U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`
`
`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 7,421,032
`_________________________________________
`
`PETITIONER’S REPLY TO PATENT OWNER’S RESPONSE
`
`
`
`
`
`
`
`
`Apple v. California Institute of Technology
`
`
`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 7,421,032
`_________________________________________
`
`PETITIONER’S REPLY TO PATENT OWNER’S RESPONSE
`
`
`
`
`
`
`
`
`
`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`TABLE OF CONTENTS
`
`
`I.
`
`INTRODUCTION ........................................................................................... 2
`
`II.
`
`ARGUMENT ................................................................................................... 2
`
`A.
`
`Caltech Fails to Overcome Petitioner’s Showing that the
`
`Challenged Claims are Obvious ............................................................ 2
`
`1.
`
`Claims 11, 12, and 14-16 are Obvious in view of Ping,
`
`MacKay, and Divsalar ................................................................ 2
`
`2.
`
`Claim 13 is Obvious in view of Ping, MacKay, Divsalar,
`
`and Luby97 ............................................................................... 20
`
`3.
`
`Caltech Fails To Establish A Nexus Between Its Alleged
`
`Objective Evidence Of Non-Obviousness And The
`
`Claimed Invention ..................................................................... 21
`
`B.
`
`Caltech Mischaracterizes The Testimony Of Professor Davis ........... 24
`
`III. CONCLUSION .............................................................................................. 27
`
`
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`- 1 -
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`
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`I.
`
`INTRODUCTION
`
`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`
`Caltech’s Patent Owner Response (“POR”) repeats arguments that the Board
`
`has already rejected and fails to rebut Petitioner’s showing that the challenged
`
`claims are unpatentable. First, Caltech mischaracterizes the teachings of the Ping
`
`and MacKay references. Second, Caltech has failed to demonstrate secondary
`
`considerations of non-obviousness. Finally, Caltech mischaracterizes the testimony
`
`of Petitioner’s expert, Prof. Davis.
`
`II. ARGUMENT
`A. Caltech Fails to Overcome Petitioner’s Showing that the
`Challenged Claims are Obvious
`1.
`
`Claims 11, 12, and 14-16 are Obvious in view of Ping, MacKay,
`and Divsalar
`
`The Petition showed that Ping in view of MacKay and Divsalar renders claims
`
`11, 12, and 14-16 obvious. Caltech’s arguments about the combination are incorrect
`
`for at least the reasons below.
`
`i.
`
`Contrary to Caltech’s Argument, MacKay teaches
`that information bits appear in a variable number of
`subsets
`
`Caltech’s suggestion that it is unclear in MacKay whether a column of the
`
`parity check matrix corresponds to an information bit or a parity bit is incorrect.
`
`(POR, 22.) To even attempt to make this argument, Caltech must ignore MacKay’s
`
`actual disclosure. MacKay teaches profiles, e.g., 93y, that correspond to parity
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`check matrices. (Ex. 1002, 1450.) Those matrices have uneven column weights.
`
`For example, as shown in MacKay’s Figure 2, in 93y matrices, most columns have
`
`weight three but some columns have weight nine. MacKay also teaches that codes
`
`with such parity check matrices, i.e., matrices with uneven column weights, can
`
`outperform their regular counterparts. (Ex. 1065, ¶¶20-24.)1
`
`Caltech only attempts to contend that the correspondence between
`
`information bits and the columns of a parity check matrix may be unclear in some of
`
`MacKay’s parity check matrices (e.g., profile 93y). Caltech does not (and cannot)
`
`dispute that this correspondence is perfectly clear in other disclosed matrices (e.g.,
`
`profile 193y). In particular, in Figures 5 and 6, MacKay states that the first K
`
`columns (all columns to the left of the diagonal) correspond to information bits. (Ex.
`
`1002, 1452 (“Bits t1 … tK are defined to be source bits.”).) As shown in profile 193y,
`
`some of these information bits correspond to columns with weight nine and others
`
`correspond to columns with weight three, i.e., some information bits appear in nine
`
`subsets and others appear in three subsets. MacKay’s Figures 5 and 6 thus clearly
`
`teach that information bits appear in a variable number of subsets. Using those
`
`1 After submitting his declaration, Dr. Davis relocated to Europe pursuant to a
`
`Fulbright Global Scholar Award. (Ex. 1073, ¶2.) As a result, he was unavailable to
`
`work on the Reply. (Id.) Petitioner’s Reply is instead supported by the Declaration
`
`of Dr. Frey.
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`weightings in Ping results in information bits appearing in variable numbers of
`
`subsets (i.e., either nine or three) as claimed. (Ex. 1065, ¶¶20-24.)
`
`ii.
`
`Even if MacKay’s Irregular Column Weights Could
`Be Limited As Caltech Contends, Its Argument Would
`Still Fail
`
`Caltech argues that MacKay’s columns with uneven weight could all
`
`correspond to parity bits such that the columns corresponding to information bits all
`
`had the same weight. (POR, 21.) By Caltech’s incorrect logic, that would result in
`
`MacKay – standing alone – failing to teach that information bits appear in a variable
`
`number of subsets. (Id.)
`
`Caltech’s argument is false for the reasons demonstrated in Part A(1)(i) above.
`
`But even if it were true, Caltech’s argument would still fail because it ignores the
`
`combination of MacKay’s column weight teaching with Ping’s unambiguous
`
`teaching that all columns in its Hd matrix represent information bits. (Ex. 1065,
`
`¶25.)
`
`The Petition showed, and the Board agreed, that a POSA would have been
`
`motivated to use MacKay’s uneven column weights in Ping’s Hd matrix (or outer
`
`coder) to improve the performance of Ping’s code. (DI, 13-19.) Doing so would
`
`have resulted in information bits appearing in a variable number of subsets, which
`
`corresponds exactly to some information bits contributing to more parity bits than
`
`others. This is true even if all of MacKay’s uneven column weights corresponded to
`
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`parity bits. That is, applying MacKay’s fundamental teaching—that use of matrices
`
`with uneven column weights can outperform codes with evenly weighted
`
`matrices—to Ping’s Hd matrix causes information bits to appear in a variable
`
`number of subsets. Therefore, even if Caltech’s false premise were correct, and
`
`neither Ping nor MacKay alone teaches that information bits appear in a variable
`
`number of subsets, the combination of Ping in view of MacKay would teach that
`
`limitation and therefore render the claims obvious. (Ex. 1065, ¶¶25-27.)
`
`Each column of Ping’s Hd matrix corresponds to an information bit. The
`
`weight of a column of the Hd matrix, i.e., the number of ones appearing in that
`
`column, equals the number of subsets in which the information bit appears (and
`
`correspondingly equals the number of parity bits to which the information bit
`
`contributes). Therefore, using MacKay’s uneven column weights in Ping’s Hd
`
`matrix would have resulted in some information bits appearing in more subsets than
`
`others as claimed.2 Caltech does not dispute this. Instead, Caltech merely addresses
`
`the disclosure of Ping alone and MacKay alone. (POR, 19-25.) Thus, Petitioner’s
`
`showing stands unrebutted. (Ex. 1065, ¶¶25-27.)
`
`
`2 Also, as explained below, repeating some information bits more than others was, in
`
`view of Divsalar, an obvious way to implement having some information bits
`
`contribute to more parity bits than others.
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`iii. Caltech fails to overcome Petitioner’s showing that a
`POSA would have been motivated to combine Ping
`and MacKay
`
`Caltech repeats the argument it made in its Preliminary Response (“POPR”)
`
`that Ping is already irregular and therefore a POSA would not have been motivated
`
`to use MacKay’s irregularity in Ping. (POR, 26; POPR, 12-14.) The Board has
`
`already correctly rejected this argument and should do so again for at least the
`
`reasons in the Petition and DI. (DI, 13-19.) (Ex. 1065, ¶27.)
