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SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems

New Min-Sum Decoders Based on Deep Learning for Polar Codes

Bin Dai, Rongke Liu, Zhiyuan Yan

Published Oct 1, 2018• 14 citations
Publisher

Abstract

In this paper, we propose two novel min-sum (MS) decoding algorithms based on deep learning for polar codes, an offset min-sum (OMS) and a scaling offset min-sum (SOMS) algorithm. The parameters of both algorithms are different from iteration to iteration, and are obtained by training over a deep neural network. Our simulation results show that the OMS algorithm has roughly the same error performance as a previously proposed multiple scaling min-sum (MSMS) algorithm, and that the SOMS algorithm performs better than all existing BP-based algorithms. Since the OMS algorithm requires only an addition as opposed to a multiplication in the MSMS algorithm, the OMS algorithm is more suitable for hardware implementation. The two proposed decoding algorithms provide a tradeoff between complexity and error performance.

DOI
10.1109/sips.2018.8598384

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IEEE International Conference on Computer and Communications (ICCC)•Dec 9, 2022•1 citation
In this paper, we propose two novel min-sum (MS) decoding algorithms based on deep learning for polar codes, an offset min-sum (OMS) and a scaling offset min-sum (SOMS) algorithm. The parameters of both algorithms are different from iteration to iteration, and are obtained by training over a deep neural network. Our simulation results show that the OMS algorithm has roughly the same error performance as a previously proposed multiple scaling min-sum (MSMS) algorithm, and that the SOMS algorithm performs better than all existing BP-based algorithms. Since the OMS algorithm requires only an addition as opposed to a multiplication in the MSMS algorithm, the OMS algorithm is more suitable for hardware implementation. The two proposed decoding algorithms provide a tradeoff between complexity and error performance.
In recent years, the emerging Deep Learning (DL) technology has made progress in the field of decoding. Current polar code neural network decoder has faster convergence speed and better Bit Error Rate (BER) performance than Belief Propagation (BP) decoding. However, it still has the problem of high computational complexity. Therefore, in order to improve this problem, this paper adopts the idea of improving information update in the iterative process, and proposes a Recurrent Neural Network (RNN) Offset Min-Sum (OMS) BP decoding algorithm that improves Left information update (RNN-OMSBP-L) . The simulation results show that, compared with the Deep Neural Network (DNN) BP(DNN-BP) decoding algorithm, this algorithm replaces all multiplications with a cost of 6.25% addition. Compared with the current optimized RNN OMS and approximate BP(RNN-OMS-BP) decoding algorithm, the decoding algorithm in this paper uses improved information to reduce 25% of the addition operations with almost no loss in BER performance, while saving part of the storage space overhead. Under the same BER performance, it reduces the number of iterations by 37.5%.
This paper presents deep learning (DL) methods to optimize polar belief propagation (BP) decoding and concatenated LDPC-polar codes. First, two-dimensional offset Min-Sum (2-D OMS) decoding is proposed to improve the error-correction performance of existing normalized Min-Sum (NMS) decoding. Two optimization methods used in DL, namely back-propagation and stochastic gradient descent, are exploited to derive the parameters of proposed algorithms. Numerical results demonstrate that there is no performance gap between 2-D OMS and exact BP on various code lengths. Then the concatenated OMS algorithms with low complexity are presented for concatenated LDPC-polar codes. As a result, the optimized concatenated OMS decoding yields error-correction performance with CRC-aided successive cancellation list (CA-SCL) decoder of list size 2 on length-1024 polar codes. In addition, the efficient hardware architectures of scalable polar OMS decoder are described and the proposed decoder is reconfigurable to support three code lengths (N = 256, 512, 1024) and two decoding algorithms (2-D OMS and concatenated OMS). The polar OMS decoder implemented on 65 nm CMOS technology achieves a maximum coded throughput of 5.4 Gb/s at Eb/N0= 4 dB for code length 1024 and 7.5 Gb/s at Eb/N0= 3.5 dB for code length 256, which are comparable to the state-of-the-art polar BP decoders. Moreover, a 5.1 Gb/s throughput at Eb/N0= 4 dB is achieved under concatenated OMS decoding mode for code length 1024 with a latency of 200 ns, which is superior to existing CA-SCL decoders that have similar error-correction performance.
With the wide application of Deep Neural Network (DNN) in the field of communication, this technique has also been applied in the coding and decoding technology, but there are few neural network structures with good performance in the decoder. This paper proposes a new polar code decoding network structure, which uses a modular network structure to train the empirical parameters in the iterative belief propagation (BP) algorithm model. The experiment part uses the new structure to implement scaling min-sum (SMS) algorithm and offset min-sum (OMS) algorithm. Through comparing the performance of the above algorithms with the traditional structure, it is found that the new structure has the advantages of better bit error rate (BER) and faster convergence performance compared with the traditional network structure.
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.
Deep learning has shown an unprecedented success in many fields such as computer vision and speech recognition, providing solutions to intractable problems. Deep learning has also provided solutions to several intractable problems in communications systems. This paper uses a deep learning approach to optimize the analytically intractable offset value in the offset-min-sum (OMS) algorithm. OMS algorithm is a very attractive low complexity algorithm that is used in the belief propagation decoding of linear codes. The contributions of this paper are: First, providing a low complexity offset optimization framework based on gradient descent and back propagation on the original Tanner graph. Our proposed algorithm has comparable complexity and similar operation as the forward belief propagation decoding algorithm and hence, can be trained much more efficiently. Second, the framework can be easily extended to any decoding scheduling such as flooding or layered scheduling. Training results show that the proposed framework can find the optimal offset value under different decoding scheduling with the same complexity of the belief propagation algorithm.
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%.