Sparsifying Parity-Check Matrices
| Autor: | Russo, Luís M. S., Dietz, Tobias, Figueira, José Rui, Francisco, Alexandre P., Ruzika, Stefan |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
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