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Journal of Signal Processing Systems

Optimization and Hardware Implementation of Learning Assisted Min-Sum Decoders for Polar Codes

Ning Lyu, Bin Dai, Hongfei Wang, Zhiyuan Yan

Published Jun 27, 2020• 2 citations
Publisher
DOI
10.1007/s11265-020-01561-y

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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.

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As to realize believe propagation (BP) for polar decoding, the scaled min-sum (SMS) algorithm is widely used in hardware realization for polar decoders. However, the decoding performance of SMS algorithm is still not good as the length of polar codes increase, and its computing architecture,which called processing elements (PE) needs to be further optimized due to its long critical path. In this paper, referring to the method used in LDPC/Turbo decoding, a look-up-table (LUT) algorithm and its modified version called LUT-SMS are proposed for polar decoding. The simulation result shows that, compared with the SMS algorithm, the proposed LUT-SMS algorithm can lead to 0.3 dB extra decoding gain when the code length up to 2048. For a different trade-off, a new SMS computing architecture which has shorter computing path is proposed to solve the long delay of the polar decoders. The hardware implementation result shows that, the optimized SMS computing architecture can also achieve more than 32% increase in throughput for the case of (256,128) polar decoder without much extra hardware consumption. As a result, both these two optimization schemes have good promotion for polar decoding.
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.
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.