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US 11,770,135 B2Granted
Method and apparatus for low density parity check channel coding in wireless communication system
AssigneeHuawei Technologies Co., Ltd.
InventorsLiang Ma, Chen Zheng, Xiaojian Liu, Yuejun Wei, Xin Zeng
Life of this patent
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Abstract
A low density parity check (LDPC) channel encoding method for use in a wireless communications system includes a communication device encoding an input bit sequence by using a LDPC matrix to obtain an encoded bit sequence for transmission. The LDPC matrix is obtained based on a lifting factor Z and a base matrix. The encoding method can be used in various communications systems including the fifth generation (5G) telecommunication systems, and can support various encoding requirements for information bit sequences with different code lengths.
Claims22
A method for wireless communication, comprising:
- encoding, by a communication apparatus, an input sequence using a matrix H to obtain an encoded sequence, wherein the input sequence comprises K bits, wherein the encoded sequence comprises N bits, and wherein K>1 and N>1;
- and
- outputting, by the communication apparatus, the encoded sequence;
- wherein the matrix H is determined according to a base matrix and a lifting factor Z, and wherein Z is a positive integer;
- wherein the base matrix comprises a plurality of rows and columns of a first matrix;
- wherein each element in the first matrix corresponds to either an all-zero matrix of size Z×Z or a circular permutation matrix of size Z×Z, wherein a respective circular permutation matrix corresponding to a respective element at row i and column j of the first matrix is equal to a matrix obtained by circularly shifting an identity matrix of size Z×Z to the right for Pi,j times, wherein Pi,j=mod (Vi,j,Z), wherein a plurality of Vi,j values for respective elements of the first matrix corresponding to respective circular permutation matrices of size Z×Z are as follows:
- with respect to row index i=0, for column indexes j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, Vi,j is respectively 211, 198, 188, 186, 219, 4, 29, 144, 116, 216, 115, 233, 144, 95, 216, 73, 261, 1, 0;
- with respect to row index i=1, for column indexes j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24, Vi,j is respectively 179, 162, 223, 256, 160, 76, 202, 117, 109, 15, 72, 152, 158, 147, 156, 119, 0, 0, 0;
- with respect to row index i=2, for column indexes j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25, Vi,j is respectively 258, 167, 220, 133, 243, 202, 218, 63, 0, 3, 74, 229, 0, 216, 269, 200, 234, 0, 0;
- with respect to row index i=3, for column indexes j=0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 25, Vi,j is respectively 187, 145, 166, 108, 82, 132, 197, 41, 162, 57, 36, 115, 242, 165, 0, 113, 108, 1, 0;
- with respect to row index i=4, for column indexes j=0, 1, 26, Vi,j is respectively 246, 235, 0;
- with respect to row index i=5, for column indexes j=0, 1, 3, 12, 16, 21, 22, 27, Vi,j is respectively 261, 181, 72, 283, 254, 79, 144, 0;
- with respect to row index i=6, for column indexes j=0, 6, 10, 11, 13, 17, 18, 20, 28, Vi,j is respectively 80, 144, 169, 90, 59, 177, 151, 108, 0;
- with respect to row index i=7, for column indexes j=0, 1, 4, 7, 8, 14, 29, Vi,j is respectively 169, 189, 154, 184, 104, 164, 0;
- with respect to row index i=8, for column indexes j=0, 1, 3, 12, 16, 19, 21, 22, 24, 30, Vi,j is respectively 54, 0, 252, 41, 98, 46, 15, 230, 54, 0;
- with respect to row index i=9, for column indexes j=0, 1, 10, 11, 13, 17, 18, 20, 31, Vi,j is respectively 162, 159, 93, 134, 45, 132, 76, 209, 0;
- with respect to row index i=10, for column indexes j=1, 2, 4, 7, 8, 14, 32, Vi,j is respectively 178, 1, 28, 267, 234, 201, 0;
- with respect to row index i=11, for column indexes j=0, 1, 12, 16, 21, 22, 23, 33, Vi,j is respectively 55, 23, 274, 181, 273, 39, 26, 0;
