A method includes defining a model matrix of size (n−k)×n, where n and k are positive integers, and where the model matrix includes a first sub-matrix corresponding to positions of data bits and a second sub-matrix corresponding to positions of parity bits. The second sub-matrix includes a multi-diagonal matrix with a triple diagonal structure. The triple diagonal structure includes a first and second central diagonals and a last row diagonal. Bits of the first and 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. The method further includes: 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, based on the parity bits, over a channel and between communication devices.