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DEStech Transactions on Computer Science and Engineering

Performances of the Decoding Algorithms near Shannon Limit

V. V. Zolotarev, Gennady V. Ovechkin, Дина Сатыбалдина, Нурлан Наркенович Ташатов, Erlanbek OMIRBAYEV

Published Sep 9, 2019• 0 citations
Publisher

Abstract

Forward error correction technique based on the optimization procedures for multithreshold decoding algorithms is considered. Recent advances as well as new opportunities of the multithreshold decoders for use in the systems working at the Shannon’s limit are analysed. Performances of the multithreshold decoders for self-orthogonal binary and non-binary codes over Gaussian channels are presented. Simulation results of BER performance of proposed decoder is shown to be close to the results provided by optimum total search methods.

DOI
10.12783/dtcse/ica2019/30767

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Forward error correction technique based on the optimization procedures for multithreshold decoding algorithms is considered. Recent advances as well as new opportunities of the multithreshold decoders for use in the systems working at the Shannon’s limit are analysed. Performances of the multithreshold decoders for self-orthogonal binary and non-binary codes over Gaussian channels are presented. Simulation results of BER performance of proposed decoder is shown to be close to the results provided by optimum total search methods.
The article discusses self-orthogonal error-correcting codes (SOC) for the decoding of which multithreshold algorithms (MTD) are usually used. The work gives the results of the research of MTD efficiency in binary erasure channels. Also new, longer and more efficient convolutional SOCs are received, comparative analysis of MTD efficiency and the efficiency of best methods to recover erasures is made. It is offered new concatenated code consisting of SOC and parity-check code for binary erasure channel allowing to decrease bit unrecovered erasure probability in the area of MTD efficient operation to 2..3 decimal orders. Lower bounds on bit unrecovered erasure probabilities for a decoder of the concatenated code are given; the its simulation results are discussed.
The article discusses self-orthogonal error-correcting codes (SOC) for the decoding of which multithreshold algorithms (MTD) are usually used. To decode SOC the algorithms used for low-density parity-check (LDPC) codes can also be applied. The article shows that using a min-sum decoder for SOC over a channel with additive white Gaussian noise (AWGN) in case of binary phase shift keying allows to receive additional coding gain about 1..1,5 dB in comparison with MTD usage. At the same time computing complexity in a min-sum algorithm turns out to be 6...7 times higher than MTD. For SOC decoding the work offers a combined decoder including the elements of MTD and min-sum algorithms. The first several decoding iterations require the usage of min-sum decoder while later MTD is added. The results of offered decoder simulation show about 1 dB increase of coding gain in comparison with MTD for SOC over a channel with AWGN with binary phase shift keying in case of twofold increase of computing complexity. The gain received depends on the SOC used, the number of min-sum decoding iterations and MTD.
Non-binary multithreshold decoding (qMTD) for q-ary self-orthogonal codes (qSOC) is considered. The SER performance of qMTD is shown to be close to the results provided by optimum total search methods, which are not realizable for non-binary codes in general. qMTD decoders are compared with different decoders for Reed-Solomon codes. The performance provided with qMTD in some cases is unattainable with classical decoders for arbitrary long Reed-Solomon codes. The result of concatenation of qSOC with simple to decode outer codes is described. Method of improving of qMTD decoder's performance for qSOC is offered. Some simulated results obtained by using these two decoding techniques (the base and modified ways) are presented as well. Comparison of the results showed that the change in the threshold element's algorithm can significantly improve speed of qMTD work. It's shown that for a larger gain this modification qMTD should be used after conventional decoding iterations.
Multithreshold decoders (MTD) of self-orthogonal codes (SOC) for erasure channels implementing error correction methods based on searching global extremum of functions in discrete spaces are considered. To increase the efficiency of erasure recoveries the concatenated codes comprising inner SOC and outer codes being simple for decoding such as parity-check codes, Hamming codes or BCH codes are offered. The usage of the codes offered provides efficient erasure recovery when operating near channel capacity with linear decoder complexity. The questions of high-throughput software MTD implementation recovering erasures using GPU are considered. The MTD versions developed are shown to be able to perform data flow decoding with the rate of several hundred MB/s using GPU.