- with respect to row index i=12, for column indexes j=0, 1, 10, 11, 13, 18, 34, Vi,j is respectively 225, 162, 244, 151, 238, 243, 0;
- with respect to row index i=13, for column indexes j=0, 3, 7, 20, 23, 35, Vi,j is respectively 231, 0, 216, 47, 36, 0;
- with respect to row index i=14, for column indexes j=0, 12, 15, 16, 17, 21, 36, Vi,j is respectively 0, 186, 253, 16, 0, 79, 0;
- with respect to row index i=15, for column indexes j=0, 1, 10, 13, 18, 25, 37, Vi,j is respectively 170, 0, 183, 108, 68, 64, 0;
- with respect to row index i=16, for column indexes j=1, 3, 11, 20, 22, 38, Vi,j is respectively 270, 13, 99, 54, 0, 0;
- with respect to row index i=17, for column indexes j=0, 14, 16, 17, 21, 39, Vi,j is respectively 153, 137, 0, 0, 162, 0;
- with respect to row index i=18, for column indexes j=1, 12, 13, 18, 19, 40, Vi,j is respectively 161, 151, 0, 241, 144, 0;
- with respect to row index i=19, for column indexes j=0, 1, 7, 8, 10, 41, Vi,j is respectively 0, 0, 118, 144, 0, 0;
- with respect to row index i=20, for column indexes j=0, 3, 9, 11, 22, 42, Vi,j is respectively 265, 81, 90, 144, 228, 0;
- with respect to row index i=21, for column indexes j=1, 5, 16, 20, 21, 43, Vi,j is respectively 64, 46, 266, 9, 18, 0;
- with respect to row index i=22, for column indexes j=0, 12, 13, 17, 44, Vi,j is respectively 72, 189, 72, 257, 0;
- with respect to row index i=23, for column indexes j=1, 2, 10, 18, 45, Vi,j is respectively 180, 0, 0, 165, 0;
- with respect to row index i=24, for column indexes j=0, 3, 4, 11, 22, 46, Vi,j is respectively 236, 199, 0, 266, 0, 0;
- with respect to row index i=25, for column indexes j=1, 6, 7, 14, 47, Vi,j is respectively 205, 0, 0, 183, 0;
- with respect to row index i=26, for column indexes j=0, 2, 4, 15, 48, Vi,j is respectively 0, 0, 0, 277, 0;
- with respect to row index i=27, for column indexes j=1, 6, 8, 49, Vi,j is respectively 45, 36, 72, 0;
- with respect to row index i=28, for column indexes j=0, 4, 19, 21, 50, Vi,j is respectively 275, 0, 155, 62, 0;
- with respect to row index i=29, for column indexes j=1, 14, 18, 25, 51, Vi,j is respectively 0, 180, 0, 42, 0;
- with respect to row index i=30, for column indexes j=0, 10, 13, 24, 52, Vi,j is respectively 0, 90, 252, 173, 0;
- with respect to row index i=31, for column indexes j=1, 7, 22, 25, 53, Vi,j is respectively 144, 144, 166, 19, 0;
- with respect to row index i=32, for column indexes j=0, 12, 14, 24, 54, Vi,j is respectively 0, 211, 36, 162, 0;
- with respect to row index i=33, for column indexes j=1, 2, 11, 21, 55, Vi,j is respectively 0, 0, 76, 18, 0;
- with respect to row index i=34, for column indexes j=0, 7, 15, 17, 56, Vi,j is respectively 197, 0, 108, 0, 0;
- with respect to row index i=35, for column indexes j=1, 6, 12, 22, 57, Vi,j is respectively 199, 278, 0, 205, 0;
- with respect to row index i=36, for column indexes j=0, 14, 15, 18, 58, Vi,j is respectively 216, 16, 0, 0, 0;
- with respect to row index i=37, for column indexes j=1, 13, 23, 59, Vi,j is respectively 72, 144, 0, 0;
- with respect to row index i=38, for column indexes j=0, 9, 10, 12, 60, Vi,j is respectively 190, 0, 0, 0, 0;
- with respect to row index i=39, for column indexes j=1, 3, 7, 19, 61, Vi,j is respectively 153, 0, 165, 117, 0;
- with respect to row index i=40, for column indexes j=0, 8, 17, 62, Vi,j is respectively 216, 144, 2, 0;
- with respect to row index i=41, for column indexes j=1, 3, 9, 18, 63, Vi,j is respectively 0, 0, 0, 183, 0;
- with respect to row index i=42, for column indexes j=0, 4, 24, 64, Vi,j is respectively 27, 0, 35, 0;
- with respect to row index i=43, for column indexes j=1, 16, 18, 25, 65, Vi,j is respectively 52, 243, 0, 270, 0;
- with respect to row index i=44, for column indexes j=0, 7, 9, 22, 66, Vi,j is respectively 18, 0, 0, 57, 0;
- and
- with respect to row index i=45, for column indexes j=1, 6, 10, 67, Vi,j is respectively 168, 0, 144, 0.
