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Error Correction Enhancement in SCL Decoding of Polar Codes Using LSTM Network

Fatemeh Alia, Bahareh Akhbari, Mahmoud Ahmadian‐Attari

Published May 13, 2025• 0 citations
Publisher

Abstract

Polar codes have been selected as the channel coding scheme for the Enhanced Mobile Broadband (eMBB) control channel in 5G, which requires short length codes. One of the main challenges in utilizing polar codes is the design of low-complexity decoders with adequate error-correcting performance. The Successive Cancellation (SC) decoder was introduced as the first algorithm enabling polar codes to achieve the channel capacity for long codelengths. However, for shorter codelengths, this decoder does not provide satisfactory error-correction performance. To address this limitation, the Successive Cancellation List (SCL) decoder has been proposed, which performs decoding by maintaining a list of candidate paths and selecting the best one based on a path metric. In this paper, we propose improving the error-correction performance of the SCL decoder using concatenated Cyclic Redundancy Check (CRC) codes and Long Short-Term Memory (LSTM) network. Simulation results demonstrate that the proposed method outperforms the Belief Propagation (BP) decoder in terms of Bit Error Rate (BER) curves. Furthermore, the accuracy of the LSTM model in this study improves from 73 percent in previous research to 93.77 percent.

DOI
10.1109/icee67339.2025.11213577

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Polar codes have been selected as the channel coding scheme for the Enhanced Mobile Broadband (eMBB) control channel in 5G, which requires short length codes. One of the main challenges in utilizing polar codes is the design of low-complexity decoders with adequate error-correcting performance. The Successive Cancellation (SC) decoder was introduced as the first algorithm enabling polar codes to achieve the channel capacity for long codelengths. However, for shorter codelengths, this decoder does not provide satisfactory error-correction performance. To address this limitation, the Successive Cancellation List (SCL) decoder has been proposed, which performs decoding by maintaining a list of candidate paths and selecting the best one based on a path metric. In this paper, we propose improving the error-correction performance of the SCL decoder using concatenated Cyclic Redundancy Check (CRC) codes and Long Short-Term Memory (LSTM) network. Simulation results demonstrate that the proposed method outperforms the Belief Propagation (BP) decoder in terms of Bit Error Rate (BER) curves. Furthermore, the accuracy of the LSTM model in this study improves from 73 percent in previous research to 93.77 percent.
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.
Polar codes have garnered significant attention since they were proposed due to their capacity-achieving properties and their low-complexity decoding process, and they were selected as the coding scheme for the control channel in 5G mobile communication technology. A successive cancellation list (SCL) decoder, aided by a cyclic redundancy check (CRC), performs the competitive error correcting performance for polar codes compared to other sophisticated codes. The SCL-Flip decoding algorithm is proposed to enhance the error correction performance of the SCL. However, the SCL-Flip is hampered by a high decoding complexity due to the necessary selection and sorting process of path metrics (PMs). Additionally, it requires a large number of iterations to achieve a good error correction performance. In this paper, we propose the error segment bit-flip (ES-SCL-Flip) decoding algorithm, a simplified bit-flip approach for the SCL decoder based on analyzing the distributions of the first error bit. Firstly, we construct an index set with a high probability of the first erroneous bit. Second, a bit-flip criterion is introduced to prevent the costly operation of the PM selection and sorting without compromising the error correction performance. Finally, a search strategy is employed that utilizes segmented error indication to target and rectify the initial error segment sequentially. The simulation results demonstrate that the ES-SCL-Flip decoder provides an improved error correction performance with only a minimal increase in decoding complexity compared to the conventional CRC-aided SCL decoder. This algorithm attains a commendable equilibrium between the error correction performance and decoding complexity.
Polar code is envisioned as a promising candidate for ultra-reliable low-latency communications (URLLC) in fifth-generation (5G) communication and beyond. To decode polar code, a successive cancellation list (SCL) decoder with a large list size can provide near maximum likelihood (ML) decoding performance. However, a large list size will lead to unacceptable spatial complexity, making it impractical. When the list size is small, although the complexity is low, its performance still needs to be improved. The main reason is that the sequence features implied in log-likelihood ratio (LLR) sequences are lost during calculating path metrics used for path selection. Because of the excellent sequence feature extraction ability of the long short-term memory (LSTM) network, we propose an LSTM-based path selection mechanism to replace the path metric-based path selection mechanism in SCL. In our proposed scheme, the LSTM network selects the surviving path according to the LLR sequences corresponding to the current paths. Simulation results show the effectiveness of the proposed LSTM-based path selection mechanism.
Polar codes have attracted much attention in the past decade due to their capacity-achieving performance. The higher decoding capacity is required for 5G and beyond 5G (B5G). Although the cyclic redundancy check (CRC)- assisted successive cancellation list bit-flipping (CA-SCLF) decoders have been developed to obtain a better performance, the solution to error bit correction (bit-flipping) problem is still imperfect and hard to design. In this work, we leverage the expert knowledge in communication systems and adopt deep learning (DL) technique to obtain the better solution. A low-complexity long short-term memory network (LSTM)-assisted CA-SCLF decoder is proposed to further improve the performance of conventional CA-SCLF and avoid complexity and memory overhead. Our test results show that we can effectively improve the BLER performance by 0.11dB compared to prior work and reduce the complexity and memory overhead by over 30% of the network.
Polar codes have attracted much attention in the past decade due to their capacity-achieving performance. The higher decoding capacity is required for 5G and beyond 5G (B5G). Although the cyclic redundancy check (CRC)- assisted successive cancellation list bit-flipping (CA-SCLF) decoders have been developed to obtain a better performance, the solution to error bit correction (bitflipping) problem is still imperfect and hard to design. In this work, we leverage expert knowledge in communication systems and adopt deep learning (DL) techniques to obtain a better solution. A low-complexity long short-term memory network (LSTM)-assisted CASCLF decoder is proposed to further improve the performance of conventional CA-SCLF and avoid complexity and memory overhead. Our test results show that we can effectively improve the BLER performance by 0.11dB compared to prior work and reduce the complexity and memory overhead by over 30% of the network.
Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10-5and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead.