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IEEE Globecom Workshops (GC Wkshps)

An Iterative Approach to Syndrome-based Deep Learning Decoding

Emmanouil Kavvousanos, Vassilis Paliouras

Published Dec 1, 2020• 5 citations
Publisher

Abstract

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.

DOI
10.1109/gcwkshps50303.2020.9367553

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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.
In modern communication systems, multiple types of error-correcting codes can be utilized for different transmission scenarios. Therefore, the receiver should include the decoder compatible with multiple codes used in the transmission scheme, which results in the increase of the resources required for its implementation. In this paper, we investigate the possibility of training a single syndrome-based DNN decoder to solve the problem of unified decoding. We observe, that the syndrome-based approach allows to extend the unified decoding capabilities to the codes with considerably larger lengths in comparison to the initially described by Wang et al. (2018) method. Through numerical experiments, we show that the model trained for decoding a pair of moderate lengths codes (BCH and CRC-Aided Polar) achieves performance results comparable with classical decoding solutions, while sharing the same architecture and the set of trainable weights. We note, that the unification of a syndrome-based DNN decoder does not lead to large performance degradation, in comparison to the decoder trained on a single code. The approach described in the paper is promising in terms of reducing the hardware resources required to implement the decoder.
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.
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.
Error-correcting codes are very important in modern communication systems. In this paper, we investigate efficient reduced-complexity deep neural network (DNN)-aided channel decoders. Specifically, we leverage DNN training to obtain individual scaling parameters for normalized min-sum algorithms, thereby leading to much faster convergence for the same target bit error rate (BER). Also, we propose to compress the DNN-aided channel decoders via weight sharing. A case study on DNN-aided BCH decoders is investigated. Simulation results and hardware complexity analysis show that our method can reduce 2.59 times of memory cost than non-compressed DNN-aided BCH decoders. Meanwhile, compared to the conventional BCH decoders, our method can improve convergence rate by 6 times with similar decoding performance.
Deep learning recently shows strong competitiveness to improve polar code decoding. However, suffering from prohibitive training and computation complexity, the conventional deep neural network (DNN) is only possible for very short code length. In this paper, the main problems of deep learning in decoding are well solved. We first present the multiple scaled belief propagation (BP) algorithm, aiming at obtaining faster convergence and better performance. Based on this, deep neural network decoder (NND) with low complexity and latency, is proposed for any code length. The training only requires a small set of zero codewords. Besides, its computation complexity is close to the original BP. Experiment results show that the proposed (64,32) NND with 5 iterations achieves even lower bit error rate (BER) than the 30-iteration conventional BP and (512, 256) NND also outperforms conventional BP decoder with same iterations. The hardware architecture of basic computation block is given and folding technique is also considered, saving about 50% hardware cost.
Syndrome-based neural decoding (SBND) has emerged as a promising deep learning approach for soft-decision decoding of high-rate, short-length codes. However, this approach still has substantial room for improvement. In this paper, we show how to leverage code automorphisms to enhance the ability of existing SBND models to learn and generalize through data augmentation during training and inference. As a result, for the short high-rate codes considered, we obtain models that closely approach MLD performance using small datasets and proper training. Our findings also suggest that many prior results for SBND models in the literature underestimate their true correction capability due to undertraining. Code to reproduce all results is available at: https://github.com/lebidan/sbnd.