`
`Caltech then goes on to argue that Ping is even more irregular than MacKay so,
`
`again, a POSA supposedly would not have been motivated to use MacKay’s
`
`irregularity in Ping. (POR, 28.) To make this argument, Caltech is reduced to
`
`presenting a contrived example of Ping’s parity check matrix that is neither
`
`discussed in Ping nor the Petition. (POR, 28.) Specifically, whereas Ping discloses
`
`a matrix in which t=4,3 Caltech’s example changes this variable to set t=9. In that
`
`case, half the columns in the parity check matrix would have weight 9. In the other
`
`half, all but one would have weight 2 and the one remaining column would have
`
`weight 1. (POR, 28.) The non-zero differences in column weights for this contrived
`
`matrix are either 7 or 8 (i.e., 9 minus 2 or 9 minus 1). Dr. Mitzenmacher’s
`
`computation of “variance” is based solely on this contrived matrix with t=9. (Ex.
`
`3 Ping refers to the number of 1s in a column as the “column weight” and uses the
`
`variable “t” to refer to it. (Petition, 32.)
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`2038, 330:10-18, 331:14-21.) And Caltech relies solely on this same contrived t=9
`
`matrix to incorrectly argue that Ping is more irregular than MacKay. (Ex. 1065,
`
`¶¶28-29.)
`
`Of course, Ping does not state that t=9. Instead, in Ping’s disclosed matrix t=4.
`
`Half of Ping’s columns have weight 4 and, in the other half, all but one of the
`
`columns have weight 2 and the one remaining column has weight 1. In Ping’s
`
`disclosed matrix, the non-zero differences in column weights are thus either 2 or 3
`
`(i.e., 4 minus 2 or 4 minus 1). In MacKay’s matrices, where the weights are either 9
`
`or 3, the non-zero difference between column weights is 6 (i.e., 9-3). Thus, the
`
`difference in column weights in MacKay’s matrix (6) is twice as large as any
`
`difference in the matrix Ping actually discloses, and is three times as large as the
`
`most common difference. Only by arbitrarily setting t=9 was Caltech able to
`
`contrive an example in which the difference in column weights in Ping would
`
`exceed the difference in column weights of MacKay. (Ex. 1065, ¶¶28-30.)
`
`Further, Caltech’s comparison of Ping’s H matrix to MacKay’s is improper.
`
`Ping teaches a randomly generated parity matrix H, which is decomposed into “H =
`
`[Hp, Hd].” (Ex. 1003, 38.) The proper comparison is between Ping’s Hd matrix (in
`
`which all columns have the same weight) and MacKay’s matrix. The Board already
`
`recognized this. (DI, 13-19.) Even Caltech acknowledges that the other portion of
`
`Ping’s matrix, Hp, can have only a single form. (POR, 27.) Specifically, Hp
`
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`corresponds to an accumulator, which can be implemented simply and cheaply. A
`
`POSA would not have been motivated to modify Hp because, as Caltech notes, it has
`
`only a single form and because doing so would have complicated a simple encoder.
`
`A POSA would not have considered the use of an accumulator such as Hp to make
`
`codes irregular. In summary, a POSA who wanted to obtain the benefit of
`
`MacKay’s irregularity in Ping would have had only one option—to incorporate
`
`MacKay’s irregularity into Hd. Doing so would have been simple, and a POSA
`
`would have been motivated to do so to obtain the benefit of MacKay’s irregularity
`
`(which MacKay itself instructs will improve code performance) in Ping. (Ex. 1065,
`
`¶¶27-30.)
`
`Caltech argues that the Ping, MacKay and Divsalar references do not contain
`
`any Tanner graphs and therefore do not meet the claimed Tanner graph limitations.
`
`(POR, 19-20.) Caltech is incorrect. As explained in the Petition, parity check
`
`matrices and Tanner graphs are interchangeable ways of representing the same code.