50 more elements
An apparatus for wireless communication, comprising at least one processor coupled to a memory having instructions stored thereon, wherein the at least one processor is configured to execute the instructions to perform the following:
- encoding an input sequence using a matrix H to obtain an encoded sequence, wherein the input sequence comprises K bits, wherein the encoded sequence comprises N bits, and wherein K>1 and N>1;
- and
- outputting the encoded sequence;
- wherein the matrix H is determined according to a base matrix and a lifting factor Z, and wherein Z is a positive integer;
- wherein the base matrix comprises a plurality of rows and columns of a first matrix;
- wherein each element in the first matrix corresponds to either an all-zero matrix of size Z×Z or a circular permutation matrix of size Z×Z, wherein a respective circular permutation matrix corresponding to a respective element at row i and column j of the first matrix is equal to a matrix obtained by circularly shifting an identity matrix of size Z×Z to the right for Pi,j times, wherein Pi,j=mod (Vi,j,Z), wherein a plurality of Vi,j values for respective elements of the first matrix corresponding to respective circular permutation matrices of size Z×Z are as follows:
- with respect to row index i=0, for column indexes j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, Vi,j is respectively 211, 198, 188, 186, 219, 4, 29, 144, 116, 216, 115, 233, 144, 95, 216, 73, 261, 1, 0;
- with respect to row index i=1, for column indexes j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24, Vi,j is respectively 179, 162, 223, 256, 160, 76, 202, 117, 109, 15, 72, 152, 158, 147, 156, 119, 0, 0, 0;
- with respect to row index i=2, for column indexes j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25, Vi,j is respectively 258, 167, 220, 133, 243, 202, 218, 63, 0, 3, 74, 229, 0, 216, 269, 200, 234, 0, 0;
- with respect to row index i=3, for column indexes j=0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 25, Vi,j is respectively 187, 145, 166, 108, 82, 132, 197, 41, 162, 57, 36, 115, 242, 165, 0, 113, 108, 1, 0;
- with respect to row index i=4, for column indexes j=0, 1, 26, Vi,j is respectively 246, 235, 0;
- with respect to row index i=5, for column indexes j=0, 1, 3, 12, 16, 21, 22, 27, Vi,j is respectively 261, 181, 72, 283, 254, 79, 144, 0;
- with respect to row index i=6, for column indexes j=0, 6, 10, 11, 13, 17, 18, 20, 28, Vi,j is respectively 80, 144, 169, 90, 59, 177, 151, 108, 0;
- with respect to row index i=7, for column indexes j=0, 1, 4, 7, 8, 14, 29, Vi,j is respectively 169, 189, 154, 184, 104, 164, 0;
- with respect to row index i=8, for column indexes j=0, 1, 3, 12, 16, 19, 21, 22, 24, 30, Vi,j is respectively 54, 0, 252, 41, 98, 46, 15, 230, 54, 0;
- with respect to row index i=9, for column indexes j=0, 1, 10, 11, 13, 17, 18, 20, 31, Vi,j is respectively 162, 159, 93, 134, 45, 132, 76, 209, 0;
- with respect to row index i=10, for column indexes j=1, 2, 4, 7, 8, 14, 32, Vi,j is respectively 178, 1, 28, 267, 234, 201, 0;
- with respect to row index i=11, for column indexes j=0, 1, 12, 16, 21, 22, 23, 33, Vi,j is respectively 55, 23, 274, 181, 273, 39, 26, 0;
- with respect to row index i=12, for column indexes j=0, 1, 10, 11, 13, 18, 34, Vi,j is respectively 225, 162, 244, 151, 238, 243, 0;
- with respect to row index i=13, for column indexes j=0, 3, 7, 20, 23, 35, Vi,j is respectively 231, 0, 216, 47, 36, 0;
- with respect to row index i=14, for column indexes j=0, 12, 15, 16, 17, 21, 36, Vi,j is respectively 0, 186, 253, 16, 0, 79, 0;
