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IEEE Transactions on Signal Processing

Iterative and Adjustable Soft List Decoding for Polar Codes

Bowen Feng, Jian Jiao, Shaohua Wu, Ye Wang, Qinyu Zhang

Published Jan 1, 2020• 5 citations
Publisher

Abstract

List decoding of polar codes is an outstanding decoding method, in which a fixed-size list is applied to retain the most probable paths. In general, it is preferable to use a large-size list in the decoding to achieve excellent error-control performance, but this can lead to high complexity. Moreover, the list decoding is still a one-time-pass algorithm with hard-decision outputs, which is not well suited for advanced concatenated coding systems. In this paper, a novel adjustable list decoding is proposed, in which the list size can be adjusted appropriately. Based on the reliability analyses of the decoding list, dynamic thresholds are designed to precisely guide the adjustments. The adjustable list decoding can also achieve excellent error-control performance, but the complexity is significantly reduced. Moreover, we propose an iterative adjustable list decoding scheme with soft-decision outputs for concatenated polar-coding systems, in which a log-likelihood-ratio update strategy is elaborately designed. It can achieve much better error-control performance compared with the existing iterative decoding schemes, such as the belief propagation (BP) decoding, and soft cancellation (SCAN) decoding. As the number of iterations increases, the decoding performance gradually improves, but the complexity increases little due to efficient complexity control designs.

DOI
10.1109/tsp.2020.3020226

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List decoding of polar codes is an outstanding decoding method, in which a fixed-size list is applied to retain the most probable paths. In general, it is preferable to use a large-size list in the decoding to achieve excellent error-control performance, but this can lead to high complexity. Moreover, the list decoding is still a one-time-pass algorithm with hard-decision outputs, which is not well suited for advanced concatenated coding systems. In this paper, a novel adjustable list decoding is proposed, in which the list size can be adjusted appropriately. Based on the reliability analyses of the decoding list, dynamic thresholds are designed to precisely guide the adjustments. The adjustable list decoding can also achieve excellent error-control performance, but the complexity is significantly reduced. Moreover, we propose an iterative adjustable list decoding scheme with soft-decision outputs for concatenated polar-coding systems, in which a log-likelihood-ratio update strategy is elaborately designed. It can achieve much better error-control performance compared with the existing iterative decoding schemes, such as the belief propagation (BP) decoding, and soft cancellation (SCAN) decoding. As the number of iterations increases, the decoding performance gradually improves, but the complexity increases little due to efficient complexity control designs.
This paper proposes a novel iterative decoder based on concatenated belief propagation (BP) for CRC-aided polar codes. Compared to the conventional BP-based decoders for polar codes, soft cancellation (SCAN) decoder can generate a log likelihood ratio (LLR) of coded bit with lower computational complexity without sacrificing the detection capability. Unfortunately, its performance is not as good as that of CRC-aided successive cancellation list decoder (SCLD) although SCAN decoder has advantage of hardware implementation. To compensate the performance gap, we exploit CRC structure for not only error detection but also error correction with the assistance of its error correction capability at a short code length by exchanging LLRs between SCAN decoder and BP decoder on the basis of CRC. Moreover, the sub-optimal criterion for selecting a parity check matrix of CRC for BP decoder is proposed. Finally, computer simulations are conducted to confirm the validity of our proposed method. The proposed method can obtain the gain of about 0.6 dB at BER=10-3compared to the native SCAN decoder without requiring huge memory size as in SCLD.
The soft-decision decoding of polar codes is a trend that will be extensively applied in modern complex communication systems. However, the existing soft-decision decoding of polar codes is not satisfied due to the poor performance and high complexity. In this paper, a novel adjustable list decoding and its soft-decision type are proposed. Some bounds are given to depict the features of the decoding list with a correct path, which provides a guide to adjust the decoding list. The proposed adjustable list decoding scheme can achieve an equivalent performance to conventional SCL with significant lower complexity. Moreover, the soft adjustable list decoding can also outperform than the conventional soft-decision decoding schemes in concatenated structures.
We propose a belief propagation list (BPL) decoder with comparable performance to the successive cancellation list (SCL) decoder of polar codes, which already achieves the maximum likelihood (ML) bound of polar codes for sufficiently large list size L. The proposed decoder is composed of multiple parallel independent belief propagation (BP) decoders based on differently permuted polar code factor graphs. A list of possible transmitted codewords is generated and the one closest to the received vector, in terms of Euclidean distance, is picked. To the best of our knowledge, the proposed BPL decoder provides the best performance of plain polar codes under iterative decoding known so far. The proposed algorithm does not require any changes in the polar code structure itself, rendering the BPL into an alternative to the SCL decoder, equipped with a soft output capability enabling, e.g., iterative detection and decoding to further improve performance. Further benefits are the lower decoding latency than the SCL decoder and the possibility of high throughput implementations. Additionally, we show that a different selection strategy of frozen bit positions can further enhance the error-rate performance of the proposed decoder.
The soft cancellation decoding of polar codes achieves a better performance than the belief propagation decoding with lower computational time and space complexities. However, because the soft cancellation decoding is based on the successive cancellation decoding, the decoding efficiency and performance with finite-length blocks can be further improved. Exploiting the idea of the successive cancellation list decoding, the soft cancellation decoding can be improved in two aspects: one is by adding branch decoding to the error-prone information bits to increase the accuracy of the soft information, and the other is through using partial iterative decoding to reduce the time and computational complexities. Compared with the original method, the improved soft cancellation decoding makes progress in the error correction performance, increasing the decoding efficiency and reducing the computational complexity, at the cost of a small increase of space complexity.
Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7 dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.
Although the successive cancellation list (SCL) decoding of polar codes exhibits excellent performance, it retains many decoding paths in the list with negligible contribution to the final output, resulting in high sorting and computational complexity. In this letter, we propose a novel pruning strategy to mitigate the decoding complexity. By leveraging the blockwise soft output extraction process of soft-output SCL and soft-output fast SCL decoding, we provide an accurate approximation of the probability that a decoding path is correct, and thus accordingly prune the paths failing to meet a pre-defined reliability threshold. The complexity reduction achieved by the proposed soft-output-based pruned SCL (SOP-SCL) decoder and its fast version, SOP-FSCL decoder, is significant, without any compromise in error-correction performance. Meanwhile, they also prove to be more efficient than state-of-the-art pruned polar decoders.