Research on encoding and decoding of non-binary polar codes over GF(2m)

Li, S., Cai, M., Edwards, R., Sun, Y. and Jin, L. (2022) Research on encoding and decoding of non-binary polar codes over GF(2m). Digital Communications and Networks, 8(3), pp. 359-372. (doi: 10.1016/j.dcan.2022.01.005)

Abstract

Binary Polar Codes (BPCs) have advantages of high-efficiency and capacity-achieving but suffer from large latency due to the Successive-Cancellation List (SCL) decoding. Non-Binary Polar Codes (NBPCs) have been investigated to obtain the performance gains and reduce latency under the implementation on parallel architectures for multi-bit decoding. However, most of the existing works only focus on the Reed-Solomon matrix-based NBPCs and the probability domain-based non-binary polar decoding, which lack flexible structure and have a large computation amount in the decoding process, while little attention has been paid to general non-binary kernel-based NBPCs and Log-Likelihood Ratio (LLR) based decoding methods. In this paper, we consider a scheme of NBPCs with a general structure over GF(2m). Specifically, we pursue a detailed Monte-Carlo simulation implementation to determine the construction for proposed NBPCs. For non-binary polar decoding, an SCL decoding based on LLRs is proposed for NBPCs, which can be implemented with non-binary kernels of arbitrary size. Moreover, we propose a Perfect Polarization-Based SCL (PPB-SCL) algorithm based on LLRs to reduce decoding complexity by deriving a new update function of path metric for NBPCs and eliminating the path splitting process at perfect polarized (i.e., highly reliable) positions. Simulation results show that the bit error rate of the proposed NBPCs significantly outperforms that of BPCs. In addition, the proposed PPB-SCL decoding obtains about 40% complexity reduction of SCL decoding for NBPCs.

• Item Type: Articles
• Additional Information: This work was supported in part by the National Natural Science Foundation of China under Grant 61401407, and in part by the Fundamental Research Funds for the Central Universities under Grant CUC2019B067.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Sun, Dr Yao
• Authors: Li, S., Cai, M., Edwards, R., Sun, Y., and Jin, L.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Journal Name: Digital Communications and Networks
• Publisher: Elsevier
• ISSN: 2352-8648
• ISSN (Online): 2352-8648
• Published Online: 05 February 2022
• Copyright Holders: Copyright © 2022 Chongqing University of Posts and Telecommunications
• First Published: First published in Digital Communications and Networks 8(3): 359-372
• Publisher Policy: Reproduced under a Creative Commons License