Communication techniques involving pairwise orthogonality of adjacent rows in LPDC code

An apparatus for wireless communication, comprising:

• at least one processor coupled with a memory and comprising an encoder circuit configured to encode a set of information bits based on a low density parity check (LDPC) code to produce a codeword wherein:
• the LDPC code is stored in the memory and defined by a base matrix having a first number of columns corresponding to variable nodes of a base graph and a second number of rows corresponding to check nodes of the base graph, and
• for each of the first number of columns, all adjacent rows are orthogonal in a last portion of the second number of rows;
• and
• a transmitter configured to transmit the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements arranged proximal the transmitter.

A method for wireless communication, comprising:

• receiving a codeword in accordance with a radio technology across a wireless channel via one or more antenna elements situated proximal a receiver;
• and
• decoding the codeword via decoder circuitry based on a low density parity check (LDPC) code to produce a set of information bits, wherein:
• the LDPC code is stored and defined by a base matrix having a first number of columns corresponding to variable nodes of a base graph and a second number of rows corresponding to check nodes of the base graph, and
• for each of the first number of columns, all adjacent rows are orthogonal in a last portion of the second number of rows.

A method for wireless communication, comprising:

• encoding a set of information bits with encoder circuitry based on a low density parity check (LDPC) code to produce a codeword wherein:
• the LDPC code is defined by a base matrix having a first number of columns corresponding to variable nodes of a base graph and a second number of rows corresponding to check nodes of the base graph, and
• for each of the first number of columns, all adjacent rows are orthogonal in a last portion of the second number of rows;
• and
• transmitting the codeword in accordance with a radio technology across a wireless channel via one or more antenna elements.

An apparatus for wireless communication, the apparatus comprising:

• a receiver configured to receive a codeword;
• and
• at least one processor coupled with a memory and configured to decode the codeword based on a low density parity check (LDPC) code to produce a set of information bits, wherein:
• the LDPC code is based on a base matrix and a lifting factor Z;
• the base matrix comprises sixty-eight columns indexed by column indices j=0-67 and forty-six rows indexed by row indices i=0-45;
• elements in the base matrix are represented by the row indices i and the column indices j;
• and
• the elements in the base matrix are zero elements except for the elements:
• i=25, j=1, 6, 7, 14, and 47;
• i=26, j=0, 2, 4, 15, and 48;
• i=27, j=1, 6, 8, and 49;
• i=28, j=0, 4, 19, 21, and 50;
• i=29, j=1, 14, 18, 25, and 51;
• i=30, j=0, 10, 13, 24, and 52;
• i=31, j=1, 7, 22, 25, and 53;
• i=32, j=0, 12, 14, 24, and 54;
• i=33, j=1, 2, 11, 21, and 55;
• i=34, j=0, 7, 15, 17, and 56;
• i=35, j=1, 6, 12, 22, and 57;
• i=36, j=0, 14, 15, 18, and 58;
• i=37, j=1, 13, 23, and 59;
• i=38, j=0, 9, 10, 12, and 60;
• i=39, j=1, 3, 7, 19, and 61;
• i=40, j=0, 8, 17, and 62;
• i=41, j=1, 3, 9, 18, and 63;
• i=42, j=0, 4, 24, and 64;
• i=43, j=1, 16, 18, 25, and 65;
• i=44, j=0, 7, 9, 22, and 66;
• and i=45, j=1, 6, 10, and 67.

An apparatus for wireless communication, the apparatus comprising:

• at least one processor coupled with a memory and configured to encode a set of information bits based on a low density parity check (LDPC) code to produce a codeword, wherein:
• the LDPC code is based on a base matrix and a lifting factor Z;
• the base matrix comprises sixty-eight columns indexed by column indices j=0-67 and forty-six rows indexed by row indices i=0-45;
• elements in the base matrix are represented by the row indices i and the column indices j;
• and
• the elements in the base matrix are zero elements except for the elements:
• i=25, j=1, 6, 7, 14, and 47;
• i=26, j=0, 2, 4, 15, and 48;
• i=27, j=1, 6, 8, and 49;
• i=28, j=0, 4, 19, 21, and 50;
• i=29, j=1, 14, 18, 25, and 51;
• i=30, j=0, 10, 13, 24, and 52;
• i=31, j=1, 7, 22, 25, and 53;
• i=32, j=0, 12, 14, 24, and 54;
• i=33, j=1, 2, 11, 21, and 55;
• i=34, j=0, 7, 15, 17, and 56;
• i=35, j=1, 6, 12, 22, and 57;
• i=36, j=0, 14, 15, 18, and 58;
• i=37, j=1, 13, 23, and 59;
• i=38, j=0, 9, 10, 12, and 60;
• i=39, i=1, 3, 7,19, and 61;
• i=40, i=0, 8,17, and 62;
• i=41, j=1, 3, 9, 18, and 63;
• i=42, i=0, 4, 24, and 64;
• i=43, i=1, 16, 18, 25, and 65;
• i=44, i=0, 7, 9, 22, and 66;
• and i=45, j=1, 6, 10, and 67;
• and
• a transmitter configured to transmit the codeword.

