The decoding of binary quasi-cyclic codes

P. Heijnen, Henk van Tilborg, S. Weijs

Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes. Furthermore we present a decoding algorithm for the binary quasi-cyclic codes of rate 1/m.

P. Heijnen, F.M.J. Willems, T.J. Tjalkens

Kanat Abdukhalikov, Tushar Bag, Daniel Panario

Keke Liu, Juane Li, Shu Lin +1 more

This paper presents a reduced-complexity iterative scheme and an algorithm for decoding non-binary quasi-cyclic (QC) LDPC codes of a specific type. The proposed decoding scheme and the algorithm together significantly reduce the hardware implementation complexity of a decoder with no performance degradation. Also presented in the paper is a simple method for constructing a class of non-binary QC-LDPC codes.

Shumei Song, Bo Zhou, Shu Hwa Lin +1 more

A unified approach for constructing binary and nonbinary quasi-cyclic LDPC codes under a single framework is presented. Six classes of binary and nonbinary quasi-cyclic LDPC codes are constructed based on primitive elements, additive subgroups, and cyclic subgroups of finite fields. Numerical results show that the codes constructed perform well over the AWGN channel with iterative decoding.

Chao Chen