System and method for low density parity check (ldpc) code with 3/4 code rate

An apparatus comprising:

• baseband circuitry configured to:
• identify, according to a code rate of 3/4 and a code block size of 3888 bits, a first binary parity check matrix for a quasi-cyclic-low-density parity-check (QC-LDPC) code, the first binary parity check matrix corresponding to a first exponent matrix having 144 values;
• and
• decode, using a decoder of the baseband circuitry, encoded data received by a receiver using the first binary parity check matrix,
• wherein the first exponent matrix comprises the following values:
• [96 59 56 78 18 122 −1 −1 −1 126 90 161 −1 −1 −1 74 65 45 2 0 −1 −1 −1 −1 8 98 85 97 22 61 −1 −1 −1 98 35 82 74 31 −1 108 −1 −1 −1 0 0 −1 −1 −1 71 153 156 102 74 70 42 −1 35 128 −1 −1 −1 118 14 −1 −1 65 −1 −1 0 0 −1 −1 18 131 88 18 109 113 146 69 84 −1 −1 −1 71 −1 −1 −1 92 79 0 −1 −1 0 0 −1 7 124 15 161 137 53 −1 161 110 −1 72 −1 53 −1 18 −1 145 −1 −1 −1 −1 −1 0 0 53 151 66 42 138 118 6 77 −1 −1 −1 70 −1 125 72 53 −1 −1 2 −1 −1 −1 −1 0].

A non-transitory computer readable medium storing program instructions for causing one or more processors to:

• identify, according to a code rate of 3/4 and a code block size of 3888 bits, a first binary parity check matrix for a quasi-cyclic-low-density parity-check (QC-LDPC) code, the first binary parity check matrix corresponding to a first exponent matrix having 144 values;
• encode, by an encoder, data using the first binary parity check matrix;
• and
• transmit, by a transmitter, the encoded data over a channel,
• wherein the first exponent matrix comprises the following values:
• [96 59 56 78 18 122 −1 −1 −1 126 90 161 −1 −1 −1 74 65 45 2 0 −1 −1 −1 −1 8 98 85 97 22 61 −1 −1 −1 98 35 82 74 31 −1 108 −1 −1 −1 0 0 −1 −1 −1 71 153 156 102 74 70 42 −1 35 128 −1 −1 −1 118 14 −1 −1 65 −1 −1 0 0 −1 −1 18 131 88 18 109 113 146 69 84 −1 −1 −1 71 −1 −1 −1 92 79 0 −1 −1 0 0 −1 7 124 15 161 137 53 −1 161 110 −1 72 −1 53 −1 18 −1 145 −1 −1 −1 −1 −1 0 0 53 151 66 42 138 118 6 77 −1 −1 −1 70 −1 125 72 53 −1 −1 2 −1 −1 −1 −1 0].