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.
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.
In recent years, neural network-based BP decoders for polar codes have draw much attention, due to their faster convergence and better error-correction performance compared with conventional BP decoders. However, the prior neural BP decoders have high storage cost and training complexity due to massive number of training weights, and the performance improvement is slight. In this work, we first propose a 2D-MSMS algorithm with a shared weight scheme, in which the nodes in the same layer share a weight among different iterations. These learnable weights are optimized by deep learning techniques. Then, we propose a CRC-Aided relaxed 2D-MSMS polar de-coder by introducing relaxation method and CRC-Aided early termination scheme. Simulation results show that our proposed decoder can effectively improve BER performance at medium to high SNR and reduce the amount of training weights by more than 95%.
With the applications of deep learning networks booming in physical layer communication, deep-learning-based channel decoding methods have become a research hotspot. However, the high complexity hinders the application of deep neural network (DNN) on long code. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding. First, we propose a neural normalized min-sum (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feedforward propagation network, we can make use of the advantages of both model-driven deep learning methods and conventional normalized min-sum (CNMS) LDPC decoding method. Second, considering that the NNMS decoder needs large number of multipliers, we propose a shared neural normalized min-sum (SNNMS) decoding network to reduce the number of correction factors. Experimental results show that the BER performance of the proposed NNMS decoder is 1.5dB better than the conventional LDPC decoder, using fewer iterations. Furthermore, the proposed SNNMS decoder outperforms the proposed NNMS decoder and reduces the computation complexity.
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.
For recent years, deep learning has been studied and utilized among decoders in wireless and optical communication. For low density parity check (LDPC) codes, most works use neural network (NN) to implement the belief propagation (BP) decoder and unfold its iterations into layers activated by different functions. However, the whole decoder composed by neural network performs lots of non-linear operations, which are time consuming and unfriendly to hardware implementation. In this work, a neural network-aided normalized min-sum (NN-aided NMS) decoder for LDPC code is proposed, in which the normalization factors are inferred from input log likelihood ratio (LLR) by apre-trained NN, while maintaining check and variable nodes processing the same as in min-sum (MS) decoder. In order to test the proposed decoder with irregular LDPC code, a rate-7/8 one was constructed using progressive edge growth (PEG) algorithm, showing better error correction capability than the standard of consultative committee for space data systems (CCSDS) LDPC (8176,7154) code by 0.08 dB with the same rate. Simulation results show that, NN-aided NMS decoder outperforms MS decoder by 0.3 dB, and its performance approaches BP decoder with a gap of 0.02 dB, which is 50% closer than the best NMS decoder using 0.7 as the normalization factor. The proposed decoder has good performance for both regular and irregular LDPC codes, and needs much less computation complexity than BP decoder. It introduces more linear computation than NMS decoder but achieves better bit error rate (BER) performance, thus becoming a good complement between BP and NMS decoder when trading off among complexity, error correction performance and hardware implementation for wireless and satellite communication.
We investigate the application of machine learning techniques (in particular, deep neural networks, DNN) to improve the decoding algorithms of short quasi-cyclic low-density paritycheck (LDPC) codes adopted to the 5G standard. We note that straightforward application of general-purpose DNNs is not possible due to the curse of dimensionality problem – the training set size grows exponentially with the number of information bits. In our opinion, the only way to deal with this problem is to combine deep learning methods with existing decoding algorithms. We start with a Tanner-based neural network decoder with Min-Sum activation functions proposed by Nachmani et al. and extend it as follows. First, the quasi-cyclic nature of 5G LDPC codes allows us to use a single weight per circular matrix (circulant). We refer to this as weight sharing. This idea significantly reduces the training time, preserving the error-correcting performance. Second, we add residual connections to our NN architecture. Residual connections improve the performance and reduce the training time. We also present the results for the rate and length adaptation techniques. Rate adaptation allows multiple DNNs corresponding to different coding rates to run with a single set of trained weights. Length adaptation allows optimally reusing weights for multiple lifting size indices.
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.