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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.
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.
The authors are very grateful to the editor and reviewers for their comments and constructive suggestions, which help to enrich the content and improve the presentation of this paper. This work was supported by the Interdisciplinary Scientific Research Foundation of GuangXi University (No. 2022JCC015), the National Natural Science Foundation of China (Nos. 61761006, 61961004, and 61762011), and the Natural Science Foundation of Guangxi of China (Nos. 2017GXNSFAA198263 and 2018GXNSFAA294059).
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/).