`
`(Petition, 18.) Caltech’s own expert concedes that he “can’t think of an example” of
`
`a parity check matrix that cannot be expressed as a Tanner graph. (Ex. 2038 at
`
`9:19-12:15.) (Ex. 1065, ¶31.)
`
`Ping and MacKay both describe their codes in terms of parity check matrices.
`
`Even assuming, as Caltech asserts, that none of Ping, MacKay, or Divsalar expressly
`
`shows a Tanner graph, a POSA would have understood that the codes disclosed by
`
`- 8 -
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`the references have corresponding Tanner graphs. Thus, Caltech’s assertion is
`
`irrelevant. The Petition explained in detail how the art teaches the claimed Tanner
`
`graph. (Petition, 47-57.) The drawings below show Tanner graphs corresponding to
`
`Ping’s code and a code described in MacKay’s profile 93y.
`
`
`
`
`
`
`
`Ex. 1048
`
`Ex. 1049
`
`When questioned about these drawings, Dr. Mitzenmacher conceded that they show
`
`Tanner graphs of Ping’s and MacKay’s codes, respectively. Indeed, the only
`
`objection Dr. Mitzenmacher was able to raise was that the random permutation is
`
`not entirely random and is instead constrained. (Ex. 2038, 426:11-428:2.) (Ex. 1065,
`
`¶32.)
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`The similarity of these Tanner graphs illustrates the similarity, and
`
`combinability, of Ping’s and MacKay’s codes. As shown, both Ping’s code and
`
`MacKay’s code connect message nodes (open circles on the left) to check nodes
`
`(grey circles on the right) via a random permutation. Ping’s coder includes the extra
`
`step shown at the right side of the Tanner graph, which corresponds to Ping’s
`
`accumulating Hp matrix, or outer coder. The left sides of the Tanner graphs are
`
`similar, i.e., they both include message nodes and a random permutation. However,
`
`whereas Ping’s message nodes all have degree four (i.e., four edges intersect each
`
`node), MacKay’s do not, i.e., some nodes have degree three and others have degree
`
`nine. It would have been obvious for a POSA to use MacKay’s irregular degree
`
`profile in Ping by making the degree of Ping’s d nodes irregular. Making the degree
`
`of the d nodes in Ping’s Tanner graph uneven corresponds exactly to making the
`
`column weights of Hd uneven. (Ex. 1065, ¶33.)
`
`Caltech also argues that Ping’s Hd matrix does not correspond to an outer
`
`code and that Ping’s encoding is not performed in two steps. (POR, 35-36.) Caltech
`
`is incorrect. As the Petition explains, Ping discloses two stages of encoding.
`
`(Petition, 27-32.) Indeed, Ping explicitly states its H matrix is a combination of two
`
`sub-matrices, Hd and Hp, such that H = [Hp, Hd]. (Ex. 1003, 38.) Ping’s two-step
`
`encoding, as modified to use Divsalar’s repetition and MacKay’s irregularity, can be
`
`depicted graphically as shown below. (Petition, 39-45.)
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`
`Exhibit 1072
`
`
`
`(Ex. 1065, ¶¶33-35.)
`
`As shown, a repeater repeats incoming information bits irregularly and stores
`
`the irregularly repeated bits in a shift-register. As an example, bit i1 is shown as
`
`having been repeated three times and bit i2 is shown as having been repeated nine
`
`times. Other information bits are also repeated, e.g., such that each information bit
`
`is repeated either three or nine times. Once the information bits have all been
`
`repeated, XOR gates combine them to produce new combined bits, which are stored
`
`in registers shown highlighted yellow, pink and purple. In this example, each such
`
`bit equals the sum of two repeated information bits. This matches Ping’s example of
`
`a rate 1/3 code, in which each new bit is the sum of exactly two information bits.
`
`(Petition, 67.) (Ex. 1065, ¶36.)
