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IEEE International Symposium on Information Theory (ISIT)

On Fast SC-Based Polar Decoders: Metric Polarization and a Pruning Technique

Mohsen Moradi, Hessam Mahdavifar

Published Jun 22, 2025• 2 citations
Publisher

Abstract

In this paper, we propose a method for obtaining metric functions for each depth of the channel polarization tree through a process that we call polarization of the metric function. One of the major advantages of the proposed metric function is that it can be utilized in fast successive cancellation-based (FSC) and SC list-based (FSCL) decoders, i.e., decoders that opt to skip the so-called rate-1 and rate-0 nodes in the binary tree representation for significantly more efficient implementation. Furthermore, we relate the average and variance values of the polarized metric function of FSC-based decoders to the polarized channel capacity and polarized varentropy. By leveraging this observations, we introduce a pruning technique that keeps only the paths in the FSCL decoder whose metric values are close to the average value. As a result, our proposed technique significantly reduces the number of required sorting operations for FSCL-based decoding algorithms. For instance, for a highrate PAC (128,99) code, SCL decoding with a list size of 32 achieves error-correction performance comparable to the Fano algorithm. FSCL decoding requires visiting only 28 nodes of the polarization tree, significantly fewer than the 254 nodes required for conventional SCL decoding. Additionally, our method reduces the number of sorting operations by a factor of 3, further decreasing latency and complexity.

DOI
10.1109/isit63088.2025.11195561

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Journal of Communications and Networks•Dec 1, 2021•20 citations
In this paper, we propose a method for obtaining metric functions for each depth of the channel polarization tree through a process that we call polarization of the metric function. One of the major advantages of the proposed metric function is that it can be utilized in fast successive cancellation-based (FSC) and SC list-based (FSCL) decoders, i.e., decoders that opt to skip the so-called rate-1 and rate-0 nodes in the binary tree representation for significantly more efficient implementation. Furthermore, we relate the average and variance values of the polarized metric function of FSC-based decoders to the polarized channel capacity and polarized varentropy. By leveraging this observations, we introduce a pruning technique that keeps only the paths in the FSCL decoder whose metric values are close to the average value. As a result, our proposed technique significantly reduces the number of required sorting operations for FSCL-based decoding algorithms. For instance, for a highrate PAC (128,99) code, SCL decoding with a list size of 32 achieves error-correction performance comparable to the Fano algorithm. FSCL decoding requires visiting only 28 nodes of the polarization tree, significantly fewer than the 254 nodes required for conventional SCL decoding. Additionally, our method reduces the number of sorting operations by a factor of 3, further decreasing latency and complexity.
Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting operations without visible degradation in the code’s error-correction performance. In an SCL decoding with an optimum metric function we show that, on average, the correct branch’s bit-metric value must be equal to the bit-channel capacity, and on the other hand, the average bit-metric value of a wrong branch can be at most zero. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. For relatively reliable bit-channels, the bit metric for a wrong branch becomes very large negative number, which enables us to detect and prune such paths. We prove that, for a threshold lower than the bit-channel cutoff rate, the probability of pruning the correct path decreases exponentially by the given threshold. Based on these findings, we presented a pruning technique, and the experimental results demonstrate a substantial decrease in the amount of sorting procedures required for SCL decoding. In the stack algorithm, a similar technique is used to significantly reduce the average number of paths in the stack.
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.
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.
This work presents a fast successive-cancellation list flip (Fast-SCLF) decoding algorithm for polar codes that addresses the high latency issue associated with the successive-cancellation list flip (SCLF) decoding algorithm. We first propose a bit-flipping strategy tailored to the state-of-the-art fast successive-cancellation list (FSCL) decoding that avoids tree-traversal in the binary tree representation of SCLF, thus reducing the latency of the decoding process. We then derive a parameterized path selection error model to accurately estimate the bit index at which the correct decoding path is eliminated from the initial FSCL decoding. The trainable parameter is optimized online based on an efficient supervised learning framework. Simulation results show that for a polar code of length 512 with 256 information bits, with similar error-correction performance and memory consumption, the proposed Fast-SCLF decoder reduces up to 73.4% of the average decoding latency of the SCLF decoder with the same list size at the frame error rate of 10−4, while incurring a maximum computational complexity overhead of 27.6%. For the same polar code of length 512 with 256 information bits and at practical signal-to-noise ratios, the proposed decoder with list size 4 reduces 89.3% and 43.7% of the average complexity and decoding latency of the FSCL decoder with list size 32 (FSCL-32), respectively, while also reducing 83.2% of the memory consumption of FSCL-32. The significant improvements of the proposed decoder come at the cost of 0.07 dB error-correction performance degradation compared with FSCL-32.
Successive cancellation list (SCL) decoding enables polar codes and their generalizations to deliver satisfactory performance in finite-length scenarios but it comes with high latency and complexity. To reduce latency, a partitioned SCL (PSCL) decoding algorithm, implemented over a PSCL decoding tree, can be utilized. In this work, we aim to lower down the complexity of the PSCL decoding, resulting in an efficient decoding algorithm with low latency and complexity for polar-like codes. To achieve this, we define two metrics at each level of the PSCL decoding tree. One is for evaluating the reliability of a path and the other is for estimating the probability of the correct path being included in a list of paths. Then, we propose a double-threshold strategy in the PSCL decoding process where unreliable valid paths are pruned based on the first metric, and then a list of surviving paths is selected based on the second metric. Simulation results demonstrate that when polar/CRC-polar/PAC codes are decoded using the proposed low-complexity PSCL decoder, both the sorting complexity and the computational complexity are reduced and significantly decrease as the signal-to-noise ratio (SNR) increases.
In this paper, an improvement for SC list flip (SCL-Flip) decoding is presented for polar codes. A novel bit-selection metric for critical set (set of information symbols of polar codes being flipped during additional decoding attempts) based on path metric of successive cancellation list (SCL) decoding is suggested. With the proposed metric, the improved SCL scheme based on special nodes (SN) decoders was developed. This decoder will be denoted by GSCLF. The main idea of the proposed decoder is joint using of two approaches: first one is a fast decoding of special nodes in binary tree representation of polar code (e.g., some special nodes in tree representation of polar code that allow efficient list decoding with low complexity) and the second one is an applying of additional decoding attempts (flips) in the case when initial decoding was erroneous. The simultaneous use of these two approaches results in both a significant reduction in spatial complexity and a significant reduction in the number of computations required for decoding whereas keeping excellent performance. Simulation results presented in this paper allow us to conclude that the computational complexity of the proposed GSCLF decoder is from 66% to 80% smaller than the one of SCL-32 decoder.