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Stochastic Decoding of LDPC Codes over GF(q)
McGill University, Canada .
Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
Technion Israel Institute Technology, Israel .
McGill University, Canada .
2013 (English)In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 61, no 3, 939-950 p.Article in journal (Refereed) Published
Abstract [en]

Despite the outstanding performance of non-binary low-density parity-check (LDPC) codes over many communication channels, they are not in widespread use yet. This is due to the high implementation complexity of their decoding algorithms, even those that compromise performance for the sake of simplicity. less thanbrgreater than less thanbrgreater thanIn this paper, we present three algorithms based on stochastic computation to reduce the decoding complexity. The first is a purely stochastic algorithm with error-correcting performance matching that of the sum-product algorithm (SPA) for LDPC codes over Galois fields with low order and a small variable node degree. We also present a modified version which reduces the number of decoding iterations required while remaining purely stochastic and having a low per-iteration complexity. less thanbrgreater than less thanbrgreater thanThe second algorithm, relaxed half-stochastic (RHS) decoding, combines elements of the SPA and the stochastic decoder and uses successive relaxation to match the error-correcting performance of the SPA. Furthermore, it uses fewer iterations than the purely stochastic algorithm and does not have limitations on the field order and variable node degree of the codes it can decode. less thanbrgreater than less thanbrgreater thanThe third algorithm, NoX, is a fully stochastic specialization of RHS for codes with a variable node degree 2 that offers similar performance, but at a significantly lower computational complexity. less thanbrgreater than less thanbrgreater thanWe study the performance and complexity of the algorithms; noting that all have lower per-iteration complexity than SPA and that RHS can have comparable average per-codeword computational complexity, and NoX a lower one.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2013. Vol. 61, no 3, 939-950 p.
Keyword [en]
Non-binary LDPC codes, LDPC codes over GF(q), stochastic decoding, relaxed half-stochastic decoding
National Category
Signal Processing
URN: urn:nbn:se:liu:diva-93867DOI: 10.1109/TCOMM.2013.012913.110340ISI: 000318420800011OAI: diva2:627330

Funding Agencies|Natural Sciences and Engineering Research Council of Canada (NSERC)||

Available from: 2013-06-11 Created: 2013-06-11 Last updated: 2015-04-16Bibliographically approved

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