- with respect to row index i=15, for column indexes j=0, 1, 10, 13, 18, 25, 37, Vi,j is respectively 170, 0, 183, 108, 68, 64, 0;
- with respect to row index i=16, for column indexes j=1, 3, 11, 20, 22, 38, Vi,j is respectively 270, 13, 99, 54, 0, 0;
- with respect to row index i=17, for column indexes j=0, 14, 16, 17, 21, 39, Vi,j is respectively 153, 137, 0, 0, 162, 0;
- with respect to row index i=18, for column indexes j=1, 12, 13, 18, 19, 40, Vi,j is respectively 161, 151, 0, 241, 144, 0;
- with respect to row index i=19, for column indexes j=0, 1, 7, 8, 10, 41, Vi,j is respectively 0, 0, 118, 144, 0, 0;
- with respect to row index i=20, for column indexes j=0, 3, 9, 11, 22, 42, Vi,j is respectively 265, 81, 90, 144, 228, 0;
- with respect to row index i=21, for column indexes j=1, 5, 16, 20, 21, 43, Vi,j is respectively 64, 46, 266, 9, 18, 0;
- with respect to row index i=22, for column indexes j=0, 12, 13, 17, 44, Vi,j is respectively 72, 189, 72, 257, 0;
- with respect to row index i=23, for column indexes j=1, 2, 10, 18, 45, Vi,j is respectively 180, 0, 0, 165, 0;
- with respect to row index i=24, for column indexes j=0, 3, 4, 11, 22, 46, Vi,j is respectively 236, 199, 0, 266, 0, 0;
- with respect to row index i=25, for column indexes j=1, 6, 7, 14, 47, Vi,j is respectively 205, 0, 0, 183, 0;
- with respect to row index i=26, for column indexes j=0, 2, 4, 15, 48, Vi,j is respectively 0, 0, 0, 277, 0;
- with respect to row index i=27, for column indexes j=1, 6, 8, 49, Vi,j is respectively 45, 36, 72, 0;
- with respect to row index i=28, for column indexes j=0, 4, 19, 21, 50, Vi,j is respectively 275, 0, 155, 62, 0;
- with respect to row index i=29, for column indexes j=1, 14, 18, 25, 51, Vi,j is respectively 0, 180, 0, 42, 0;
- with respect to row index i=30, for column indexes j=0, 10, 13, 24, 52, Vi,j is respectively 0, 90, 252, 173, 0;
- with respect to row index i=31, for column indexes j=1, 7, 22, 25, 53, Vi,j is respectively 144, 144, 166, 19, 0;
- with respect to row index i=32, for column indexes j=0, 12, 14, 24, 54, Vi,j is respectively 0, 211, 36, 162, 0;
- with respect to row index i=33, for column indexes j=1, 2, 11, 21, 55, Vi,j is respectively 0, 0, 76, 18, 0;
- with respect to row index i=34, for column indexes j=0, 7, 15, 17, 56, Vi,j is respectively 197, 0, 108, 0, 0;
- with respect to row index i=35, for column indexes j=1, 6, 12, 22, 57, Vi,j is respectively 199, 278, 0, 205, 0;
- with respect to row index i=36, for column indexes j=0, 14, 15, 18, 58, Vi,j is respectively 216, 16, 0, 0, 0;
- with respect to row index i=37, for column indexes j=1, 13, 23, 59, Vi,j is respectively 72, 144, 0, 0;
- with respect to row index i=38, for column indexes j=0, 9, 10, 12, 60, Vi,j is respectively 190, 0, 0, 0, 0;
- with respect to row index i=39, for column indexes j=1, 3, 7, 19, 61, Vi,j is respectively 153, 0, 165, 117, 0;
- with respect to row index i=40, for column indexes j=0, 8, 17, 62, Vi,j is respectively 216, 144, 2, 0;
- with respect to row index i=41, for column indexes j=1, 3, 9, 18, 63, Vi,j is respectively 0, 0, 0, 183, 0;
- with respect to row index i=42, for column indexes j=0, 4, 24, 64, Vi,j is respectively 27, 0, 35, 0;
- with respect to row index i=43, for column indexes j=1, 16, 18, 25, 65, Vi,j is respectively 52, 243, 0, 270, 0;
- with respect to row index i=44, for column indexes j=0, 7, 9, 22, 66, Vi,j is respectively 18, 0, 0, 57, 0;
- and
- with respect to row index i=45, for column indexes j=1, 6, 10, 67, Vi,j is respectively 168, 0, 144, 0.
