Method of codifying data including generation of a quasi-cyclic code

A method comprising:

• selecting a factor at a first device, wherein the factor is equal to a number of bits in a codeword divided by a natural number;
• generating a model matrix, wherein the model matrix includes (i) a first matrix comprising data, and (ii) a second matrix comprising parity bits, wherein Hamming weights of columns and rows of the model matrix are not constant and the Hamming weights of the columns correspond to a codification rate of a channel such that the model matrix is irregular;
• generating a compact matrix by replacing (i) each element of the model matrix that is equal to 1 with a pseudo-random positive whole number, and (ii) each element of the model matrix that is equal to 0 with a −1, wherein the pseudo-random positive whole number is greater than or equal to 0 and less than the factor;
• generating a quasi-cyclic code including a parity matrix by replacing (i) each positive element of the compact matrix with an identity matrix, and (ii) each element of the compact matrix equal to −1 with a null matrix, wherein each of the identity matrices is rotated cyclically a number of times indicated by a corresponding one of the positive elements of the compact matrix, wherein a number of rows in each of the identity matrices and each of the null matrices is equal to the factor, and wherein a number of columns in each of the identity matrices and each of the null matrices is equal to the factor;
• applying the quasi-cyclic code to a word of the data via a codification device to generate the codeword;
• and
• transmitting the codeword on the channel from the first device to a second device.