repeat accumulate (RA) code. EX2031 ¶ 16-32.
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`RA codes as taught in Divsalar are nonsystematic codes, meaning that only
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`the encoded codeword bits (parity bits) are transmitted. RA codes always perform
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`regular repetition of information bits and every repeated bit in an RA code is
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`separately accumulated to generate a new parity bit.1 At a rate of 1/q (where q is
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`the amount of repetition), RA codes are impractically slow. Indeed, Dr. Divslar
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`explains that the codes were never intended to be competitive error-correction
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`codes, nor would they have been mistaken as such—they were designed as a
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`research tool for learning about certain characteristics of turbo codes and similar
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`codes. EX2031 ¶ 27, 28, 32; EX2004 ¶ 58.
`
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`1 In contrast, subsets of information bits in IRA codes are summed, and the
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`sums are then accumulated. As a result of these differences, IRA codes exhibit
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`significantly better performance than RA codes.
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`-9-
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`

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`Additionally, Divsalar did not analyze RA codes using parity-check matrices
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`or Tanner graphs, because at the time of the invention of the ’032 patent, such an
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`analysis would not have been common: turbo codes and LDPC codes were viewed
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`as two distinct types of codes using different approaches to code design and
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`analysis. EX2031 ¶26; EX2004 ¶¶ 54-56.
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`IV. WEIGHT TO BE GIVEN RESPECTIVE EXPERT TESTIMONY
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`A. Dr. Davis’s testimony includes basic errors demonstrating a lack
`of credibility
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`Basic technical errors are an important clue to witness credibility. See, e.g.,
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`Merck & Co. v. Teva Pharm. USA, Inc., 347 F.3d 1367, 1371 (Fed. Cir. 2003)
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`(noting chemist made errors that those in the art would have considered basic).
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`Here, Dr. Davis could not answer basic questions about Berrou, the seminal paper
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`on turbo codes, without rereading the entire article. EX2033, 54:17-60:3. He
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`could not give an opinion on what “irregular” meant in the field, and implied such
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`information was unhelpful to the Board. Id., 87:7-89:16.
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`With regard to Ping and MacKay, Dr. Davis inaccurately testified that
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`MacKay’s “super-Poisson” pattern was consistent with Ping’s teaching of
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`“increas[ing] the recurrence distance.” Ping teaches that its Hd submatrix is
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`designed to “best increase the recurrence distance of each bit” (EX1103, p. 38),
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`which means “spread[ing] your 1s around.” EX2033, 233:7. Yet Dr. Davis
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`incorrectly testified that “MacKay teaches in this same direction, when he is
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`-10-
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`talking about sub-Poisson, super-Poisson, Poisson ways of constructing parity-
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`check matrices.” Id., 233:14-17. MacKay actually teaches the opposite, that its
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`best-performing “super-Poisson constructions” have a “distribution of high weight
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`columns per row [with] greater variance” (EX1102, p. 1451)—in other words, the
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`1s in MacKay’s super-Poisson construction are more clustered instead of spread
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`out. See infra, Section V.E; EX2004, ¶128.
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`His unfamiliarity with the actual teachings of cited references,2 as well as
`
`with the actual knowledge in the relevant art, compels him to use hindsight to
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`define irregularity in terms of Caltech’s claims. The testimony of Dr. Davis should
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`be discounted accordingly.3
`
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`2 As explained in Caltech’s POR in IPR2017-00210, Dr. Davis’s testimony
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`includes basic errors with many of the references he assessed.
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`3 Dr. Davis’s unfamiliarity with the key references should also be considered in
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`view of his admission that none of his publications related to repeat-accumulate
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`codes, low-density parity-check codes, turbo codes, or irregular codes in general.
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`EX2033, 27:4-28:9. Unsurprisingly, he never attended the Allerton Conference on
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`Communication, Control and Computing because “the work that I do in coding
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`theory wasn’t being presented at that conference.” Id., 32:14-22.
