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arXiv:2205.08857 · IEEE Transactions on Signal Processing

A Sequence Repetition Node-Based Successive Cancellation List Decoder for 5G Polar Codes: Algorithm and Implementation

Yuqing Ren, Andreas Toftegaard Kristensen, Yifei Shen, Alexios Balatsoukas‐Stimming, Chuan Zhang, Andreas Peter Burg

Published Jan 1, 2022• 53 citations
arXivHTMLPDF

Abstract

Due to the low-latency and high-reliability requirements of 5G, low-complexity node-based successive cancellation list (SCL) decoding has received considerable attention for use in 5G communications systems. By identifying special constituent codes in the decoding tree and immediately decoding these, node-based SCL decoding provides a significant reduction in decoding latency compared to conventional SCL decoding. However, while there exists many types of nodes, the current node-based SCL decoders are limited by the lack of a more generalized node that can efficiently decode a larger number of different constituent codes to further reduce the decoding time. In this paper, we extend a recent generalized node, the sequence repetition (SR) node, to SCL decoding, and describe the first implementation of an SR-List decoder. By merging certain SR-List decoding operations and applying various optimizations for 5G New Radio (NR) polar codes, our optimized SR-List decoding algorithm increases the throughput by almost$\bm {2\times }$compared to a similar state-of-the-art node-based SCL decoder. We also present our hardware implementation of the optimized SR-List decoding algorithm which supports all 5G NR polar codes. Synthesis results show that our SR-List decoder can achieve a$2.94 \,\mathrm{Gbps}$throughput and$6.70 \,\mathrm{Gbps}\mathrm{m}^{-1}\,\mathrm{m}^{2}\,$area efficiency for$\bm {L=8}$.

DOI
10.1109/tsp.2022.3216921

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IEEE Transactions on Communications•Mar 19, 2019•62 citations
Due to the low-latency and high-reliability requirements of 5G, low-complexity node-based successive cancellation list (SCL) decoding has received considerable attention for use in 5G communications systems. By identifying special constituent codes in the decoding tree and immediately decoding these, node-based SCL decoding provides a significant reduction in decoding latency compared to conventional SCL decoding. However, while there exists many types of nodes, the current node-based SCL decoders are limited by the lack of a more generalized node that can efficiently decode a larger number of different constituent codes to further reduce the decoding time. In this paper, we extend a recent generalized node, the sequence repetition (SR) node, to SCL decoding, and describe the first implementation of an SR-List decoder. By merging certain SR-List decoding operations and applying various optimizations for 5G New Radio (NR) polar codes, our optimized SR-List decoding algorithm increases the throughput by almost2×\bm {2\times }2×compared to a similar state-of-the-art node-based SCL decoder. We also present our hardware implementation of the optimized SR-List decoding algorithm which supports all 5G NR polar codes. Synthesis results show that our SR-List decoder can achieve a2.94 Gbps2.94 \,\mathrm{Gbps}2.94Gbpsthroughput and6.70 Gbpsm−1 m2 6.70 \,\mathrm{Gbps}\mathrm{m}^{-1}\,\mathrm{m}^{2}\,6.70Gbpsm−1m2area efficiency forL=8\bm {L=8}L=8.
Compared with the bit-wise successive cancellation list (SCL) decoding of polar codes, the node-based Fast SCL decoding significantly reduces the decoding latency by identifying special constituent codes and decoding these in parallel. To further reduce the latency of current Fast SCL decoders, we first propose a fast sequence repetition (SR) node-based SCL (Fast SR-SCL) decoding algorithm, which only involves one type of node in the SCL decoding tree. Furthermore, we employ the adaptive path splitting (APS) strategy to terminate the path splitting in the SR node early, without degrading the error-correcting performance. Numerical results show that for 5G uplink codes with a length of 1024 and rates of 1/4, 1/2, and 3/4, our decoder can deliver the same decoding performance while reducing the average latency by 34.5%, 38.0%, and 39.6% compared with the state-of-the-art Fast SCL decoder for a list size L = 8.
Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. To reduce the decoding latency, developing tailored fast and efficient list decoding algorithms of specific polar constituent codes (special nodes) is a promising solution. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming to further speedup the SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) nodes and sequence rate one or single-parity-check (SR1/SPC) nodes. In particular, we develop two classes of fast list decoding algorithms for these nodes, where the first class uses a sequential decoding procedure to yield decoding latency that is linear with the list size, and the second further parallelizes the decoding process by pre-determining the redundant candidate paths offline. Simulation results show that the proposed list decoding algorithms are able to achieve up to 70.7% lower decoding latency than state-of-the-art fast SCL decoders, while exhibiting the same error-correction performance.
As two common successive cancellation (SC)-based decoding algorithms of polar codes, the SC list (SCL) and SC stack (SCS) decoder can achieve satisfactory error correction performance, especially with increased list size or stack depth. Nevertheless, a large list size or stack depth will lead to high computational complexities and hardware resources. To this end, successive cancellation priority (SCP) decoding with priority- first searching strategy and trellis-like storage is proposed to offer one solution. In this paper, an efficient SCP decoder is first proposed to verify its advantages over SCL and SCS decoders. Furthermore, an adaptive node-inserting scheme is proposed to reduce the number of bits insert into the priority queue. Numerical results have shown that for the polar code with transmission length 1024 and rate 1/2, the proposed adaptive SCP (ASCP) decoder can achieve significant time complexity reduction on average compared with the standard SCL decoder. The hardware architecture of SCP decoding is implemented using 65-nm CMOS technology and the results show better throughput compared with the SCS decoder.
Being able to provide excellent error-correction performance for polar codes with short-to-moderate code length, successive-cancellation list (SCL) is regarded as one of the most promising decoding algorithms. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming at achieving further speedup for SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) and sequence rate-1(SRI) nodes, based on the minimum-combinations set (MCS) which is able to significantly narrow the search space of candidate paths. Typically, SPC nodes can be directly decoded within one round of path splitting procedure, whereas SR1 nodes, as a group of parallel SPC nodes, can also be decode efficiently. Simulation results show that the proposed fast SCL decoder is able to reduce the decoding latency by 68.4% as compared to the state of the art, without any error-correction performance degradation.
In this paper, we present a novel scheduling method that reduces the latency of polar decoders significantly. Unlike the prior pruning-based successive cancellation list (SCL) decoding that suffers from a number of idle cycles, the proposed overlapped SCL scheme immediately begins node operations without waiting for the list to be sorted, being exempt from such unfavorable cycles. All possible candidates for the next node operations are precomputed in parallel with the pruning operations, and are readily selected to minimize the latency. For the 5G New Radio systems, the proposed method shortens the decoding latency of the state-of-the-art approaches by up to 22% without degrading the error-correcting performance.
The successive-cancellation list (SCL) and successive-cancellation flip (SCF) decoding can be used to improve the performance of polar codes, especially for short to moderate length codes. However, their serial decoding nature results in significant decoding latencies. Implementing some operations in parallel can reduce their decoding latencies. This paper presents fast implementations of the SCL and SCF decoders. In particular, we propose fast parallel list decoders for five newly identified types of nodes in the decoding tree of a polar code, which significantly improves the decoding latency. We also present novel fast SCF decoders that decode some special nodes in the decoding tree of a polar code without serially computing bit log-likelihood ratios. Using our proposed fast parallel SCF decoders, we observed an improvement up to 81% with respect to the original SCF decoder. This significant reduction in the decoding latency is observed without sacrificing the bit-error-rate performance of the code.