2025/01/31 by François Arnault, Philippe Gaborit, Arnault, François +7
Computer Science · Engineering · #Error Correcting Code Techniques #Cooperative Communication and Network Coding #Advanced Wireless Communication Techniques
paper · pdf · doi:10.48550/arxiv.2501.19125
We investigate the minimum distance of structured binary Low-Density Parity-Check (LDPC) codes whose parity-check matrices are of the form [C \vert M] where C is circulant and of column weight 2, and M has fixed column weight r ≥ 3 and row weight at least 1. These codes are of interest because they are LDPC codes which come with a natural linear-time encoding algorithm. We show that the minimum distance of these codes is in O(n(r-2)/(r-1) + ε), where n is the code length and ε> 0 is arbitrarily small. This improves the previously known upper bound in O(n(r-1)/(r)) on the minimum distance of such codes.