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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
`
`Claim Language
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`Analysis
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`Claim 1
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`
`
`[1] A method of encoding a signal,
`comprising:
`
`To the extent this preamble is construed to be limiting, the Accused Products practice a
`method of encoding a signal.
`
`For example, the Accused Products implement the IEEE Standards, which provide a
`method of encoding a signal.
`
`For example, the IEEE 802.11n-2009 amendment to the IEEE 802.11-2007 standard and
`the IEEE 802.11-2012 version of the 802.11 standard include “low-density parity check
`(LDPC) encoding.”
`
`IEEE 802.11n-2009 at § 5.2.9; IEEE 802.11-2012 at § 4.3.10; IEEE 802.11-2020 at
`§ 4.3.13 (emphasis added).
`
`
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`SAMSUNG EXHIBIT 1018
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
`
`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at § 7.3.2.56.2; IEEE 802.11-2012 at § 8.4.2.58.2; IEEE 802.11-2020
`at § 9.4.2.55 (emphasis added).
`
`IEEE 802.11n-2009 at Table 7-43j; see also IEEE 802.11-2012 at Table 8-124; IEEE
`802.11-2020 at Table 9-184.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
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`IEEE 802.11n-2009 at § 9.6.0e.5.5; IEEE 802.11-2012 at § 9.7.6.5.5; IEEE 802.11-2020 at
`§ 10.6.6.5.7 (emphasis added).
`
`IEEE 802.11n-2009 at § 9.6.0e.7; IEEE 802.11-2012 at § 9.7.6.7; IEEE 802.11-2020 at
`§ 10.6.6.7 (emphasis added)
`
`LDPC coding was incorporated into the IEEE 802.11 standard via the 802.11n-2009
`amendment. In general, the following sections of 802.11n discuss LDPC coding: § 9.7f,
`§ 20.3.11.6, Annex G at sections G.2 and G.3 and Annex R.
`
`IEEE 802.11n-2009 at § 9.7f; see also IEEE 802.11-2012 at § 9.14; IEEE 802.11-2020 at
`§ 10.15.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`* * *
`
`IEEE 802.11n-2009 at Table 20-1; IEEE 802.11-2012 at Table 20-1; IEEE 802.11-2020 at
`Table 19-1 (emphasis added).
`
`IEEE 802.11n-2009 at § 20.3.3 (emphasis added); see also IEEE 802.11-2012 at § 20.3.3;
`IEEE 802.11-2020 at § 19.3.3
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Fig. 20-3; IEEE 802.11-2012 at Fig. 20-3; IEEE 802.11-2020 at
`Fig. 19-3 (emphasis added)
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`* * *
`
`* * *
`
`IEEE 802.11n-2009 at § 20.3.4 (emphasis added); see also IEEE 802.11-2012 at § 20.3.4;
`IEEE 802.11-2020 at § 19.3.4.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`* * *
`
`IEEE 802.11n-2009 at § 20.3.9.4.3, Table 20-10; see also IEEE 802.11-2012 at Table 20-
`11; IEEE 802.11-2020 at Table 19-11.
`
`IEEE 802.11n-2009 at § 20.3.11 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.1; IEEE 802.11-2020 at § 19.3.11.1.
`
`
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`
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`
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`IEEE 802.11n-2009 at § 20.3.11.3 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.4; IEEE 802.11-2020 at § 19.3.11.4.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at § 20.3.11.6.1 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7; IEEE 802.11-2020 at § 19.3.11.7.
`
`* * *
`
`* * *
`
`IEEE 802.11n-2009 at Table 20-23; see also IEEE 802.11-2012 at Table 20-24; IEEE
`802.11-2020 at Table 19-24.
`
`* * *
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Table 20-27 (emphasis added); see also IEEE 802.11-2012 at Table
`20-28.
`
`
`
`* * *
`
`
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`
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`IEEE 802.11n-2009 at Annex A, § A.4.19.2; see also IEEE 802.11-2012 at Annex B,
`§ B.4.19.2; IEEE 802.11-2020 at Annex B, § B.4.17.2.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`IEEE 802.11ax-2021 at Annex B, § B.4.33.2.