A method for wireless communication, the method comprising:

• receiving a codeword;
• and
• decoding the codeword based on a low density parity check (LDPC) code to produce a set of information bits, wherein:
• the LDPC code is based on a base matrix and a lifting factor Z;
• the base matrix comprises sixty-eight columns indexed by column indices i=0-67 and forty-six rows indexed by row indices i=0-45;
• elements in the base matrix are represented by the row indices i and the column indices j. and
• the elements in the base matrix are zero elements except for the elements:
• i=25, j=1, 6, 7, 14, and 47;
• i=26, j=0, 2, 4, 15, and 48;
• i=27, j=1, 6, 8, and 49;
• i=28, j=0, 4, 19, 21, and 50;
• i=29, j=1, 14, 18, 25, and 51;
• i=30, j=0, 10, 13, 24, and 52;
• i=31, j=1, 7, 22, 25, and 53;
• i=32, j=0, 12, 14, 24, and 54;
• i=33, j=1, 2, 11, 21, and 55;
• i=34, j=0, 7, 15, 17, and 56;
• i=35, j=1, 6, 12, 22, and 57;
• i=36, j=0, 14, 15, 18, and 58;
• i=37, j=1, 13, 23, and 59;
• i=38, j=0, 9, 10, 12, and 60;
• i=39, j=1, 3, 7, 19, and 61;
• i=40, j=0, 8, 17, and 62;
• i=41, j=1, 3, 9, 18, and 63;
• i=42, j=0, 4, 24, and 64;
• i=43, j=1, 16, 18, 25, and 65;
• i=44, j=0, 7, 9, 22, and 66;
• and i=45, j=1, 6, 10, and 67.

A method for wireless communication, the method comprising:

• encoding a set of information bits based on a low density parity check (LDPC) code to produce a codeword, wherein:
• the LDPC code is based on a base matrix and a lifting factor Z;
• the base matrix comprises sixty-eight columns indexed by column indices j=0-67 and forty-six rows indexed by row indices i=0-45;
• elements in the base matrix are represented by the row indices i and the column indices j;
• and
• the elements in the base matrix are zero elements except for the elements:
• i=25, j=1, 6, 7, 14, and 47;
• i=26, j=0, 2, 4, 15, and 48;
• i=27, j=1, 6, 8, and 49;
• i=28, j=0, 4, 19, 21, and 50;
• i=29, j=1, 14,18, 25, and 51;
• i=30, j=0, 10, 13, 24, and 52;
• i=31, j=1, 7, 22, 25, and 53;
• i=32, j=0, 12, 14, 24, and 54;
• i=33, j=1, 2, 11, 21, and 55;
• i=34, j=0, 7, 15, 17, and 56;
• i=35, j=1, 6, 12, 22, and 57;
• i=36, j=0, 14, 15, 18, and 58;
• i=37, j=1, 13, 23, and 59;
• i=38, j=0, 9, 10, 12, and 60;
• i=39, j=1, 3, 7, 19, and 61;
• i=40, j=0, 8, 17, and 62;
• i=41, j=1, 3, 9, 18, and 63;
• i=42, j=0, 4, 24, and 64;
• i=43, j=1, 16, 18, 25, and 65;
• i=44, j=0, 7, 9, 22, and 66;
• and i=45;
• j=1;
• 6;
• 10;
• and 67;
• and
• transmitting the codeword.