`
`The ones in each row of Hd determine which information bits are summed to
`
`produce a particular bit, e.g., with the top row of Hd corresponding to the XOR gate
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`that feeds the yellow register and the last row of Hd corresponding to the XOR gate
`
`that feeds the purple register. If a row of Hd had more than two ones, such that more
`
`than two bits were summed to produce a new combined bit, the corresponding XOR
`
`gate would be generalized to a multi-bit mod-2 adder. (Ex. 1065, ¶36.)
`
`In Exhibit 1072, each bit of the shift-register drives only a single gate, which
`
`would have been an obvious choice both due to the ease of implementing repeating
`
`with Divsalar’s repeater and to avoid having any of the shift register outputs driving
`
`more inputs than it was capable of driving. Once the new combined bits have been
`
`produced, they are shifted into the inner coder, which is an accumulator, and which
`
`produces the final output parity bits. The recursive nature of Ping’s equations would
`
`have encouraged a POSA to implement Ping as an outer coder followed by an inner
`
`coder as shown in Exhibit 1072.4 (Ex. 1065, ¶37.)
`
`4 Exhibit 1071 depicts another way to incorporate MacKay’s irregularity in Ping.
`
`The implementations shown in Exhibit 1071 and Exhibit 1072 both would have been
`
`obvious. The implementation shown in Exhibit 1071 can be flexibly programmed to
`
`implement all possible versions of Hd. The implementation shown in Exhibit 1072
`
`implements only one specific version of Hd, i.e., because the combinations used to
`
`form the outer coder parity bits are hard-wired into connections between XOR gates
`
`and the shift register. The Exhibit 1072 implementation is therefore less flexible,
`
`but is also simpler. A POSA would have found either implementation obvious and
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`MacKay’s irregularity in Exhibit 1072 is incorporated in Ping by having the
`
`repeater repeat the bits irregularly, e.g., repeating some bits three times and other
`
`bits nine times. This is how a POSA would have understood Ping’s encoder to work
`
`as well as an encoder for the combination of Ping, MacKay, and Divsalar. Ping’s Hd
`
`matrix represents an encoding and a POSA would have been motivated to use
`
`MacKay’s irregularity, or uneven weights, to obtain the benefits of MacKay’s
`
`improved performance in Ping. (Ex. 1065, ¶38.)
`
`Caltech incorrectly argues that Ping’s statements at page 38 regarding
`
`memory use teach away from such an implementation. But Ping’s statement about
`
`memory use relates to memory required to store the parity check matrix. This
`
`implementation does not use any memory to store Hd. Instead, the constraints
`
`imposed by Hd are reflected in the connections between the XOR gates and
`
`shift-register. Also, no memory is used to store Hp because it is implemented as a
`
`simple accumulator. (Ex. 1065, ¶39.)
`
`Caltech also incorrectly argues that Ping teaches away from the combination
`
`with MacKay. (POR, 31-34.) As shown in Equation (3), Ping divides Hd into t
`
`sub-blocks. Ping randomly places ones within those sub-blocks such that each
`
`column of each sub-block contains a single one, which results in each column of Hd
`
`would have selected one or the other, or some other obvious variant, suitable for an
`
`application.
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`having t ones. In the combination of Ping and MacKay, instead of each column of
`
`Hd having the same number of ones, some columns contain more than others. But
`
`nothing about the combination with MacKay prevents the ones from still being
`
`distributed and randomly placed. For example, in the modification suggested in the
`
`Petition where some columns have weight nine and others have weight three, Hd can
`
`be divided into nine sub-blocks, such that the columns with weight nine have a one
`
`in every column of every sub-block and the columns with weight three have a one in
`
`only three of the sub-blocks. In both the original Ping and in the proposed
`
`combination, the structure of Hp is fixed. In the combination, Hd has uneven column
`
`weights. That is the point of the combination, and a POSA would have been
`
`motivated to make that change to obtain the benefit of MacKay. (Ex. 1065, ¶40.)