50 more elements
A non-transitory computer-readable storage medium having instructions stored thereon, wherein the instructions, when executed by a processor, facilitate performance of the following:
- encoding an input sequence using a matrix H to obtain an encoded sequence, wherein the input sequence comprises K bits, wherein the encoded sequence comprises N bits, and wherein K>1 and N>1;
- and
- outputting the encoded sequence;
- wherein the matrix H is determined according to a base matrix and a lifting factor Z, and wherein Z is a positive integer;
- wherein the base matrix comprises a plurality of rows and columns of a first matrix;
- wherein each element in the first matrix corresponds to either an all-zero matrix of size Z×Z or a circular permutation matrix of size Z×Z, wherein a respective circular permutation matrix corresponding to a respective element at row i and column j of the first matrix is equal to a matrix obtained by circularly shifting an identity matrix of size Z×Z to the right for Pi,j times, wherein Pi,j=mod (Vi,j,Z), wherein a plurality of values for respective elements of the first matrix corresponding to respective circular permutation matrices of size Z×Z are as follows:
- with respect to row index i=0, for column indexes j=0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, Vi,j is respectively 211, 198, 188, 186, 219, 4, 29, 144, 116, 216, 115, 233, 144, 95, 216, 73, 261, 1, 0;
- with respect to row index i=1, for column indexes j=0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24, Vi,j is respectively 179, 162, 223, 256, 160, 76, 202, 117, 109, 15, 72, 152, 158, 147, 156, 119, 0, 0, 0;
- with respect to row index i=2, for column indexes j=0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25, Vi,j is respectively 258, 167, 220, 133, 243, 202, 218, 63, 0, 3, 74, 229, 0, 216, 269, 200, 234, 0, 0;
- with respect to row index i=3, for column indexes j=0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 25, Vi,j is respectively 187, 145, 166, 108, 82, 132, 197, 41, 162, 57, 36, 115, 242, 165, 0, 113, 108, 1, 0;
- with respect to row index i=4, for column indexes j=0, 1, 26, Vi,j is respectively 246, 235, 0;
- with respect to row index i=5, for column indexes j=0, 1, 3, 12, 16, 21, 22, 27, Vi,j is respectively 261, 181, 72, 283, 254, 79, 144, 0;
- with respect to row index i=6, for column indexes j=0, 6, 10, 11, 13, 17, 18, 20, 28, Vi,j is respectively 80, 144, 169, 90, 59, 177, 151, 108, 0;
- with respect to row index i=7, for column indexes j=0, 1, 4, 7, 8, 14, 29, Vi,j is respectively 169, 189, 154, 184, 104, 164, 0;
- with respect to row index i=8, for column indexes j=0, 1, 3, 12, 16, 19, 21, 22, 24, 30, Vi,j is respectively 54, 0, 252, 41, 98, 46, 15, 230, 54, 0;
- with respect to row index i=9, for column indexes j=0, 1, 10, 11, 13, 17, 18, 20, 31, Vi,j is respectively 162, 159, 93, 134, 45, 132, 76, 209, 0;
- with respect to row index i=10, for column indexes j=1, 2, 4, 7, 8, 14, 32, Vi,j is respectively 178, 1, 28, 267, 234, 201, 0;
- with respect to row index i=11, for column indexes j=0, 1, 12, 16, 21, 22, 23, 33, Vi,j is respectively 55, 23, 274, 181, 273, 39, 26, 0;
- with respect to row index i=12, for column indexes j=0, 1, 10, 11, 13, 18, 34, Vi,j is respectively 225, 162, 244, 151, 238, 243, 0;
- with respect to row index i=13, for column indexes j=0, 3, 7, 20, 23, 35, Vi,j is respectively 231, 0, 216, 47, 36, 0;
- with respect to row index i=14, for column indexes j=0, 12, 15, 16, 17, 21, 36, Vi,j is respectively 0, 186, 253, 16, 0, 79, 0;
