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IEEE Communications Letters

Sequential Decoding of Polar Codes

V. Miloslavkaya, Peter Trifonov

Published May 13, 2014• 81 citations
Publisher

Abstract

The problem of efficient decoding of polar codes is considered. A low-complexity sequential soft decision decoding algorithm is proposed. It is based on the successive cancellation approach, and it employs most likely codeword probability estimates for selection of a path within the code tree to be extended.
DOI
10.1109/lcomm.2014.2323237

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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.
Successive cancellation list (SCL) decoding algorithm for polar codes is one of the best decoding algorithms due to its excellent decoding performance. The decoding complexity of conventional SCL decoding algorithm is O(LN log N). The decoding complexity will increase as the size of the list increases. To solve this problem, we introduce an improved SCL decoding algorithm based on the sequential probability ratio test (SPRT). The proposed algorithm use double thresholds to decode the polar codes instead of single threshold decision used by the conventional SCL algorithm. Numerical results have shown that for (1024, 512) polar code, the proposed SPRT-SCL decoder can achieve a reduction in decoding complexity, and keep the similar decoding performance compared with conventional SCL decoder.
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.