Generating partially sparse generator matrix for a quasi-cyclic low-density parity-check encoder

摘要

A method and system for constructing a generator matrix is disclosed. The method includes: receiving a parity check matrix H, wherein the parity check matrix H includes multiple circulant sub-matrices; rearranging the parity check matrix H by column and row permutations to obtain a rearranged parity check matrix H′; and constructing the generator matrix G based on the rearranged parity check matrix H′.

主权项

1. A method for constructing a generator matrix using a Computer processor, the method comprising:
receiving a parity check matrixH=[H1,1H1,2…H1,NH2,1H2,2…H2,N⋮⋮⋱⋮HM,1HM,2…HM,N],  wherein each sub-matrix Hi,j is a q×q circulant matrix; rearranging the parity check matrix H by column and row permutations to obtain a rearranged parity check matrixH′=[Hu⁢⁢1It0t×(M-t)Hu⁢⁢2Hp⁢⁢1Hp⁢⁢2];  wherein It is an identity matrix of size t, 0t×(m−t) is a zero matrix of size t×(M−t), and Hu1,Hu2, Hp1 and Hp2 corresponds to sub-matrices in the rearranged parity check matrix H′ identified based on relative positions of the sub-matrices with respect to It and 0t×(m−t); and constructing the generator matrix G=[IN−M Hu1T {tilde over (G)}T ], wherein IN−M is an identity matrix of size N-M, Hu1T is a transpose of Hu1 and {tilde over (G)}T is a part of the generator matrix in systematic-circulant form constructed based on H′.