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IEEE Communications Letters

Improved Successive-Cancellation Decoding of Polar Codes Based on Recursive Syndrome Decomposition

Jaejoon Choi, In‐Cheol Park

Published Jul 24, 2017• 3 citations
Publisher

Abstract

In this letter an improved method for the successive-cancellation decoding of polar codes is proposed. To avoid computations associated with redundant tree-traversals and syndrome calculations, recursive properties of polar codes are newly exploited in the proposed algorithm. Instead of computing a syndrome vector at every node, some syndrome vectors are directly obtained by recursively decomposing the syndrome vector computed previously. Furthermore, a modified syndrome check rule is proposed to prune unnecessary sub-trees efficiently. Compared with the latest pruning method, the proposed method reduces the latency by 23% for a (2048, 1024) polar code without sacrificing the error-correcting performance.

DOI
10.1109/lcomm.2017.2730860

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IEEE Communications Letters•Oct 12, 2018•14 citations
In this letter an improved method for the successive-cancellation decoding of polar codes is proposed. To avoid computations associated with redundant tree-traversals and syndrome calculations, recursive properties of polar codes are newly exploited in the proposed algorithm. Instead of computing a syndrome vector at every node, some syndrome vectors are directly obtained by recursively decomposing the syndrome vector computed previously. Furthermore, a modified syndrome check rule is proposed to prune unnecessary sub-trees efficiently. Compared with the latest pruning method, the proposed method reduces the latency by 23% for a (2048, 1024) polar code without sacrificing the error-correcting performance.
This letter presents an efficient pruning method for the successive-cancellation (SC) decoding of polar codes. In the proposed method, unnecessary sub-trees are pruned if the syndrome check of a constituent code is satisfied. Without sacrificing the error-rate performance, the recursive operation associated with such a constituent code is replaced with simple computations. Compared with the traditional SC decoding, the proposed pruning decreases the decoding latency by 85% on the average for the polar (1024, 512) code.
The Successive-Cancellation List (SCL) algorithm is a popular decoding algorithm for polar codes. Although SCL algorithm overcomes the error propagation problem in polar codes decoding, the improvement of error correction performance needs to pay the price of high latency. To solve this problem, a simplified SCL (SSCL) algorithm is proposed. For some special nodes, the SSCL algorithm can calculate path metric (PM) without traversing the decoding tree to achieve direct decoding, reducing the latency and complexity of decoding. In this paper, a new special node has been discovered, it is also possible to calculate PM without traversing decoding tree. Based on this, we propose an improved SSCL algorithm. Simulation results show that improved SSCL algorithm can further reduce the decoding latency and the loss of error-correction performance is negligible.
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.
Polar codes are the first capacity-achieving error-correction code which has attracted much research attention. Among many decoding methods, successive cancellation list decoding (SCLD) is considered as a representative decoding method that can achieve a good error-correcting performance. However, the long latency of SCLD is a significant matter that hinders practical applications, which is mainly caused by two features of the SCLD process: tree traversal and path-splitting. To alleviate the main reasons, a new multi-bit SCLD algorithm is proposed in this paper to decode several bits simultaneously without conducting any tree traversal and path-splitting when a node in the decoding tree holds a specific condition. In addition, a path ignoring (PI) technique is proposed to mitigate the condition of the multi-bit SCLD, which results in an additional reduction of latency. The proposed multi-bit decoding method and the PI technique play a significant role in reducing the number of path-splitting cases, by 96% compared to the conventional SCLD method. Simulation results show that compared to the conventional SCLD with list sizes 8 and 16, the proposed multi-bit decoding associated with the PI technique reduces the overall decoding cycles by 77% and 79%, respectively, with almost no degradation of error-correcting performance.
In order to reduce the latency of polar codes, several decoding methods have been proposed. However, most of them need a particular structure of nodes in the decoding tree. Thus, they ignore some unstructured nodes. To this end, we propose a modified version of the simplified successive cancellation decoder based on node error probability to complement the structured scheme. By a proper design, simulation results in additive white Gaussian noise channel show that the proposed method can efficiently reduce the decoding latency of the structured scheme while keeping the error performance almost unchanged.