Sparsifying Parity-Check Matrices
Abstract
Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the problem of minimizing the number of one-entries in parity-check matrices. In the maximum-likelihood (ML) decoding method, the number of ones in PCMs is directly related to the time required to decode messages. We propose a simple matrix row manipulation heuristic which alters the PCM, but not the code itself. We apply simulated annealing and greedy local searches to obtain PCMs with a small number of one entries quickly, i.e. in a couple of minutes or hours when using mainstream hardware. The resulting matrices provide faster ML decoding procedures, especially for large codes.
Cite
@article{arxiv.2005.05051,
title = {Sparsifying Parity-Check Matrices},
author = {Luís M. S. Russo and Tobias Dietz and José Rui Figueira and Alexandre P. Francisco and Stefan Ruzika},
journal= {arXiv preprint arXiv:2005.05051},
year = {2020}
}
Comments
This work was supported by Funda\c{c}\~ao para a Ci\^encia e Tecnologia (FCT) ref. UID/CEC/50021/2019; European Union's Horizon 2020, Marie Sk{\l}odowska-Curie Actions grant agreement No 690941; The DAAD-CRUP Luso-German bilateral cooperation 2017-2018 research project MONO-EMC; The DFG (project-ID: RU 1524/2-3). Jos{\'e} Rui Figueira acknowledges FCT grant SFRH/BSAB/139892/2018