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`-11-
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`B. Dr. Davis’s testimony is not independent
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`While the petition and expert declaration are expected to be consistent,
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`expert testimony that simply tracks and repeats the petition is entitled to little
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`weight. Wowza Media Sys., LLC v. Adobe Sys., Inc., IPR2013-00054, Paper 16, 4
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`(2013). The petition and the Davis declaration are essentially identical in language.
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`For example, the sections discussing Ground 1 are nearly identical. Compare Pet.,
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`37-74, with EX1104, ¶¶103-201. This significantly undercuts the independence
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`and objectivity of Dr. Davis’s testimony.
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`C. Dr. Davis’s evasiveness during his deposition undermines his
`credibility
`
`In 10X Genomics, Inc. v. Univ. of Chicago, the Board explained that expert
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`evasiveness or unresponsiveness during cross examination would reduce the
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`weight of the expert’s direct testimony. IPR2015-01157, Paper 30, 2 (2016). Dr.
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`Davis evaded straightforward questions about the art that an artisan of the time
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`should have been able to give straightforward answers. For example, he evaded
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`questions on whether Berrou’s Figure 5 showed a relationship between bit error
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`rate and signal-to-noise ratio despite the axes being clearly labeled as such. Id.,
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`56:19-57:6, 58:19-59:3.
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`Regarding “irregular,” a key term in this trial, he evaded answering whether
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`his definition of irregular was the conventional meaning in the field of error-
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`correction codes. Id., 66:10-68:4. He evaded answering where the prior art
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`-12-
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`provided a definition of “irregular” that was the same as his definition. Id., 72:17-
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`75:18. He avoided answering what definition of “irregular” he would use in the
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`field of error-correction codes generally. Id., 78:18-81:12. He avoided answering
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`whether his definition of “irregular” was consistent with the definition used with
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`Tanner graphs. Id., 83:21-87:6. His unresponsiveness during cross-examination on
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`this pivotal term warrants that his direct testimony be given little or no weight.
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`He also avoided answering where MacKay expressly discloses irregular
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`repetition of information bits (it does not). Id., 249:2-251:21. And he was evasive
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`on the self-evident question of whether Ping depicts a Tanner graph (it does not).
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`Id., 269:21-272:12.
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`The contrast between cross-examination and redirect is also striking.
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`Redirect occurred after a break during which Dr. Davis had a “discussion about the
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`substance of the testimony and the general nature of the redirect” with Apple’s
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`counsel. Id., 275:9-13. This discussion enabled Dr. Davis to be far more responsive
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`and direct for Apple’s counsel. This witness behavior is precisely the sort of
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`behavior the Board has condemned in decisions like 10X Genomics. The
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`appropriate response is to accord little or no weight to the direct and redirect
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`testimony of Dr. Davis.
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`-13-
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`

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`V. CLAIM CONSTRUCTION
`
`A claim subject to inter partes review receives the broadest reasonable
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`construction or interpretation in light of the specification of the patent in which it
`
`appears (“BRI”). See 37 C.F.R. § 42.100(b); Cuozzo Speed Techs., LLC v. Lee, 136
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`S. Ct. 2131, 2142-45 (2016). However, the Board may not construe a term “so
`
`broadly that its constructions are unreasonable under general claim construction
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`principles.” Microsoft Corp. v. Proxyconn, Inc., 789 F.3d 1292, 1298 (Fed. Cir.
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`2015).
`
`A.
