Sparsifying Parity-Check Matrices

• URL: http://arxiv.org/abs/2005.05051v1
• Date: Fri, 8 May 2020 05:51:40 GMT
• Title: Sparsifying Parity-Check Matrices
• Authors: Lu\'is M. S. Russo, Tobias Dietz, Jos\'e Rui Figueira, Alexandre P. Francisco, Stefan Ruzika
• Abstract summary: 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 which alters the PCM, but not the code itself.
• Score: 60.28601275219819
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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