US Patent 9450612 Encoding method and system for quasi-cyclic low-density parity-check code

A method and system are provided. The method includes applying a quasi-cyclic matrix M to an input vector X− of encoded data to generate a vector Y. The method further includes applying a matrix Q to the vector Y to generate a vector Z. The method also includes recursively generating, using a processor, parity check bits P for the encoded data from the vector Z and an identity matrix variant I*. The encoded data includes quasi-cyclic low-density parity-check code. The identity matrix variant I* is composed of Toeplitz sub-matrices.