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Journal of Communications and Networks

Deep-learning-aided fast successive cancellation decoding of polar codes

Haogang Feng, H. L. Xiao, Shida Zhong, Zhuqing Gao, Tao Yuan, Zhi Quan

Published Dec 1, 2024• 2 citations
Publisher

Abstract

With the continuous evolution of 5G communication technology to B5G and the next generation of communication technology, Deep Learning technology will also lead the automation and intelligent transformation of communication systems. Existing research has shown that the combination of deep learning and communication technology is expected to break some performance bottlenecks of traditional communication algorithms and solutions. This paper explores the application of deep learning (DL) in polar decoding algorithms, proposing a DL-aided-FSC (DL-FSC) polar code decoder algorithm. For the DL-FSC decoding algorithm, the conventional successive cancellation (SC) decoder is partitioned into multiple sub-blocks, which are replaced by R0 nodes, R1 nodes and sub-DL decoder. The log-likelihood ratio (LLR) and frozen bit pattern are input to the sub-DL decoder to predict decode codewords under any decoding code rate. Through simulation verification, under the PBCH channel of 5G communication, the DL-FSC decoder achieves similar block error rate (BLER) performance to the SC decoder, even improving by about 1%. In order to verify the performance optimization effect of the proposed algorithm at the hardware level, the DL-FSC deocder circuit design was completed. Through FPGA synthesis, the proposed decoder achieves a throughput of about 4571 Mbps, which is 1.71× improvement in decoding throughput at the expense of increased logic resources.

DOI
10.23919/jcn.2024.000070

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With the continuous evolution of 5G communication technology to B5G and the next generation of communication technology, Deep Learning technology will also lead the automation and intelligent transformation of communication systems. Existing research has shown that the combination of deep learning and communication technology is expected to break some performance bottlenecks of traditional communication algorithms and solutions. This paper explores the application of deep learning (DL) in polar decoding algorithms, proposing a DL-aided-FSC (DL-FSC) polar code decoder algorithm. For the DL-FSC decoding algorithm, the conventional successive cancellation (SC) decoder is partitioned into multiple sub-blocks, which are replaced by R0 nodes, R1 nodes and sub-DL decoder. The log-likelihood ratio (LLR) and frozen bit pattern are input to the sub-DL decoder to predict decode codewords under any decoding code rate. Through simulation verification, under the PBCH channel of 5G communication, the DL-FSC decoder achieves similar block error rate (BLER) performance to the SC decoder, even improving by about 1%. In order to verify the performance optimization effect of the proposed algorithm at the hardware level, the DL-FSC deocder circuit design was completed. Through FPGA synthesis, the proposed decoder achieves a throughput of about 4571 Mbps, which is 1.71× improvement in decoding throughput at the expense of increased logic resources.
A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing additional rounds of SCL decoding when the first SCL decoding attempt fails, using a novel bit-flipping metric. The proposed bit-flipping metric exploits the inherent relations between the information bits in polar codes that are represented by a correlation matrix. The correlation matrix is then optimized using emerging deep-learning techniques. Performance results on a polar code of length 128 with 64 information bits concatenated with a 24-bit cyclic redundancy check show that the proposed bit-flipping metric in the proposed DL-SCL decoder requires up to 66% fewer multiplications and up to 36% fewer additions, without any need to perform transcendental functions, and by providing almost the same error-correction performance in comparison with the state of the art.
Polar codes are the first error-correcting code proven to achieve channel capacity based on infinite code length. The Successive Cancellation List Flip (SCLF) decoding algorithm was proposed by flipping an erroneous bit during the next decoding attempt. To identify the erroneous bits, the Log-Likelihood Ratio (LLR) is used to indicate the reliability of each decision bit. To improve the accuracy of the erroneous bit prediction, we propose deep-learning-aided (DL-aided) SCLF decoding algorithms. We first offer a stacked LSTM network that contains new features to train our models, which are able to improve the accuracy of the prediction of positions of erroneous bits. Then we separately train the stacked LSTM models to predict the position of both the first and second erroneous bits and whether to continue flipping. As a result, the DL-aided SCLF decoding algorithms based on the proposed stacked LSTM flip-1 model, stacked LSTM flip-2 model, and the stacked LSTM continue-flipping check (CFC) model are able to provide a better performance at a lower number of average decoding attempts when compared to other state-of-the-art decoding algorithms.
We investigate the cyclic redundancy check (CRC) codes aided successive cancellation list (SCL) decoding schemes to improve the performance of Polar codes. Distinguished from the existing literatures of Polar codes that only consider the error detection capability of CRC, we attempt to take advantage of the inherent error correction capability of CRC and we first devise a segmented CRC-error-correcting aided SCL decoding (SCC-SCL) framework. Based on this framework, an error-correcting table based SCC-SCL (ET-SCC-SCL) decoding scheme is proposed, by introducing the look-up-table based CRC error correction method into the segmented Polar SCL decoding process. Since the error correction capability is limited by the size of the look-up table, which in turn limits the performance gain, we further propose a deep learning based SCC-SCL (DL-SCC-SCL) decoding scheme. In this scheme, a long short-term memory (LSTM) network replaces the error correction table to perform error correction, combining the sequence of log likelihood ratios (LLRs) with the syndromes to determine the error patterns. Simulation results show that both of the proposed decoding schemes have significant performance gain over the classic CRC error-detection aided SCL decoding scheme. Especially for the DL-SCC-SCL, the performance gain at bit error rate of 10-5is about 0.5 dB.
The key to successive cancellation (SC) flip decoding of polar codes is to accurately identify the first error bit. The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, we propose a deep learning aided SC flip algorithm. Specifically, before each SC decoding attempt, a long short-term memory (LSTM) network is exploited to either (i) locate the first error bit, or (ii) undo a previous "wrong" flip. In each SC attempt, the sequence of log likelihood ratios (LLRs) derived in the previous SC attempt is exploited to decide which action to take. Accordingly, a two-stage training method of the LSTM network is proposed, i.e., learn to locate first error bits in the first stage, and then to undo "wrong" flips in the second stage. Simulation results show that the proposed approach identifies error bits more accurately and achieves better block error rate performance than the state-of-the-art SC flip algorithms.
Recently, the dynamic-successive cancellation list flip (D-SCLF) decoder has been proposed to improve the high-order flipping performance of existing successive cancellation list flip (SCLF) decoders in polar codes decoding. However, the D-SCLF decoder involves a large number of exponential and logarithmic operations, resulting in an exponential increase in computational complexity. To further improve the performance and reduce the average complexity of D-SCLF decoding, the deep learning-assisted adaptive dynamic-SCLF (DL-AD-SCLF) decoding is proposed in this paper. The error metric of D-SCLF decoding is re-derived, and an approximation scheme is proposed to reduce computational complexity. To compensate the loss of performance due to approximation, two learnable parameters are introduced. Customized neural network structures are proposed to optimize these learnable parameters according to the improved error metric by employing deep learning (DL), and the deep learning-assisted dynamic-SCLF (DL-D-SCLF) decoding is proposed. Furthermore, the adaptive list is introduced into the DL-D-SCLF decoding to further reduce decoding complexity. Simulation results show that the proposed decoder performance is improved up to 0.35dB and 0.25dB, the average complexity is reduced by up to 57.65% and 51.48% for single-bit and multi-bit flipping, respectively. Additionally, the proposed decoder exhibits good robustness to changes in code rates, code lengths, and channel conditions.
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.