`
`See also IEEE 802.11n-2009 at § 20.3.11.6.3, Annex G, Annex R; IEEE 802.11-2012 at
`§ 20.3.11.7.3, Annex L, Annex F; IEEE 802.11-2020 at § 19.3.11.7.3, Annex I, Annex F.
`
`The Very High Throughput (“VHT”) PHY specification of the IEEE 802.11ac-2013
`amendment to the IEEE 802.11-2012 standard, which uses LDPC coding, is based on and
`incorporates the LDPC coding used in the High Throughput (“HT”) PHY, as defined in
`Clause 20 of the IEEE 802.11-2012 standard.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`IEEE 802.11ac-2013 at § 22.1.1 (emphasis added).
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`IEEE 802.11ac-2013 at § 22.3.10.5.4 (emphasis added).
`
`The High Efficiency (“HE”) PHY specification of the IEEE 802.11ax-2021 amendment to
`the IEEE 802.11-2020 standard, which uses LDPC coding, is based on and incorporates
`the LDPC coding used in the High Throughput (“HT”) PHY, as defined in Clause 19 of the
`IEEE 802.11-2020 standard.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`IEEE 802.11ax-2021 at § 27.1.1 (emphasis added).
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
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`
`
`
`
`IEEE 802.11ax-2021 at § 27.3.12.5.2 (emphasis added).
`
`On information and belief, products made or sold by Samsung that implement the IEEE
`Standards do so in such a way that infringes this limitation. To the extent that Samsung
`contends that their LDPC encoding and/or decoding implementations do not literally
`infringe the limitations of this claim, such differences are insubstantial and thus the claim
`limitations are satisfied under the doctrine of equivalents.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
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`[1a] receiving a collection of message
`bits having a first sequence in a source
`data stream;
`
`The Accused Products receive a collection of message bits having a first sequence in a
`source data stream.
`
`For example, the Accused Products implement the IEEE Standards, which receive a
`collection of message bits having a first sequence in a source data stream.
`
`For example, the process of LDPC-encoding a signal per IEEE 802.11 includes receiving a
`collection of message bits having a first sequence in a source data stream. The IEEE
`802.11 LDPC codes are block codes. Each source data stream to be encoded, e.g. an
`MPDU from the MAC layer, is divided into one or more collections of message bits as
`shown in Table 20-14.
`
`\
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at § 20.3.11.6.2 (emphasis added); see also 802.11-2012 at
`§ 20.3.11.7.2; 802.11-2020 at § 19.3.11.7.2.
`
`
`
`IEEE 802.11n-2009 at § 20.3.11.6.3 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7.3; IEEE 802.11-2020 at § 19.3.11.7.3.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Figure 20-13; see also IEEE 802.11-2012 at Figure 20-13; IEEE
`802.11-2020 at Figure 19-13.
`
`Annex G of IEEE 802.11n-2009 and Annex L of IEEE 802.11-2012 and Annex I of IEEE
`802.11-2020 provide examples of how a collection of message bits in the source data
`stream is received.
`
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
`
`IEEE 802.11n-2009 at Annex G, § G.2.1; see also IEEE 8022.11-2012 at Annex L,
`§ L.2.1; IEEE 802.11-2020 at Annex I, § I.2.2.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`* * *
`
`IEEE 802.11n-2009 at Annex G, § G.2.5; see also IEEE 802.11-2012 at Annex L, § L.2.5;
`IEEE 802.11-2020 at Annex I, § I.2.6.
`
`See also IEEE 802.11n-2009 at Annex G, § § G.3.1, G.3.5; IEEE 802.11-2012 at Annex L,
`§ L.3.1, L.3.5; IEEE 802.11-2020 at Annex I, § I.3.2, I.3.6.
`
`
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`IEEE 802.11n-2009 at Figure 20-20 (emphasis added); see also IEEE 802.11-2012 at
`Figure 20-22; IEEE 802.11-2020 at Figure 19-22.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Fig. 20-3; IEEE 802.11-2012 at Fig. 20-3; IEEE 802.11-2020 at
`Fig. 19-3 (emphasis added)
`
`Further, the message bits have a first sequence. More specifically, the sequence of the
`message bits is defined as having a first sequence as part of the specification of the
`systematic code. Each LDPC codeword is of the form c=(i0,i1,…, i(k-1),p0,p1,…,p(n-k-1)),
`where the message bits have a first sequence a listed from i0 to i(k-1). The subscripts 0 to k-1
`specify the individual message bits and index their order.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`
`
`IEEE 802.11n-2009 at § 20.3.11.6.3 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7.3; IEEE 802.11-2020 at § 19.3.11.7.3.
