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REMAT Revista Eletrônica da Matemática

Decodificador baseado em Rede Neural Profunda para Códigos de Bloco Lineares Curtos Transmitidos via Canal Binário Simétrico

Jorge Kysnney Santos Kamassury

Published Feb 22, 2021• 1 citation
Publisher

Abstract

Short-length codes have been the subject of recent studies mainly due to the need for specific communication requirements expressed by emerging technologies. However, for the most promising code class (BCH), decoding is complex when using traditional decoders. In this context, projects that use neural networks for this purpose appear as interesting alternatives. That said, in this article, the decoder project proposed in the literature that applies the neural network to estimate the error pattern considering the received vector syndrome extends to the BCH codes of length n less than or equal to 31. In addition, a new decoder is introduced, one that iteratively estimates the most reliable positions to be the erroneous bits of the error pattern previously predicted by a neural network. The results presented show that, for all the analyzed codes, the new decoder reaches the maximum theoretical performances.

DOI
10.35819/remat2021v7i1id4389

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Short-length codes have been the subject of recent studies mainly due to the need for specific communication requirements expressed by emerging technologies. However, for the most promising code class (BCH), decoding is complex when using traditional decoders. In this context, projects that use neural networks for this purpose appear as interesting alternatives. That said, in this article, the decoder project proposed in the literature that applies the neural network to estimate the error pattern considering the received vector syndrome extends to the BCH codes of length n less than or equal to 31. In addition, a new decoder is introduced, one that iteratively estimates the most reliable positions to be the erroneous bits of the error pattern previously predicted by a neural network. The results presented show that, for all the analyzed codes, the new decoder reaches the maximum theoretical performances.
In this letter, we introduce a new syndrome-based decoder where a deep neural network (DNN) estimates the error pattern from the reliability and syndrome of the received vector. The proposed algorithm works by iteratively selecting the most confident positions to be the error bits of the error pattern, updating the vector received when a new position of the error pattern is selected. Simulation results for the (63,45) and (63,36) BCH codes show that the proposed approach outperforms existing neural network decoders. In addition, the new decoder is flexible in that it can be applied on top of any existing syndrome-based DNN decoder without retraining.
No presente trabalho, introduz-se no contexto dos códigos corretores de erros uma estratégia de decodificação onde uma rede neural é treinada para predizer padrões de erros usando simultaneamente as informações dos módulos e das síndromes dos vetores recebidos. No decodificador proposto, as posições mais confiáveis são selecionadas de forma iterativa para serem os bits errôneos do padrão de erro estimado, de modo que estas são posteriormente subtraídas do vetor recebido antes que uma nova decodificação seja realizada. Para a predição do padrão de erro, projeta-se uma rede neural profunda com complexidade reduzida. Os experimentos realizados para os códigos BCH curtos transmitindo via canal AWGN evidenciam que os desempenhos obtidos com essa estratégia de decodificação superam àqueles obtidos exclusivamente com a rede neural.
Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce a recurrent neural network architecture for decoding linear block codes. Our method shows comparable bit error rate results compared to the feed-forward neural network with significantly less parameters. We also demonstrate improved performance over belief propagation on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the RNN decoder can be used to improve the performance or alternatively reduce the computational complexity of the mRRD algorithm for low complexity, close to optimal, decoding of short BCH codes.
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.
Effective iterative decoding of short BCH codes faces two primary challenges: identifying an appropriate parity-check matrix and accelerating decoder convergence. To address these issues, we propose a systematic scheme to derive an optimized parity-check matrix through a heuristic approach. This involves a series of binary sum and row shift operations, resulting in a low-density, quasi-regular column weight distribution with a reduced number of shortest cycles in the underlying redundant Tanner graph. For the revised normalized min-sum decoder, we concurrently integrate three types of random permutations into the alternated messages across iterations, leading to significantly faster convergence compared to existing methods. Furthermore, by utilizing the iterative trajectories of failed normalized min-sum decoding, we enhance the reliability measurement of codeword bits with the assistance of a neural network model from prior work, which accommodates more failures for the post-processing of ordered statistics decoding. Additionally, we report the types of undetected errors for the design of iterative decoders for short BCH codes, which potentially challenge efforts to approach the maximum likelihood limit. Extensive simulations demonstrate that the proposed hybrid framework achieves an attractive balance between performance, latency, and complexity.
Recently, Machine Learning has been considered for use in various communications subsystems, providing an alternative paradigm for addressing core problems in the physical (PHY) and medium access control (MAC) layers. Several methods and neural network topologies have been proposed for channel decoding targeting short and moderate length codes. In this paper, we consider the Syndrome-based Deep Learning Decoder and propose a modification in order to enable iterative operation. The proposed modifications perform iterations of the original decoder, which are unrolled to build a larger network. The unrolled iterations are subsequently trained jointly. Moreover, the proposed iterative functionality is incorporated within the learning process by accounting for the error of each iteration in the loss function. By sharing the weights between the iterations, we show that it is possible to reduce the storage requirements of the original decoder by a factor of 2.6x for BCH(63,45), while approaching maximum-likelihood decoding performance. Finally, simulation results are provided for several code lengths and rates, which demonstrate the error-correcting capability of the proposed iterative decoder.