Algebraic Constructions of High Performance and Efficiently Encodable Non-Binary Quasi-Cyclic LDPC Codes

好一 坂庭, KOHICHI SAKANIWA

Longwen Lan, Lingqi Zeng, Y.Y. Tai +2 more

This paper presents two algebraic methods for constructing efficiently encodable quasi-cyclic (QC) LDPC codes that perform well on both the AWGN and binary erasure channels with iterative decoding in terms of bit-error performance, block error performance and error-floor, collectively. The constructions are based on the cyclic subgroups of the multiplicative groups of finite fields and affine mappings

Keke Liu, Mostafa El‐Khamy, Jungwon Lee +2 more

This paper considers the algebraic construction and performance of non-binary spatially-coupled low density parity check (LDPC) codes. A replicate-and-mask approach is presented to construct finite-length algebraic quasi-cyclic (QC) spatially-coupled (SC) LDPC codes. Numerical results show the superiority of non-binary algebraic SC QC LDPC codes over the corresponding random non-binary (block and SC) LDPC codes. In this paper, it is demonstrated that the threshold saturation phenomenon, previously demonstrated for binary SC LDPC codes, also holds for non-binary SC LDPC codes over the binary-input AWGN channel with BPSK modulation.

Baihong, Lin -, Yukui +5 more

Xiao Xiao, Lee

Shu Hwa Lin, Shumei Song, Ying Tai +2 more

In the late 1950's and early 1960's, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for correcting random errors with algebraic decoding, such as Bose-Chaudhuri-Hocqenghem (BCH) and Reed-Solomon (RS) codes. Recently it has been shown that finite fields can also be used successfully to construct binary quasi-cyclic (QC)-LDPC codes that perform very well not only over the AWGN channel but also over the binary erasure channel with iterative decoding, besides being efficiently encodable. This paper is concerned with constructions of nonbinary QC-LDPC codes based on finite fields