Patent ID: 8719655

Claim:
A method comprising: defining a model matrix of size (n−k)×n, where n and k are positive integers, wherein the model matrix comprises a first sub-matrix corresponding to positions of data bits, and a second sub-matrix corresponding to positions of parity bits, wherein the second sub-matrix comprises a multi-diagonal matrix with a triple diagonal structure, wherein the triple diagonal structure includes (i) a first central diagonal, (ii) a second central diagonal, and (iii) a last row diagonal, and wherein bits of the first central diagonal, the second central diagonal, and the last row diagonal are equal to 1 and a remainder of bits in the multi-diagonal matrix are equal to 0; generating a compact matrix based on the model matrix; generating a parity matrix based on the compact matrix; determining the parity bits based on the parity matrix; and transmitting a codeword, via a transmitter and based on the parity bits, over a channel from a first communication device to a second communication device.