`
`Caltech also incorrectly complains that the Petition does not sufficiently
`
`describe how a POSA would have modified Ping in view of MacKay or that a POSA
`
`would have had a reasonable expectation of success in doing so. (POR, 40-49.) In
`
`fact, the Petition explains that a straightforward modification of Ping’s Hd matrix
`
`would set “some columns to weight 9 and others to weight 3, as taught by MacKay.”
`
`(Petition, 42.) A POSA would have needed no more specificity to attempt to use
`
`MacKay’s irregularity in Ping. As conceded in Caltech’s POR, rigorous
`
`mathematical analysis of codes is difficult, and, as a result, POSAs routinely develop
`
`codes by experimentation. (POR, 4-5.) For a POSA, running experimental tests on
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`a version of Ping that incorporated MacKay’s irregularity would have been routine.
`
`Indeed, for a POSA who had implemented Ping’s code, the modifications suggested
`
`by MacKay would have been straightforward and would have taken very little time
`
`to implement. Also, MacKay’s teaching that the best Gallager codes are irregular
`
`would have encouraged a POSA to perform such tests. (Ex. 1065, ¶41.)
`
`The diagram below shows the results of tests comparing Ping’s original code
`
`against two versions where Ping’s Hd matrix was modified to use MacKay’s
`
`irregularity as discussed above. The vertical axis shows bit error rate (BER), while
`
`the horizontal axis shows signal to noise ratio (Eio/No (dB)), such that code
`
`performance improves as you move down and to the left.
`
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
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`Results Showing Improved BER for Irregular Codes of Ping + MacKay as
`compared with Regular Code of Ping Alone
`
`
`(Ex. 1068; Ex. 1065, ¶¶42-56.)
`
`The right-most trace on this graph plots the results from Ping’s original code.
`
`The two plots on the left show the results from modifying Ping’s Hd matrix to
`
`incorporate MacKay’s irregularity. One of the irregular versions has Hd column
`
`weights of either nine or three, and the other has Hd column weights of four, five or
`
`nine. As shown, both versions of Ping that incorporate MacKay’s irregularity
`
`substantially outperform Ping’s original code (e.g., with BER reduced by up to
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`approximately 10-4 at a given signal-to-noise ratio). Such results confirm that a
`
`POSA would have been motivated to use MacKay’s uneven column weights in
`
`Ping’s Hd matrix, and that a POSA would have had a reasonable expectation of
`
`success when doing so. (Ex. 1068; Ex. 1065, ¶¶42-56.)
`
`Exhibit 1068 shows the source code used to generate these results. As shown
`
`in the exhibit, the source code is short and simple, and would not have been difficult
`
`for a POSA to generate. Exhibit 1068 also shows the performance of Ping’s original
`
`code using the same source code. Exhibit 1068 matches the performance shown in
`
`Ping’s Figure 1, demonstrating that the simulation is accurate. (Ex. 1065, ¶¶42-56.)
`
`Caltech also argues that adding irregularity will not always improve a code,
`
`and argues that one of Prof. Davis’ examples would not have led to a performance
`
`improvement. (POR, 45.) That is irrelevant. Irregularity need not always result in
`
`improvement for a POSA to be encouraged to use it. MacKay’s teaching that the
`
`best known Gallager codes are irregular was sufficient to motivate a POSA to
`
`attempt to use irregularity in Ping’s code. (Ex. 1065, ¶57.)
`
`Caltech also disputes Petitioner’s showing that it would have been obvious for
`
`a POSA to use the Divsalar’s repeater in Ping’s code. (POR, 49.) Caltech is
`
`incorrect. (Petition, 43-45.)5 Additionally, as shown above with Exhibit 1072,
`
`5 The Petition notes that repeaters were common in the prior art, identifying Frey (Ex.
