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International ICST Conference on Communications and Networking in China

Low-complexity probability generation algorithm for stochastic decoding of non-binary LDPC codes

Guanghua He, Baoming Bai

Published Aug 1, 2011• 0 citations
Publisher

Abstract

Non-binary LDPC codes offer higher performances than their binary counterpart but suffer from highest decoding complexity. A solution to reduce the decoding complexity is the use of stochastic decoding algorithm, but the computational complexity of probability generation in the first step is very high. In this paper, we propose a simple method to fast generate the probability especially in high-order modulation schemes. Simulation results show that the proposed algorithm causes negligible performance degradation with reduction in computational complexity for stochastic decoding of non-binary LDPC codes, which gives some advantages in hardware implementation of the decoders.

DOI
10.1109/chinacom.2011.6158121

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Non-binary LDPC codes offer higher performances than their binary counterpart but suffer from highest decoding complexity. A solution to reduce the decoding complexity is the use of stochastic decoding algorithm, but the computational complexity of probability generation in the first step is very high. In this paper, we propose a simple method to fast generate the probability especially in high-order modulation schemes. Simulation results show that the proposed algorithm causes negligible performance degradation with reduction in computational complexity for stochastic decoding of non-binary LDPC codes, which gives some advantages in hardware implementation of the decoders.
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Low-Density Parity-Check (LDPC) codes are one of the most popular codes used in nowadays’ communication due to their high coding efficiency at low decoding complexity. With these characteristics, LDPC codes are suitable for high-speed information transmission systems. The widely used decoding algorithm for LDPC codes is Belief Propagation (BP) decoding with which the performance of LDPC codes can approach the Shannon limit. With the development of 5G, a lot of attention is given to the so-called ultra-reliable low latency communication scenario which needs the short code to transmit. However, short codes will not have a very good performance with BP decoding. To solve this problem, investigations have been done such as multiple-bases BP decoding. Although this decoding method has a better performance than BP decoding, it will cause a high complexity in the hardware implementation. Besides, an investigation on the stochastic decoding for shortcodes was proposed in 2003. This decoding method is hardware friendly, but its performance can only approach BP decoding. Inspired by multiple-bases BP decoding and stochastic decoding, binary stochastic decoding with parallel decoders is proposed in this thesis firstly. It represents stochastic sequences with multiple parallel Tanner graphs and uses hard-decision decoding in the iterative part because of the binary input bits. However, this decoding method has a severe performance loss compared to BP decoding. To avoid this problem, the enhancement method is used to make the binary sequences be non-binary sequences that can form more powerful parallel decoders. Then the non-binary symbols of these new sequences are transformed to their corresponding log-likelihood ratio which enables the iterative part to use BP decoding. In addition, combining with the ML decision of list decoding, the decision part of our stochastic decoder can fully utilize the output to increase the efficiency of the decoding method. After ensuring the performance of our non-binary stochastic decoding to be better than BP decoding, the complexity of the decoder is reduced to save the computational resources. Finally, with constant adjustments, the bit width of each non-binary symbol is determined to be 15, and the sequence length is reduced to 20 which can let the non-binary stochastic decoding has an acceptable complexity while keeping good performance.
Non-binary LDPC codes have been shown to outperform currently used codes for magnetic recording and several other channels. Currently proposed nonbinary decoder architectures have very high complexity for high-throughput implementations and sacrifice error-correction performance to maintain realizable complexity. In this paper, we present an alternative decoding algorithm based on stochastic computation that has a very simple implementation and minimal performance loss when compared to the sum-product algorithm. We demonstrate the performance of the algorithm when applied to a GF(16) code and provide details of the hardware resources required for an implementation.
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. In 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. The 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. The 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. We 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.