An apparatus for wireless communication, the apparatus comprising:

• a receiver;
• one or more antenna elements situated proximal the receiver;
• wherein the receiver is configured to receive a codeword in accordance with a radio technology across a wireless channel via the one or more antenna elements;
• one or more memories storing at least a portion of a base matrix and computer-executable instructions;
• and
• at least one processor coupled with the one or more memories and configured to execute the computer-executable instructions to cause the apparatus to decode the codeword, according to a decoding schedule and based on a low density parity check (LDPC) code, to produce a set of information bits, wherein:
• the LDPC code is based on the base matrix and a lifting factor Z;
• the base matrix comprises sixty-eight columns indexed by column indices i=0-67 and forty-six rows indexed by row indices i=0-45;
• elements in the base matrix are represented by the row indices i and the column indices j;
• the elements in the base matrix are zero elements except for the elements:
• i=25;
• j=1;
• 6;
• 7;
• 14;
• and 47;
• i=26;
• j=0;
• 2;
• 4;
• 15;
• and 48;
• i=27;
• j=1;
• 6;
• 8;
• and 49;
• i=28;
• j=0;
• 4;
• 19;
• 21;
• and 50;
• i=29;
• j=1;
• 14;
• 18;
• 25;
• and 51;
• i=30;
• j=0;
• 10;
• 13;
• 24;
• and 52;
• i=31;
• j=1;
• 7;
• 22;
• 25;
• and 53;
• i=32;
• j=0;
• 12;
• 14;
• 24;
• and 54;
• i=33;
• j=1;
• 2;
• 11;
• 21;
• and 55;
• i=34;
• j=0;
• 7, 15;
• 17;
• and 56;
• i=35;
• j=1;
• 6;
• 12;
• 22;
• and 57;
• i=36;
• j=0;
• 14;
• 15;
• 18;
• and 58;
• i=37;
• j=1;
• 13;
• 23;
• and 59;
• i=38;
• j=0;
• 9, 10, 12;
• and 60;
• i=39;
• j=1;
• 3;
• 7, 19;
• and 61;
• i=40;
• j=0;
• 8, 17;
• and 62;
• i=41;
• j=1;
• 3;
• 9;
• 18;
• and 63;
• i=42;
• j=0;
• 4;
• 24;
• and 64;
• i=43;
• j=1;
• 16;
• 18;
• 25;
• and 65;
• i=44;
• j=0;
• 7;
• 9;
• 22;
• and 66;
• and i=45;
• j=1;
• 6;
• 10;
• and 67;
• and
• to decode the codeword based on the LPDC code, the at least one processor is configured to cause the apparatus to skip decoding of the zero elements in the base matrix.

An apparatus for wireless communication, the apparatus comprising:

• a transmitter;
• one or more antenna elements situated proximal the transmitter;
• one or more memories storing at least a portion of a base matrix and computer-executable instructions;
• and
• at least one processor coupled with the one or more memories and configured to execute the computer-executable instructions to cause the apparatus to encode a set of information bits based on a low density parity check (LDPC) code to produce a codeword, wherein:
• the LDPC code is based on the base matrix and a lifting factor Z;
• the base matrix comprises sixty-eight columns indexed by column indices j=0-67 and forty-six rows indexed by row indices i=0-45;
• elements in the base matrix are represented by the row indices i and the column indices j;
• and
• the elements in the base matrix are zero elements except for the elements:
• i=25;
• j=1;
• 6;
• 7;
• 14;
• and 47;
• i=26;
• j=0;
• 2;
• 4;
• 15;
• and 48;
• i=27;
• j=1;
• 6;
• 8;
• and 49;
• i=28;
• j=0;
• 4;
• 19;
• 21;
• and 50;
• i=29;
• j=1;
• 14;
• 18;
• 25;
• and 51;
• i=30;
• j=0;
• 10;
• 13;
• 24;
• and 52;
• i=31;
• j=1;
• 7;
• 22;
• 25;
• and 53;
• i=32;
• j=0;
• 12;
• 14;
• 24;
• and 54;
• i=33;
• j=1;
• 2;
• 11;
• 21;
• and 55;
• i=34;
• j=0;
• 7;
• 15;
• 17;
• and 56;
• i=35;
• j=1;
• 6;
• 12, 22;
• and 57;
• i=36;
• j=0;
• 14;
• 15;
• 18;
• and 58;
• i=37;
• j=1;
• 13;
• 23;
• and 59;
• i=38;
• j=0;
• 9;
• 10;
• 12;
• and 60;
• i=39;
• j=1;
• 3;
• 7;
• 19;
• and 61;
• i=40;
• j=0;
• 8;
• 17;
• and 62;
• i=41;
• j=1;
• 3;
• 9;
• 18;
• and 63;
• i=42;
• j=0;
• 4;
• 24;
• and 64;
• i=43;
• j=1;
• 16;
• 18;
• 25;
• and 65;
• i=44;
• j=0;
• 7;
• 9;
• 22;
• and 66;
• and i=45;
• j=1;
• 6;
• 10;
• and 67;
• and
• wherein the transmitter is configured to transmit the codeword in accordance with a radio technology across a wireless channel via the one or more antenna elements.