- with respect to row index i=15, for column indexes j=0, 1, 10, 13, 18, 25, 37, Vi,j is respectively 170, 0, 183, 108, 68, 64, 0;
- with respect to row index i=16, for column indexes j=1, 3, 11, 20, 22, 38, Vi,j is respectively 270, 13, 99, 54, 0, 0;
- with respect to row index i=17, for column indexes j=0, 14, 16, 17, 21, 39, Vi,j is respectively 153, 137, 0, 0, 162, 0;
- with respect to row index i=18, for column indexes j=1, 12, 13, 18, 19, 40, Vi,j is respectively 161, 151, 0, 241, 144, 0;
- with respect to row index i=19, for column indexes j=0, 1, 7, 8, 10, 41, Vi,j is respectively 0, 0, 118, 144, 0, 0;
- with respect to row index i=20, for column indexes j=0, 3, 9, 11, 22, 42, Vi,j is respectively 265, 81, 90, 144, 228, 0;
- with respect to row index i=21, for column indexes j=1, 5, 16, 20, 21, 43, Vi,j is respectively 64, 46, 266, 9, 18, 0;
- with respect to row index i=22, for column indexes j=0, 12, 13, 17, 44, Vi,j is respectively 72, 189, 72, 257, 0;
- with respect to row index i=23, for column indexes j=1, 2, 10, 18, 45, Vi,j is respectively 180, 0, 0, 165, 0;
- with respect to row index i=24, for column indexes j=0, 3, 4, 11, 22, 46, Vi,j is respectively 236, 199, 0, 266, 0, 0;
- with respect to row index i=25, for column indexes j=1, 6, 7, 14, 47, Vi,j is respectively 205, 0, 0, 183, 0;
- with respect to row index i=26, for column indexes j=0, 2, 4, 15, 48, Vi,j is respectively 0, 0, 0, 277, 0;
- with respect to row index i=27, for column indexes j=1, 6, 8, 49, Vi,j is respectively 45, 36, 72, 0;
- with respect to row index i=28, for column indexes j=0, 4, 19, 21, 50, Vi,j is respectively 275, 0, 155, 62, 0;
- with respect to row index i=29, for column indexes j=1, 14, 18, 25, 51, Vi,j is respectively 0, 180, 0, 42, 0;
- with respect to row index i=30, for column indexes j=0, 10, 13, 24, 52, Vi,j is respectively 0, 90, 252, 173, 0;
- with respect to row index i=31, for column indexes j=1, 7, 22, 25, 53, Vi,j is respectively 144, 144, 166, 19, 0;
- with respect to row index i=32, for column indexes j=0, 12, 14, 24, 54, Vi,j is respectively 0, 211, 36, 162, 0;
- with respect to row index i=33, for column indexes j=1, 2, 11, 21, 55, Vi,j is respectively 0, 0, 76, 18, 0;
- with respect to row index i=34, for column indexes j=0, 7, 15, 17, 56, Vi,j is respectively 197, 0, 108, 0, 0;
- with respect to row index i=35, for column indexes j=1, 6, 12, 22, 57, Vi,j is respectively 199, 278, 0, 205, 0;
- with respect to row index i=36, for column indexes j=0, 14, 15, 18, 58, Vi,j is respectively 216, 16, 0, 0, 0;
- with respect to row index i=37, for column indexes j=1, 13, 23, 59, Vi,j is respectively 72, 144, 0, 0;
- with respect to row index i=38, for column indexes j=0, 9, 10, 12, 60, Vi,j is respectively 190, 0, 0, 0, 0;
- with respect to row index i=39, for column indexes j=1, 3, 7, 19, 61, Vi,j is respectively 153, 0, 165, 117, 0;
- with respect to row index i=40, for column indexes j=0, 8, 17, 62, Vi,j is respectively 216, 144, 2, 0;
- with respect to row index i=41, for column indexes j=1, 3, 9, 18, 63, Vi,j is respectively 0, 0, 0, 183, 0;
- with respect to row index i=42, for column indexes j=0, 4, 24, 64, Vi,j is respectively 27, 0, 35, 0;
- with respect to row index i=43, for column indexes j=1, 16, 18, 25, 65, Vi,j is respectively 52, 243, 0, 270, 0;
- with respect to row index i=44, for column indexes j=0, 7, 9, 22, 66, Vi,j is respectively 18, 0, 0, 57, 0;
- and
- with respect to row index i=45, for column indexes j=1, 6, 10, 67, Vi,j is respectively 168, 0, 144, 0.
50 more elements
Dependencies are inferred from the claim text.