`
`1010) as one such example. The POR improperly tries to incorporate its attempt to
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`using Divsalar’s repetition in Ping would have been obvious and simply involved
`
`repeating input bits at the outer coder as shown in Fig. 3 of Divsalar. Thus, contrary
`
`to Caltech’s suggestion, Ping is easily modified to repeat information bits as shown
`
`in Divsalar. (Ex. 1065, ¶38.)
`
`iv. Caltech fails to overcome Petitioner’s showing that
`MacKay discloses nonuniform row weights
`
`Patent Owner argues that MacKay fails to teach the nonuniform row weights
`
`limitation of claim 12. (POR, 25-26.) That certain exemplary profiles in MacKay’s
`
`drawings have uniform row weights does not detract from MacKay’s express
`
`teaching of nonuniform row weights. (Ex. 1002, 1449 (“The irregular codes of
`
`Luby, Mitzenmacher, Shokrollahi, and Spielman [5] have parity check matrices with
`
`both nonuniform weight per row and nonuniform weight per column.”) (emphasis
`
`added.)) Moreover, MacKay’s instructions for creating an irregular code clearly
`
`require the selection of “the desired number of rows of each weight.” (Ex. 1002,
`
`1449-1450.) Caltech does not address this teaching. MacKay’s focus on
`
`
`antedate Frey from IPR2017-00210. (POR, 51.) To the extent the Board considers
`
`this attempt to antedate Frey, Petitioner notes it fails for the reasons set forth in its
`
`Reply in the same proceeding. (See also Exs.
`
`.) Regardless,
`
`Caltech does not dispute that repeaters were common in the prior art, only whether
`
`Petitioner’s illustrative examples qualify as prior art. (POR, 51.)
`
`- 18 -
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`experimentation with nonuniform column weights does not negate MacKay’s
`
`disclosure of nonuniform row weights. Regarding row weights, only two options
`
`exist: uniform row weights and nonuniform row weights. That coupled with
`
`MacKay’s explicit reference to nonuniform row weights renders them obvious. (Ex.
`
`1065, ¶58.)
`
`Caltech also repeats its argument that Petitioner has not shown a motivation to
`
`combine MacKay’s nonuniform row weight with Ping. A POSA would have been
`
`motivated to use nonuniform row weights given the superior performance of
`
`irregular codes disclosed by MacKay. Furthermore, as Caltech concedes, POSAs
`
`routinely develop codes through experimentation. (POR, 4-5.) MacKay itself is
`
`directed to experimenting with irregularity and methods of constructing irregular
`
`codes with high performance. (Ex. 1002,1449 (“[t]he excellent performance of
`
`irregular Gallager codes is the motivation for this paper”).) MacKay’s teaching that
`
`the best Gallager codes – i.e., codes using low density parity check matrices – are
`
`irregular would have encouraged a POSA to perform such experiments using
`
`nonuniform row weights. Thus, Caltech’s claim that there is no rationale for
`
`combining MacKay’s teaching of nonuniform row weights is unfounded. (Ex. 1065,
`
`¶59.)
`
`Furthermore, as Dr. Frey demonstrated, a POSA would have been able to
`
`easily perform tests that combined MacKay’s irregularity with Ping using both
`
`- 19 -
`
`
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`uniform and nonuniform row weights, both of which outperform the original Ping
`
`code. Dr. Frey simulated versions of Ping, modified to use MacKay’s irregularity,
`
`with uniform row weight (RW=5) and non-uniform row weight (RW= 4, 5, and 8).
`
`As shown in the simulation results reproduced above, both outperformed Ping’s
`
`original regular code with uniform row and column weight. (Ex. 1068; Ex 1065,
`
`¶¶42-56.)
`
`2.
`
`Claim 13 is Obvious in view of Ping, MacKay, Divsalar, and
`Luby97
`
`Caltech repeats the argument made in its POPR challenging Petitioner’s
`
`showing that Ping’s Hd submatrix is a low-density generator matrix (“LDGM”).