`
`As discussed above, the message bits are taken from (and thus “in”) a “source data
`stream.” The data stream is passed through to the MAC layer and then subsequently to the
`PHY layer. The PHY layer contains an LDPC encoder that receives the source data stream
`and then parses the data stream into blocks of message bits that are processed to generate a
`sequence of LDPC codewords. The 802.11 specification specficially describes how to take
`the message bits from the source data stream and parse the message bits into groups of
`message bits with specific first sequences. “A succession of LDPC codewords” results
`from LDPC encoding of the “message bits” in the “source data stream.” See, e.g., 802.11n-
`2009 at § 20.3.11.6.2-6; 802.11-2012 at § 20.3.11.7.2-6; 802.11-2020 at § 19.3.11.7.2-6.
`
`IEEE 802.11n-2009 at § 20.3.11.6.6 (emphasis added); see also IEEE802.11-2012 at
`§ 20.3.11.7.6; IEEE 802.11-2020 at § 19.3.11.7.6.
`
`On information and belief, products made or sold by Samsung that implement the IEEE
`Standards do so in such a way that infringes this limitation. To the extent that Samsung
`contends that their LDPC encoding and/or decoding implementations do not literally
`
`
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`infringe the limitations of this claim, such differences are insubstantial and thus the claim
`limitations are satisfied under the doctrine of equivalents.
`
`For example, to the extent that Samsung contends that their LDPC encoding and/or
`decoding implementations do not literally infringe because they do not receive a “stream”
`of bits, e.g., because they receive a “block” of bits, the Accused Products would infringe
`under the doctrine of equivalents even if the Court were to adopt an unduly narrow
`interpretation of “stream” (when in reality “stream” and “block” are not mutually
`exclusive) because the Accused Products receive a sequence of information bits to be
`encoded. Whether the bits are received as a stream or as a block under such an
`interpretation is an insubstantial difference, particularly because even if bits are received as
`a stream, they must be formed into a block for LDPC encoding. Thus, both scenarios
`accomplish substantially the same function of obtaining data to be encoded, in
`substantially the same way, i.e., receiving bits of data to form a block to be encoded, and
`accomplish substantially the same result of preparing data for encoding by the LDPC
`encoder.
`
`The Accused Products generate a sequence of parity bits, wherein each parity bit “xj” in
`the sequence is in accordance with the formula 𝑥𝑗 = 𝑥𝑗−1 + ∑ 𝑣(𝑗−1)𝑎+𝑖
`, where “xj-l” is
`=1
`the value of a parity bit “j-l,” and ∑ 𝑣(𝑗−1)𝑎+𝑖
` is the value of a sum of “a” randomly
`=1
`chosen irregular repeats of the message bits.
`
`𝑎𝑖
`
`𝑎𝑖
`
`For example, the Accused Products implement the IEEE Standards, which generate a
`sequence of parity bits, wherein each parity bit “xj” in the sequence is in accordance with
`the formula 𝑥𝑗 = 𝑥𝑗−1 + ∑ 𝑣(𝑗−1)𝑎+𝑖
`, where “xj-l” is the value of a parity bit “j-l,” and
`=1
`∑ 𝑣(𝑗−1)𝑎+𝑖
` is the value of a sum of “a” randomly chosen irregular repeats of the
`=1
`message bits.
`
`𝑎𝑖
`
`𝑎𝑖
`
`The use of LDPC coding requires the generation of parity bits. The LDPC codes are
`systematic codes wherein each codeword is formed by combining the message bits with
`parity bits.
`
`[1b] generating a sequence of parity
`bits, wherein each parity bit “xj” in the
`sequence is in accordance with the
`formula
`
`𝑎
`𝑥𝑗 = 𝑥𝑗−1 + ∑ 𝑣(𝑗−1)𝑎+𝑖
`𝑖=1
`
`
`
`where
`
` “xj-l” is the value of a parity bit “j-l,”
`and
`
`𝑎
`∑ 𝑣(𝑗−1)𝑎+𝑖
`𝑖=1
`
`
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`is the value of a sum of “a” randomly
`chosen irregular repeats of the message
`bits; and
`
`IEEE 802.11n-2009 at § 20.3.11.6.3 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7.3; IEEE 802.11-2020 at § 19.3.11.7.3.
`
`For example, the LDPC encoder outputs a codeword “c” of size “n” that includes “k”
`information bits and “n-k” parity bits. The bits p0 through p(n-k-1) are the a “sequence of
`parity bits.”
`
`IEEE 802.11n-2009 at § 20.3.11.6.6 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7.6; IEEE 802.11-2020 at § 19.3.11.7.6.
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Figure 20-13; IEEE 802.11-2012 at Figure 20-13; IEEE 802.11-
`2020 at Figure 19-13.
`
`
`
`𝑎𝑖
`
`The formula 𝑥𝑗 = 𝑥𝑗−1 + ∑ 𝑣(𝑗−1)𝑎+𝑖
` is a recursive formula. The parity bit xj is formed
`=1
`from summing a previously calculated parity bit xj-1 (“predecessor parity bit”) and adding it
`to another value, ∑ 𝑣(𝑗−1)𝑎+𝑖
` (value of a sum of “a” randomly chosen irregular repeats
`=1
`of the message bits). Each parity bit for each LDPC code described in the 802.11 standard
`meets this limitation.
`
`𝑎𝑖
`
`For example, in the (648, 432) (Rate=2/3) codeword, the parity bits have the following
`relationship:
`
`p1 = c1
`
`p54 = p1 + c2
`
`p81 = p54 + c3
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
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`Analysis
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`p108 = p81 + c4
`
`p135 = p108 + c5
`
`p162 = p135 + c6
`
`p189 = p162 + c7
`
`p216 = p189 + c8
`
`The 802.11 standard has specified LDPC codes where the recursive relationship between
`the parity bits does not use strictly ascending parity bit indices. Nonetheless, the parity bits
`are still generated in accordance with formulate 𝑥𝑗 = 𝑥𝑗−1 + ∑ 𝑣(𝑗−1)𝑎+𝑖
`.
`=1
`
`𝑎𝑖
`
`For example, let x1 = p1, x2 = p54, x3 = p81, x4 = p108, x5 = p135, x6 = p162, x7 = p189 and x8 =
`p216. It can be seen that xi is still a sequence of parity bits. It is simply in a different order
`than the parity bits pi. Now, writing the relationships above again provides:
`
`x1 = c1
`
`x2 = x1 + c2
`
`x3 = x2 + c3
`
`x4 = x3 + c4
`
`x5 = x4 + c5
`
`x6 = x5 + c6
`
`x7 = x6 + c7
`
`x8 = x7 + c8
`
`This can be written as:
`
`Thus each parity bit xj is in accordance with
`
`𝑥𝑗 = 𝑥𝑗−1 + 𝑐𝑗
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
`
`Claim Language
`
`Analysis
`
`𝑎
`𝑥𝑗 = 𝑥𝑗−1 + ∑ 𝑣(𝑗−1)𝑎+𝑖
`𝑖=1
`
`
`
`𝑎
`𝑐𝑗 = ∑ 𝑣(𝑗−1)𝑎+𝑖
`𝑖=1
`
`
`
`as long as
`
`which is shown below.
`
`Alternatively, these parity bits may be written as follows, which also meets the limitation
`of this section:
`
`p1 = c1
`
`p54 = p1 + c2
`
`p81 = p54 + c3
`
`p108 = p81 + c4
`
`p135 = p108 + c5
`′
`p216 = p1 + 𝑐6
`′
`p189 = p216 + 𝑐7
`′
`p162 = p189 + 𝑐8
`
`For avoidance of doubt, the (648, 432) code used here as an example has 216 parity bits.
