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IEEE Transactions on Communications

Design of Polar Subcodes for Permutation Decoding

Mikhail Chernikov, Peter Trifonov

Published Jan 1, 2026• 0 citations
Publisher

Abstract

novel construction of randomized polar subcodes and subcodes of extended BCH codes is presented. The proposed approach stems from a new heuristic for building polar code frozen set which minimizes the error probability of successive cancellation algorithm applied to permuted noisy codewords. The frame error rate (FER) of the proposed codes under permutationbased decoding is comparable to FER of existing polar subcodes under successive cancellation list or sequential algorithm.

DOI
10.1109/tcomm.2026.3686689

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novel construction of randomized polar subcodes and subcodes of extended BCH codes is presented. The proposed approach stems from a new heuristic for building polar code frozen set which minimizes the error probability of successive cancellation algorithm applied to permuted noisy codewords. The frame error rate (FER) of the proposed codes under permutationbased decoding is comparable to FER of existing polar subcodes under successive cancellation list or sequential algorithm.
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A new permutation decoding approach for polar codes is presented. The proposed decoder can be used to achieve the error correction performance of a successive cancellation list (SCL) decoder, while it can either improve latency of the SCL decoder or decrease its hardware complexity. As opposed to the SCL algorithm, the proposed permutation algorithm can be implemented without sorting operation. It is shown that the error correction performance of the algorithm is similar to that of the SCL decoder for polar codes. Moreover, a new construction aiming to improve the error correction performance of polar codes under the proposed algorithm is presented.
In the context of decoding binary linear block codes by polar code decoding techniques, we propose in this paper a new optimization of the serial nature of decoding the polar codes equivalent to binary linear block codes. In addition to the special nodes proposed by the simplified successive-cancellation list technique, we propose a new special node allowing to estimate in parallel the bits of its sub-code. The simulation is done in an additive white gaussian noise channel (AWGN) channel for several linear block codes, namely bose–chaudhuri–hocquenghem codes (BCH) codes, quadratic-residue (QR) codes, and linear block codes recently designed in the literature. The performance of the proposed technique offers the same performance in terms of frame error rate (FER) as the ordered statistics decoding (OSD) algorithm, which achieves that of maximum likelihood decoder (MLD), but with high memory requirements and computational complexity.
Polar codes have been recently shown to have an automorphism group larger than the lower-triangular affine group. Permutations from this group can be used in an automorphism successive cancellation (SC) decoding algorithm providing a lower latency compared to that of successive cancellation list decoding. In this paper, we demonstrate that any permutation from the automorphism group of Reed-Muller codes is suitable for permutation-based SC decoding of polar codes. Specifically, a code obtained by a permutation that is not in the automorphism group of the code, but is in the automorphism group of Reed-Muller codes, is shown to be a polar subcode. Simulations results show that these additional permutations allow improving performance of the automorphism SC decoding algorithm limited to the permutations from the automorphism group of the code.
Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation decoding can be increased. We extend this idea to pre-transformed polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which previously could not be decoded using permutations due to their lack of automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm outperforms the previously best performing iterative CRC-aided belief propagation list (CA-BPL) decoder both in error-rate performance and decoding latency.