`
` “irregular”
`
`Claim 1 requires that a portion of the claimed formula “is the value of a sum
`
`of ‘a’ randomly chosen irregular repeats of the message bits. Claim 5 requires “the
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`number of repeats for each message bit is irregular.” Petitioner proposes that the
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`term “irregular” be construed as “the notion that different message bits or groups
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`of message bits contribute to different numbers of parity bits.” Pet. 23-24. Caltech
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`does not believe the term needs to be construed, as the plain and ordinary meaning
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`of irregular repetition is clear. That message bits contribute in differing numbers
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`to parity bits is made clear in the claim language. (EX2004, ¶69)
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`In addition, one should be aware that the prior art’s use of the term
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`“irregular” differs from Petitioner’s proposed construction. The prior art defines
`
`an “irregular code” as having “parity-check matrices [that] have nonuniform
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`-14-
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`

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`weight per column.” EX1102, p. 1449; see also EX1109, p. 249 (“[R]andom
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`irregular bipartite graphs, which we call irregular codes.”). The prior art is
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`referring to a relationship between codeword bits (which might not even include
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`message bits) and parity-check equations, whereas the proposed construction refers
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`to a relationship between message bits and parity bits. As discussed below, regular
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`repetition can lead to nonuniform parity-check matrices, and irregular repetition
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`can lead to (nearly) uniform parity-check matrices. An “irregular code” as
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`understood in the prior art is distinct from the “irregular” repeat Petitioner seeks to
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`construe. (EX2004, ¶70)
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`VI. GROUND 1: PING IN VIEW OF MACKAY IN FURTHER VIEW OF
`DIVSALAR AND LUBY 97 DOES NOT RENDER CLAIMS 1 AND 4-
`10 OBVIOUS
`
`Petitioner fails to demonstrate that claims 1 and 4-10 would have been
`
`obvious in view of the combination of Ping, MacKay, Divsalar and Luby97 for at
`
`least the following reasons. First, Petitioner fails to demonstrate that Ping and
`
`MacKay teach irregular repetition. Second, for claim 6, Petitioner fails to show a
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`disclosure of a low-density generator matrix. Third, for claim 9, Petitioner fails to
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`explain how Divsalar’s non-systematic code would be incorporated into Ping.
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`Fourth, Petitioner fails to establish that a POSA would have been motivated by
`
`MacKay to incorporate nonuniform weights into Ping’s submatrix because
`
`MacKay’s teachings are only applicable to full parity-check matrices and Ping’s
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`-15-
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`

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`full parity-check matrix is already as nonuniform as MacKay’s irregular codes.
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`And Ping expressly teaches modifying the random codes of the type disclosed in
`
`MacKay so as to impart the specific structure the proposed modification seeks to
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`destroy. Fifth, Petitioner’s proposed modification is not taught anywhere in
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`MacKay. Sixth, Petitioner’s proposed modification lacks specificity. Seventh,
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`Petitioner fails to address, let alone establish, that its proposed combination of Ping
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`and MacKay would have any reasonable expectation of succeeding, a requirement
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`when proving obviousness. Eighth, a POSA would not have been motivated to
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`further modify Ping in view of Divsalar, and Petitioner fails to explain how that
`
`modification would be made and whether there would be a reasonable expectation
`
`of success. For these reasons, Ground 1 should be rejected. (EX2004, ¶¶67-132)
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`A. Legal Principles
`
`In order to establish that a patent claim is obvious under 35 U.S.C. § 103,
`
`one must first determine (1) the scope of the prior art, (2) differences between the
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`prior art and the claims at issue, and (3) the level of ordinary skill in the art—
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`“Against this background, the obviousness or nonobviousness of the subject matter
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`is determined,” with additional “secondary considerations” given to certain indicia
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`of nonobviousness. KSR Intern. Co. v. Teleflex Inc., 550 U.S. 398, 404 (2007)
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`(citing Graham v. John Deere Co., 383 U.S. 1, 17-18 (1950)). Those challenging a
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`claim must provide some articulated reasoning that includes identifying “a reason
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`that would have prompted a person of ordinary skill in the relevant field to
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`combine the elements in the way the claimed new invention does.” Id.
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`Importantly, it is also a petitioner’s burden to show that at the time of the
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`invention there was a “reasonable expectation of success” for the proposed
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`combination. Intelligent Bio-Sys. v. Illumina Cambridge, 821 F.3d 1359, 1367-68
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`(Fed. Cir. 2016) (challenger’s “burden to demonstrate … that the skilled artisan
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`would have had a reasonable expectation of success in [combining the
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`references].”); see also DePuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567
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`F.3d 1314, 1326 (Fed.Cir.2009); MPEP § 2143.2.I (“Obviousness requires a
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`reasonable expectation of success”). Thus, merely identifying elements in the prior
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`art is not sufficient to establish obviousness—a POSA must have reasonably
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`expected that the combination would have succeeded for its intended purpose.