`Only eight of the parity bits have been shown here for brevity. However, the remaining
`parity bits are also generated in accordance with the same equation, i.e. 𝑥𝑗 = 𝑥𝑗−1 +
`∑ 𝑣(𝑗−1)𝑎+𝑖
`.
`=1
`Further, ∑ 𝑣(𝑗−1)𝑎+𝑖
`=1
`the message bits.
`
` is the value of a sum of “a” randomly chosen irregular repeats of
`
`𝑎𝑖
`
`𝑎𝑖
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
`
`Claim Language
`
`Analysis
`
`𝑎𝑖
`
`Each of the cj = ∑ 𝑣(𝑗−1)𝑎+𝑖
` values is the sum of a message bits. For example, the (648,
`=1
`432) code has cj values as follows:
`
`c1 = i6 + i14 + i16 + i17 + … + i423 + i427
`
`c2= i24 + i52 + i67 + i127 + i163 + i219 + i304 + i366 + i422
`
`c3 = i9 + i35 + i68 + i91 + i161 + i189 + i287 + i331 + i387
`
`c4 = i15 + i28 + i73 + i106 + i128 + i167 + i216 + i268 + i303
`
`c5 = i9 + i39 + i58 + i107 + i137 + i195 + i295 + i363 + i421
`
`c6 = i5 + i13 + i15 + i16 + … + i422 + i426
`
`c7 = i5 + i48 + i62 + i100 + i159 + i205 + i250 + i310 + i368
`
`c8 = i13 + i49 + i74 + i91 + i127 + i185 + i233 + i288 + i426
`
`The number of bits summed, “a,” in each of these equations is 63, 9, 9, 9, 9, 55, 9, 9.
`
`The alternative representation is reproduced here:
`
`p1 = c1
`
`p54 = p1 + c2
`
`p81 = p54 + c3
`
`p108 = p81 + c4
`
`p135 = p108 + c5
`′
`p216 = p1 + 𝑐6
`′
`p189 = p216 + 𝑐7
`′
`p162 = p189 + 𝑐8
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`Claim Language
`
`Analysis
`
`In this representation, p1, p54, p81, p108 and p135 are determined exactly the same way. Thus,
`′ , it is also the sum “a” of message
`only analysis of p216, p189, p162 is needed. Starting with 𝑐6
`bits as shown below:
`′ = i16 + i37 + i64 + i100 + i155 + i214 + i245 + i341 + i403
`𝑐6
`′ , it relates p189 to p216. C8 also does this. Thus, they are equal:
`With respect to 𝑐7
`′ = c8 = i13 + i49 + i74 + i91 + i127 + i185 + i233 + i288 + i426
`𝑐7
`′ and c7 relate p162 to p189 and are equal to each other:
`Likewise, 𝑐8
`′ = c7 = i5 + i48 + i62 + i100 + i159 + i205 + i250 + i310 + i368
`𝑐8
`
`In this alternative representation, the number of information bits summed for summed for
`′ is 63, 9, 9, 9, 9, 9, 9 and 9, respectively. ′ , 𝑐7′ and 𝑐8
`
`
`c1, c2, c3, c4, c5, 𝑐6
`Thus the sum terms ∑ 𝑣(𝑗−1)𝑎+𝑖
`=1
`
` are sums of message bits with an associated “a” values.
`
`𝑎𝑖
`
`Further, 802.11 LDPC codes use an irregular repeat of message bits. For example, an
`analysis of an exemplary Tanner Graph for the (648, 432) code (See Appendix B) yields
`the following frequencies of irregularly repeated message bits:
`
`f5 = 18.75%
`
`f6 = 31.25%
`
`f7 = 12.5%
`
`f8 = 18.75%
`
`f13 = 6.25%
`
`f15 = 12.5%
`
`In this example, 81 info bits are repeated 5 times, 135 are repeated 6 times, 54 are repeated
`7 times, 81 are repeated 8 times, 27 are repeated 13 times, and 54 are repated 15 times.
`Thus, the message bits are repeated irregularly. These frequencies are illustrative only; to
`
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`Claim Language
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`Analysis
`
`the extent the Accused Products use alternative frequencies, they literally infringe so long
`as at least two message bits appear with different frequency.
