System and method for low density parity check (ldpc) code with 5/6 code rate

An apparatus comprising:

• baseband circuitry configured to:
• identify, according to a code rate of 5/6 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 96 values, wherein the first exponent matrix comprises at least 94 values selected from a second exponent matrix having a same number of dimensions as the first exponent matrix;
• and
• decode encoded data using the first binary parity check matrix,
• wherein the second exponent matrix comprises the following values:
• [28 96 161 134 9 149 15 61 153 105 75 120 −1 98 146 63 149 147 46 −1 2 0 −1 −1 138 127 148 114 128 156 114 130 14 33 103 −1 128 −1 136 18 96 124 109 55 −1 0 0 −1 104 32 1 160 49 52 85 108 90 144 143 18 134 70 −1 117 −1 59 −1 107 0 −1 0 0 33 58 73 83 89 114 119 75 101 49 −1 131 8 131 105 −1 9 −1 146 105 2 −1 −1 0].

A method comprising:

• identify, by baseband circuitry of a first device, according to a code rate of 5/6 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 96 values, wherein the first exponent matrix comprises at least 94 values selected from a second exponent matrix having a same number of dimensions as the first exponent matrix;
• encoding, by the baseband circuitry, data using the first binary parity check matrix;
• and
• transmitting, by the baseband circuitry, the encoded data over a channel,
• wherein the second 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 −100 −1 −1 18 131 88 18 109 113 146 69 84 −1 −1 −1 71 −1 −1 −1 92 790 −1 −100 −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].