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Mediterranean Conference on Embedded Computing (MECO)

The Performance of Multithreshold Decoders in Concatenated Schemes Over Erasure Channels

V. V. Zolotarev, Natalya N. Grinchenko, Gennady V. Ovechkin, P. V. Ovechkin

Published Jun 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1109/meco.2019.8759997

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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.
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.
It’s discusses the self-orthogonal error-correcting codes (SOC) commonly decoded with multithreshold decoders (MTD). It is shown algorithms used for low-density parity-check codes (LDPC) decoding can be applied for SOC decoding. It is shown that the use of min-sum algorithm for decoding of SOC with code rate 1/2 in a channel with additive white Gaussian noise (AWGN) with binary phase-shift keying and soft demodulation would provide additional coding gain about 1..1,5 dB compared with MTD. Thus, the computational complexity of min-sum algorithm is 6...7 times more than the complexity of MTD. In this paper is proposed the composite decoder comprising elements of MTD and min-sum algorithms for decoding of SOC. Thus on the first few iterations of decoding it is used min-sum decoder and after MTD is used. The simulation results of the proposed decoding scheme show that its use can improve the coding gain compared with MTD approximately 1 dB for SOC with code rate 1/2 over AWGN channel with binary phase-shift keying at cost of doubling in computational complexity. At the same time coding gain depends on the SOC, the number of decoding iterations of min-sum and MTD algorithms.
Non-binary multithreshold decoders (qMTD) of q-ary self-orthogonal codes (qSOC) for q-ary symmetric channels are considered. The comparison of their efficiency with the efficiency of decoders for Reed-Solomon codes and non-binary low-density parity-check codes has been made. qMTD has shown to sufficiently exceed other error correcting methods in decoding error probability provided. The operating algorithms for encoder and decoder of concatenated code containing qSOC and modulo q check code have been offered. The application of the decoder offered for a given concatenated code has proved to decrease error decoding probability by two and more decimal orders in comparison with qMTD in the conditions of more than 10% computing complexity increase.