`
`𝑎𝑖
`
`Finally, the sum ∑ 𝑣(𝑗−1)𝑎+𝑖
` is of “a” “randomly chosen” irregular repeats of the
`=1
`message bits. In the field of error control coding, randomly chosen includes the use of
`fixed randomization functions. Random selections may be made with permutations or
`interleavers.
`
`The 802.11 standard defines a codeword c = (i0,i1,…i(k-1), p0,p1,…p(n-k-1)), with information
`bits i and parity bits p. The parity bits p may be determined from a parity check matrix H
`by computing H x cT = 0.
`
`IEEE 802.11n-2009 at § 20.3.11.6.3 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7.3; IEEE 802.11-2020 at § 19.3.11.7.3.
`
`The parity check matrix H for each block size and code rate is defined in Tables R.1 to R.3
`of the 802.11n-2009 amendment, and in Tables F-1 to F-3 of the 802.11-2012 standard and
`the 802.11-2020 standard.
`
`
`
`* * *
`
`
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Annex R, Table R.1; see also IEEE 802.11-2012 at Annex F, Table
`F-1; IEEE 802.11-2020 at Annex F, Table F-1.
`
`
`
`
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at § 20.3.11.6.4; see also IEEE 802.11-2012 at § 20.3.11.7.4; IEEE
`802.11-2020 at § 19.3.11.7.4.
`
`The parity check matrices may also be represented as a combination of two matrices, H1
`and H2, where H = [H1 H2], H1 is an (n-k) x k matrix, and H2 is an (n-k) x (n-k) matrix,
`such that H1 x iT + H2 x pT = 0, i = (i0,i1,…i(k-1)) and p = (p0,p1,…p(n-k-1)).
`
`The irregular repeats are chosen via a randomizing function as specified by the parity
`check matrices, H, in the 802.11 standard.
`
`Annex G of IEEE 802.11n-2009 and Annex L of IEEE 802.11-2012 and Annex I of IEEE
`802.11-2020 provide examples of calculating the sequence of parity bits, and further
`illustrate randomly chosen irregular repeats of the message bits.
`
`IEEE 802.11n-2009 at Annex G, § G.2.1; see also IEEE 802.11-2012 at Annex L, § L.2.1;
`IEEE 802.11-2020 at Annex I, § I.2.2.
`
`
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`Claim Language
`
`Analysis
`
`
`
`
`
`
`
`* * *
`
`IEEE 802.11n-2009 at Annex G, § G.2.5; see also IEEE 802.11-2012 at Annex L, § L.2.5;
`IEEE 802.11-2020 at Annex I, § I.2.6.
`
`See also IEEE 802.11n-2009 at Annex G, § § G.3.1, G.3.5; IEEE 802.11-2012 at Annex L,
`§ L.3.1, L.3.5; IEEE 802.11-2020 at Annex I, § I.3.2, I.3.6..
`
`See also Appendix B (illustrating randomly chosen irregular repeats of the message bits in
`exemplary Tanner Graphs).
`
`On information and belief, products made or sold by Samsung that implement the IEEE
`Standards do so in such a way that infringes this limitation. To the extent that Samsung
`contends that their LDPC encoding and/or decoding implementations do not literally
`infringe the limitations of this claim, such differences are insubstantial and thus the claim
`limitations are satisfied under the doctrine of equivalents.
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`Claim Language
`
`Analysis
`
`For example, to the extent that Samsung contends that their LDPC encoding and/or
`decoding implementations do not literally infringe because they do not “repeat”
`information bits, e.g., by construing “repeat” to require copies of information bits to be
`stored in a separate memory, the Accused Products would infringe under the doctrine of
`equivalents because each information bit is used multiple times in the first encoding, and
`appears in a plurality of sums of information bits at the check nodes. Whether or not the
`information bits are duplicated and separately stored in memory before they are summed or
`combined is an insubstantial difference: both scenarios accomplish substantially the same
`function of summing pluralities of information bits at the check nodes, in substantially the
`same way, i.e., by directing each information bit to a plurality of check nodes to be
`summed or combined, and accomplish substantially the same result of forming the first
`encoded data block.
`
`[1c] making the sequence of parity bits
`available for transmission in a
`transmission data stream.