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`Based on these principles, the Board must deny obviousness challenges
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`when a petitioner, as is the case here, fails to explain or provide evidence as to how
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`the proposed combination would predictably result in the improvement that
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`allegedly motivated the combination. JTEKT Corp. v. GKN Automotive, Ltd.,
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`IPR2016-00046, Paper No. 27 at 28-29.
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`B.
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`Petitioner fails to establish that either Ping or MacKay discloses
`irregular repetition
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`Claim 1 requires “irregular repeats of the message bits.” Petitioner does not
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`establish that either reference discloses irregular repetition. (EX2004, ¶¶152, 78-
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`87)
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`Petitioner acknowledges that Ping fails to disclose irregular repetition. See,
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`e.g., Pet. 52. (EX2004, ¶79)
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`Similarly, Petitioner fails to show where MacKay discloses irregular
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`repetition. In Petitioner’s analysis of the claim language, the only reference to
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`MacKay’s irregularity is its teaching that “[t]he best known binary Gallager codes
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`are irregular codes whose parity-check matrices have nonuniform weight per
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`column.” Pet. 53 (quoting EX1102, p. 1449). However, these column weights do
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`not refer to repetition of information bits. Indeed, Dr. Davis even recognized that
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`MacKay’s “93 variations don’t give any sense of what the encoding would be for
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`the code that is associated to that.” EX2033 at 300:5-6. Moreover, that citation to
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`MacKay refers to nonuniformity across the entire matrix. As discussed below,
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`Ping’s parity-check matrix already has nonuniform column weights, and there is
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`nothing in MacKay that suggests modifying a part of a matrix. (EX2004, ¶80)
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`Petitioner also asserts, without support, that the column weights in
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`MacKay’s parity-check matrix show that “different information bits contribute to
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`different numbers of parity bits.” Id. 42. But the columns in MacKay’s parity-
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`check matrices correspond to both information bits and parity bits. Petitioner does
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`not identify any teaching in MacKay that applies nonequal column weights to the
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`information bits specifically. To the contrary, MacKay’s irregularity is applied to
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`the entire parity-check matrix. Dr. Davis even recognized that MacKay’s parity-
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`check matrices “don’t give any sense of what the encoding would be for the code
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`that is associated to that.” EX2033 at 300:5-6. Accordingly, Petitioner fails to
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`show how MacKay discloses “irregular repeats of the message bits.” (EX2004,
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`¶¶81-83)
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`Petitioner misinterprets MacKay’s teachings by claiming that “MacKay
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`teaches matrices where each information bit corresponds to a column, and where
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`the weight of that column … represents the degree of the information bit.” Pet. 39;
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`(quoting EX1102, p. 1450). As an initial matter, Petitioner fails to establish that
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`this citation to MacKay refers to a systematic code. In a non-systematic code,
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`none of the columns corresponds to information bits. Even for systematic codes,
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`however, a parity-check matrix alone does not allow a POSA to determine which
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`columns (if any) correspond to information bits, or conclude anything about the
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`treatment of information bits, much less that they “contribute to different numbers
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`of parity bits,” as Petitioner contends. Indeed, the citations to MacKay do not even
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`identify specific parity-check matrices, but only describe generalized
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`“constructions” used as a template for generating random matrices. (EX2004,
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`¶¶84-85)
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`MacKay’s definition of “irregular codes”—which is used to describe the
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`structure of a parity-check matrix, unlike Petitioner’s proposed construction—
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`further confirms that the reference does not teach irregular repetition of
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`information bits. Petitioner defines “irregular codes” as codes where “different
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`information bits or groups of information bits contribute to different numbers of
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`parity bits,” which as explained above is different than MacKay’s definition. 4 Pet.
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`18. Even Dr. Davis would not testify that Petitioner’s definition is the
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`conventional definition