An improved construction algorithm of polar codes based on the frozen bits

Abstract

In order to improve the problems that the minimum hamming weight (MHW) of the polar codes of the traditional Gaussian approximation (GA) construction is small and its performance is not good enough, an improved channel construction algorithm of polar codes based on frozen bits is proposed by combining the construction of the Reed-Muller (RM) code to effectively increase the MHW and analyzing the correcting and checking functions of the frozen bits in the successive cancellation list (SCL) decoding. The construction algorithm selects the channel with the smaller row weight corresponding to the information channel in the channel construction stage, and some channels are set as the frozen channels under the proposed frozen channel setting principle. So the proposed construction algorithm not only eliminates the channels with the smaller row weight and optimizes the distance spectrum of polar codes, but also makes full use of the checking ability of the frozen bit in SCL decoding to improve the error correction performance of polar codes. The polar codes constructed by this algorithm are named as FRM-polar codes. The simulation results show that the proposed FRM-polar codes have a larger performance gain than the RM-polar codes and the polar codes constructed by GA under different code-lengths. In addition, the proposed construction algorithm has the same complexity as the construction algorithm of the RM-polar codes.

References

[1] LiuS L, WangY. A low-complexity decoding algorithm based on parity-check-concatenated polar codes[J]. Journal of electronics & information technology, 2022, 44(2):637-645(in Chinese)

[2] ChenF T, TangC, LiuY F. Low complexity successive cancellation decoding scheme for 5G polar codes[J]. Journal of Chongqing University of Posts and Telecommunications (natural science edition), 2019, 31(6):753-759(in Chinese)

[3] LiuW, DuanH G. Adaptive successive cancellation list bit-flip decoding of polar codes[J]. Journal of Chongqing University of Posts and Telecommunications (natural science edition), 2021, 33(1):87-93(in Chinese)

[4] MiloslavskavaV, VuceticB, LiY, et al.. Recursive design of precoded polar codes for SCL decoding[J]. IEEE transactions on communications, 2021, 69(12):7945-7959

[5] ZhangH, LiR, WangJ, et al.. Parity-check polar coding for 5G and beyond[C], 2018, New York, IEEE: 8422462

[6] MiloslavskavaV, VuceticB. Design of short polar codes for SCL decoding[J]. IEEE transactions on communications, 2020, 68(11):6657-6668

[7] ChengF, LiuA, ZhangY, et al.. CRC location design for polar codes[J]. IEEE communications letters, 2018, 22(11):2202-2205

[8] SongJ W, ZhengH J, TongS. Method for designing CRC-polar codes to improve minimum distances[J]. Journal of Xidian University, 2020, 47(06):72-77(in Chinese)

[9] NiuK, LiY. Polar coded diversity on block fading channels via polar spectrum[J]. IEEE transactions on signal processing, 2021, 69: 4007-4022

[10] NiuK, LiY. Polar codes for fast fading channel: design based on polar spectrum[J]. IEEE transactions on vehicular technology, 2020, 69(9):10103-10114

[11] LI B, SHEN H, TSE D. A RM-polar codes[EB/OL]. (2014-07-21) [2023-04-20]. https://aixiv.org/abs/1407.5483.

[12] MondelliM, HassaniS H, UrbankeR L. From polar to reed-muller codes: a technique to improve the finite-length performance[J]. IEEE transactions on communications, 2014, 62(9):3084-3091

[13] WU W, ZHAI Z, SIEGEL P H. Improved hybrid RM-polar codes and decoding on stable permuted factor graphs[C]//2021 11th International Symposium on Topics in Coding (ISTC), Montreal, QC, Canada. 2021: 1–5.

[14] ZhengH, HashemiS A, ChenB, et al.. Inter-frame polar coding with dynamic frozen bits[J]. IEEE communications letters, 2019, 23(9):1462-1465

[15] CaiM, LiS, LiuZ. An improved simplified soft cancellation decoding algorithm for polar codes based on frozen bit check[C], 2021, New York, IEEE: 127-131

[16] YuanP, CoskunM C, KramerG. Polar-coded non-coherent communication[J]. IEEE communications letters, 2021, 25(6):1786-1790