`
`The Accused Products make the sequence of parity bits available for transmission in a
`transmission data stream.
`
`For example, the Accused Products implement the IEEE Standards, which make the
`sequence of parity bits available for transmission in a transmission data stream.
`
`For example, the LDPC encoder makes available for transmission a codeword “c” of size
`“n” that includes “k” information bits and “n-k” parity bits in a transmission data stream.
`
`IEEE 802.11n-2009 at § 20.3.11.6.3 (emphasis added); see also IEEE802.11-2012 at
`§ 20.3.11.7.3; IEEE 802.11-2020 at § 19.3.11.7.3.
`
`
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at § 20.3.11.6.6 (emphasis added); see also IEEE802.11-2012 at
`§ 20.3.11.7.6; IEEE 802.11-2020 at § 19.3.11.7.6.
`
`
`
`
`
`IEEE 802.11n-2009 at Figure 20-13; see also IEEE 802.11-2012 at Figure 20-13; IEEE
`802.11-2020 at Figure 19-13.
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Fig. 20-3 (emphasis added); see also IEEE 802.11-2012 at Fig. 20-
`3; IEEE 802.11-2020 at Fig. 19-3.
`
`On information and belief, products made or sold by Samsung that implement the IEEE
`Standards do so in such a way that infringes this limitation. To the extent that Samsung
`contends that their LDPC encoding and/or decoding implementations do not literally
`infringe the limitations of this claim, such differences are insubstantial and thus the claim
`limitations are satisfied under the doctrine of equivalents.
`
`
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`Claim Language
`
`Analysis
`
`Claim 2
`
`
`
`[2] The method of claim 1, wherein the
`sequence of parity bits is generated is
`in accordance with “a” being constant.
`
`The Accused Products practice the method of claim 1.
`
`See supra [1]-[1c].
`
`In the Accused Products, the sequence of parity bits is generated is in accordance with “a”
`being constant.
`
`For example, the Accused Products implement the IEEE Standards, and in said standards
`the sequence of parity bits is generated is in accordance with “a” being constant.
`
`Analysis of the twelve codes defined in the standard reveals that the following values for
`“a” being used when generating the sequence of parity bits:
`
`(1944, 974) – 5, 6, 57
`
`(1296, 648) – 5, 6, 57
`
`(648, 324) – 5, 6, 53
`
`(1944, 1296) – 9, 65
`
`(1296, 864) – 9, 69
`
`(648, 432) – 9, 63
`
`(1944, 1458) – 12, 72
`
`(1296, 972) - 12, 13, 73
`
`(648, 486) - 12, 13, 67
`
`(1944, 1620) – 17, 18, 70
`
`(1296, 1080) – 19, 74
`
`(648, 540) – 20, 75
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`Claim Language
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`Analysis
`
`At least the (648, 432) and (1944,1458) codes infringe this limitation under the doctrine of
`equivalents. Each subset of message bits in these codes contains either a first number of
`message bits, a, or a number of message bits that is a multiple of a. For example, in the
`(1944, 1458) code, each subset contains either 12 or 6 * 12 = 72 message bits. The larger
`subsets can be equivalently represented as a sequence of smaller subsets, wherein only the
`final parity bit generated by the sequence is used in the codeword. For example, a subset of
`72 can be equivalently generated using six subsets of 12, in which the parity bits generated
`by the first five subsets are not used—which would literally infringe claim 7. Whether a
`single large subset or a plurality of smaller subsets are used is insubstantial: in both
`scenarios, substantially the same function of generating parity bits from sums of message
`bits is performed, in substantially the same way, i.e., accumulating subsets of message bits,
`to obtain substantially the same result of encoding a codeword using an encoding operation
`with linear time complexity.
`
`On information and belief, products made or sold by Samsung that implement the IEEE
`Standards do so in such a way that infringes this limitation. To the extent that Samsung
`contends that their LDPC encoding and/or decoding implementations do not literally
`infringe the limitations of this claim, such differences are insubstantial and thus the claim
`limitations are satisfied under the doctrine of equivalents.
`
`Claim 3
`
`
`
`[3] The method of claim 1, wherein the
`sequence of parity bits is generated is
`in accordance with “a” varying for
`different parity bits.
