GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets

2005/02/07 by Cen Jung Tjhai, Martin Tomlinson, Tjhai, C. +7
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.cs/0502037

openalex publication_date 2005/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2^m), where m>0 cyclic low-density parity-check codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to increment the code dimension by adding more idempotents and so steadily decrease the sparseness of the parity-check matrix. We show that the constructed codes can achieve performance very close to the sphere-packing-bound constrained for binary transmission.

Citations

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