`
`(POR, 54; POPR, 22-23.) As the Board noted in its Institution Decision, the issue is
`
`“not whether the reference expressly uses the term low-density generator matrix or
`
`identifies matrix Hd as such,” but whether the references teach the limitations of
`
`claim 6 to a POSA. (DI, 21.) The Board went on to find that Petitioner had met its
`
`burden regarding claim 13. (DI, 21.) The POR fails to identify any reasons why the
`
`Board should reach a different conclusion now and simply repeats its POPR
`
`argument that attempts to contrast Ping’s Hd matrix with Petitioner’s background
`
`discussion of generator matrices. (POR, 53; POPR, 22.) (Ex 1065, ¶60.)
`
`As the Petition explains, Ping discloses two stages of encoding. (Petition,
`
`27-32.) In Ping’s first stage, summations are computed. (Id.) Each of those
`
`summations equals a row of Hd times the vector of information bits. (Id.) In other
`- 20 -
`
`
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`words, the vector of Ping’s summations equals Hd times the vector of information
`
`bits. Hd therefore meets the definition of a generator matrix. Also, as explained in
`
`the Petition, the vast majority of entries of Hd are zeroes. (Id., 67-68.) Hd is
`
`therefore also “low density,” i.e., it is a low density generator matrix. (Ex 1065,
`
`¶60.)
`
`3.
`
`Caltech Fails To Establish A Nexus Between Its Alleged
`Objective Evidence Of Non-Obviousness And The Claimed
`Invention
`
`The Federal Circuit has explained that “[f]or objective evidence of secondary
`
`considerations to be accorded substantial weight, its proponents must establish a
`
`nexus between the evidence and the merits of the claimed invention.” Merck & Cie
`
`v. Gnosis S.P.A., 808 F.3d 829, 837 (Fed. Cir. 2015) (citation omitted). Here,
`
`Caltech fails to establish such a nexus.
`
`Caltech’s nexus argument rests entirely on its contention that the DVB-S2
`
`standard practices the claimed invention. (POR, 55-58.) It does not. Judge Pfaelzer
`
`of the Central District of California addressed this issue in her summary judgment
`
`opinion. (Ex. 1067.) She expressly rejected the very argument Caltech presents
`
`here through its expert, Dr. Mitzenmacher—i.e., that the DVB-S2 standard practices
`
`- 21 -
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`
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`U.S. Patent No. 7,421,032
`Apple v. California Institute of Technology
`claim 1.6 She explained that “Caltech has not shown that DVB-S2 technology
`
`repeats information bits…as the asserted claims require” because the DVB-S2
`
`standard calls for “the reuse of a single information bit in the creation of multiple
`
`parity bits.” (Ex. 1067, *4.) Judge Pfaelzer further explains that, contrary to what
`
`the claims require, the DVB-S2 documentation “seems to assign specific
`
`information bits to contribute to specific parity bits” rather than randomly choosing
`
`the information bits that contribute to parity bits. Id. (Ex 1065, ¶¶61-65.)
`
`Caltech presents no evidence beyond what was available to Judge Pfaelzer.
`
`Its expert, Dr. Mitzenmacher, relies solely on evidence regarding the DVB-S2
`
`standard itself (Ex. 2004, ¶¶141-149); he admits that he did not review any actual
`
`implementation of the DVB-S2 standard. (Ex. 2038, 443:17-445:10.) (Ex 1065,
`
`¶¶61-65.)
`
`Without the requisite nexus to the challenged claims, Caltech’s objective
`
`evidence is entitled to no weight. See Merck, 808 F.3d at 837.
`
`i.
`
`Long-Felt Need and Failure of Others
`
`Caltech’s suggestion that IRA codes represent the endpoint of the
`
`development of certain error correction codes is false. (POR, 58-60).
`
`6 Although Judge Pfaelzer did not analyze claim 11, Caltech argues that DVB-S2
`
`“practices claim 11 for the same reasons Dr. Mitzenmacher discusses with respect to
`
`claim 1.”
`
`- 22 -
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`
`
`
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