`
`The Accused Products practice the method of claim 1.
`
`See supra [1]-[1c].
`
`In the Accused Products, the sequence of parity bits is generated is in accordance with “a”
`varying for different parity bits.
`
`For example, the Accused Products implement the IEEE Standards, and in said standards
`the sequence of parity bits is generated is in accordance with “a” varying for different
`parity bits.
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`Claim Language
`
`Analysis
`
`As shown below, the parity check matrices of the LDPC codes in the 802.11 standard use a
`dual diagonal pattern. This dual diagonal pattern permits efficient encoding.
`
`The 802.11 standard defines a codeword c = (i0,i1,…i(k-1), p0,p1,…p(n-k-1)), with information
`bits i and parity bits p. The parity bits p may be determined from a parity check matrix H
`by computing H x cT = 0.
`
`IEEE 802.11n-2009 at § 20.3.11.6.3 (emphasis added); see also IEEE 802.11-2012 at
`§ 20.3.11.7.3; IEEE 802.11-2020 at § 19.3.11.7.3.
`
`The parity check matrix H for each block size and code rate is defined in Tables R.1 to R.3
`of the 802.11n-2009 amendment, and in Tables F-1 to F-3 of the 802.11-2012 standard and
`the 802.11-2020 standard.
`
`
`
`* * *
`
`
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at Annex R, Table R.1; see also IEEE 802.11-2012 at Annex F, Table
`F-1; IEEE 802.11-2020 at Annex F, Table F-1.
`
`
`
`
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`Exhibit 2 – Preliminary Claim Chart For U.S. Patent No. 7,421,032
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`Claim Language
`
`Analysis
`
`IEEE 802.11n-2009 at § 20.3.11.6.4; see also IEEE 802.11-2012 at § 20.3.11.7.4; IEEE
`802.11-2020 at § 19.3.11.7.4.
`
`The parity check matrices may also be represented as a combination of two matrices, H1
`and H2, where H = [H1 H2], H1 is an (n-k) x k matrix, and H2 is an (n-k) x (n-k) matrix,
`such that H1 x iT + H2 x pT = 0, i = (i0,i1,…i(k-1)) and p = (p0,p1,…p(n-k-1)). .
`
`The parity check matrices may be used to generate a Tanner Graph that reflects the code
`structure. The Tanner Graph representation of the 802.11 parity check matrices show the
`varying values of a used. For example, the figure below illustrates an exemplary Tanner
`Graph for the (648, 486) (R = 3/4) code.
`
`See also Appendix B (showing exemplary Tanner Graph representations for all 12 parity
`check matrices defined in the 802.11 standards).
`
`
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`For example, in the zoomed-in portion of the exemplary Tanner Graph shown below for
`the (648, 486) code (R = 3/4), the solid, black ovals illustrate the value of “a” for various
`check nodes.
`
`Every code in the 802.11 Standards may be literally implemented with a varying. The
`following list shows the codes and the varying values of a used:
`
`
`
`(1944, 974) – 5, 6, 57
`
`(1296, 648) – 5, 6, 57
`
`(648, 324) – 5, 6, 53
`
`(1944, 1296) – 9, 65
`
`(1296, 864) – 9, 69
`
`(648, 432) – 9, 63
`
`(1944, 1458) – 12, 72
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`Claim Language
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`Analysis
`
`(1296, 972) - 12, 13, 73
`
`(648, 486) - 12, 13, 67
`
`(1944, 1620) – 17, 18, 70
`
`(1296, 1080) – 19, 74
`
`(648, 540) – 20, 75
`
`On information and belief, products made or sold by Samsung that implement the IEEE
`Standards do so in such a way that infringes this limitation. To the extent that Samsung
`contends that their LDPC encoding and/or decoding implementations do not literally
`infringe the limitations of this claim, such differences are insubstantial and thus the claim
`limitations are satisfied under the doctrine of equivalents.
`
`Claim 4
`
`
`
`[4] The method of claim 1, wherein
`generating the sequence of parity bits
`comprises performing recursive
`modulo two addition operations on the
`random sequence of bits.
`
`The Accused Products