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Open Access

Sphere Decoding for Binary Polar Codes with the Modified Multiplicative Repetition Construction

School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China
School of Electrical, Electronic and Mechanical Engineering, University of Bristol, Bristol BS8 1TR, UK
Information and Engineering College, Nanning University, Nanning 530004, China
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Abstract

Compared to the successive cancellation (SC)-based decoding algorithms, the sphere decoding (SD) algorithm can achieve better performance with reduced computational complexity, especially for short polar codes. In this paper, we propose a new method to construct the binary polar codes with the modified multiplicative repetition (MR)-based matrix. Different from the original construction, we first design a 2×2q-ary kernel to guarantee the single-level polarization effect. Then, by replacing the new-designed binary companion matrix, a novel strategy is further developed to enhance the polarization in the bit level, resulting in a better distance property. Finally, the SD-based Monte-Carlo (SDMC) method is used to construct MR-based binary polar codes, while the resulting codes without the butterfly pattern are decoded by the SD algorithm. Simulation results show that the proposed method with the SD algorithm can achieve a maximum performance gain of 0.27 dB compared to the original method with slightly lower complexity.

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Tsinghua Science and Technology
Pages 1229-1236
Cite this article:
Chen H, Liu Y, Dang S, et al. Sphere Decoding for Binary Polar Codes with the Modified Multiplicative Repetition Construction. Tsinghua Science and Technology, 2025, 30(3): 1229-1236. https://doi.org/10.26599/TST.2024.9010030

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Received: 07 October 2023
Revised: 29 January 2024
Accepted: 30 January 2024
Published: 30 December 2024
© The Author(s) 2025.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

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