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Two-Stage Constructions for the Rate-Compatible Shortened Polar Codes

School of Computer, Electronics and Information and Guangxi Colleges and Universities Key Laboratory of Multimedia Communications and Information Processing, Guangxi University, Nanning 530004, China
Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, Nanning 530004, China
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Abstract

In this paper, we propose the two-stage constructions for the rate-compatible shortened polar (RCSP) codes. For the Stage-I construction, the shortening pattern and the frozen bit are jointly designed to make the shortened bits be completely known by the decoder. Besides, a distance-greedy algorithm is presented to improve the minimum Hamming distance of the codes. To design the remaining Stage-II frozen bits, three different construction algorithms are further presented, called the Reed-Muller (RM) construction, the Gaussian Approximation (GA) construction, and the RM-GA construction. Then we give the row weight distribution numerical results of the generator matrix after the Stage-I and Stage-II constructions, which shows that the proposed constructions can efficiently increase the minimum Hamming distance. Simulation results show that the proposed RCSP codes have excellent frame error rate (FER) performances at different code lengths and code rates. More specifically, the RM-GA construction performs best and can achieve at most 0.8 dB gain compared to the Wang14 and the quasi-uniform puncturing (QUP) schemes. The RM construction is designed completely by the distance-constraint without channel evaluation thus has the simplest structure. Interestingly, it still has better FER performance than the existing shortening/puncturing schemes, especially at high signal noise ratio (SNR) region.

Keywords

polar codesrate-compatibilityReed-Muller codesHamming distanceshortening

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Tsinghua Science and Technology
Volume 28 Issue 2,
April 2023
Pages 269-282
DOI: 10.26599/TST.2021.9010086
Cite this article:
Li C, Chen H, Wang Z, et al. Two-Stage Constructions for the Rate-Compatible Shortened Polar Codes. Tsinghua Science and Technology, 2023, 28(2): 269-282. https://doi.org/10.26599/TST.2021.9010086
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