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Polar coding are the first class of provable capacity-achieving coding techniques for a wide range of channels. With an ideal recursive structure and many elegant mathematical properties, polar codes are inherently implemented with low complexity encoding and decoding algorithms. Since the block length of the original polar construction is limited to powers of two, rate-compatible polar codes (RCPC) are presented to meet the flexible length/rate transmission requirements in practice. The RCPC codes are well-conditioned to combine with the hybrid automatic repeat request (HARQ) system, providing high throughput efficiency and such RCPC-HAPQ scheme is commonly used in delay-insensitive communication system. This paper first gives a survey of both the classical and state-of-the-art encoding/decoding algorithms for polar codes. Then the RCPC construction methods are discussed, including the puncturing, shortening, multi-kernel construction, etc. Finally, we investigate several RCPC-HARQ jointly design systems and discuss their encoding gain and re-transmission diversity gain.
Polar coding are the first class of provable capacity-achieving coding techniques for a wide range of channels. With an ideal recursive structure and many elegant mathematical properties, polar codes are inherently implemented with low complexity encoding and decoding algorithms. Since the block length of the original polar construction is limited to powers of two, rate-compatible polar codes (RCPC) are presented to meet the flexible length/rate transmission requirements in practice. The RCPC codes are well-conditioned to combine with the hybrid automatic repeat request (HARQ) system, providing high throughput efficiency and such RCPC-HAPQ scheme is commonly used in delay-insensitive communication system. This paper first gives a survey of both the classical and state-of-the-art encoding/decoding algorithms for polar codes. Then the RCPC construction methods are discussed, including the puncturing, shortening, multi-kernel construction, etc. Finally, we investigate several RCPC-HARQ jointly design systems and discuss their encoding gain and re-transmission diversity gain.
R. G. Gallager, Low-density parity-check codes, IRE Transactions on Information Theory, vol. 8, no. 1, pp. 21–28, 1962.
P. Wang, L. Yin, and J. Lu, Efficient helicopter−satellite communication scheme based on check-hybrid LDPC coding, Tsinghua Science and Technology, vol. 23, no. 3, pp. 323–332, 2018.
B. Lin, Y. Pei, L. Yin, and J. Lu, Design and efficient hardware implementation shemes for non-quasi-cyclic LDPC codes, Tsinghua Science and Technology, vol. 22, no. 1, pp. 92–103, 2017.
E. Arikan, Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels, IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051–3073, 2009.
E. Arikan, On the origin of polar coding, IEEE Journal on Selected Areas Communications, vol. 34, no. 2, pp. 209–223, 2016.
M. S. Pinsker, On the complexity of decoding, Probl. Peredachi Inf., vol. 1, no. 1, pp. 113–116, 1965.
J. L. Massey, Capacity, cutoff rate, and coding for a direct-detection optical channel, IEEE Transaction Communications, vol. 29, no. 11, pp. 1615–1621, 1981.
B. Yuan and K. K. Parhi, Low-latency successive-cancellation list decoders for polar codes with multibit decision, IEEE Transactions on Very Largescale Integration(VLSI)Systems, vol. 23, no. 10, pp. 2268–2280, 2015.
K. Niu and K. Chen, Stack decoding of polar codes, Electronic Letters, vol. 48, no. 12, pp. 695–697, 2012.
K. Chen, K. Niu, and J. Lin, Improved successive cancellation decoding of polar codes, IEEE Transactions on Communications, vol. 61, no. 8, pp. 3100–3107, 2013.
J. Lin, C. Xiong, and Z. Yan, A high throughput list decoder architecture for polar codes, IEEE Transactions on Very Large Scale Integration(VLSI)Systems, vol. 24, no. 6, pp. 2378–2391, 2016.
C. Xiong, J. Lin, and Z. Yan, Symbol-decision successive cancellation list decoder for polar codes, IEEE Transactions on Signal Processing, vol. 64, no. 3, pp. 675–687, 2016.
A. Elkelesh, M. Ebada, S. Cammerer, and S. T. Brink, Belief propagation list decoding of polar codes, IEEE Communications Letters, vol. 22, no. 8, pp. 1536–1539, 2018.
S. B. Korada, E. Şaşoğlu, and R. Urbanke, Polar codes: Characterization of exponent, bounds, and constructions, IEEE Transactions on Information Theory, vol. 56, no. 12, pp. 6253–6264, 2010.
N. Presman, O. Shapira, and S. Litsyn, Mixed-kernels constructions of polar codes, IEEE Journal on Selected Areas in Communications, vol. 34, no. 2, pp. 239–253, 2016.
B. Yuan and K. K. Parhi, Low-latency successive-cancellation polar decoder architectures using 2-bit decoding, IEEE Transactions on Circuits and Systems I:Regular Papers, vol. 61, no. 4, pp. 1241–1254, 2014.
C. Sun, Z. Fei, D. Jia, C. Cao, and X. Wang, Secure transmission scheme for parallel relay channels based on polar coding, Tsinghua Science and Technology, vol. 23, no. 3, pp. 357–365, 2018.
N. Presman, O. Shapira, S. Litsyn, T. Etzion, and A. Vardy, Binary polarization kernels from code decompositions, IEEE Transactions on Information Theory, vol. 61, no. 5, pp. 2227–2239, 2015.
H. Lin, S. Lin, and K. A. S. Abdel-Ghaffar, Linear and nonlinear binary kernels of polar codes of small dimensions with maximum exponents, IEEE Transactions on Information Theory, vol. 61, no. 10, pp. 5253–5270, 2015.
J. Ha, J. Kim, and S. W. McLaughlin, Rate-compatible puncturing of low-density parity-check codes, IEEE Transactions on Information Theory, vol. 50, no. 11, pp. 2824–2836, 2004.
J. Ha, J. Kim, D. Klinc, and S. W. McLaughlin, Rate-compatible punctured low-density parity-check codes with short block lengths, IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 728–738, 2006.
K. Niu and K. Chen, CRC-aided decoding of polar codes, IEEE Communications Letters, vol. 16, no. 10, pp. 1668–1671, 2012.
L. Li, W. Song, and K. Niu, Optimal puncturing of polar codes with a fixed information set, IEEE Access, vol. 7, pp. 65965–65972, 2019.
J. Zhao, W. Zhang, and Y. Liu, A novel puncturing scheme of low rate polar codes based on fixed information set, IEEE Communications Letters, vol. 25, no. 7, pp. 2104–2108, 2021.
R. Wang and R. Liu, A novel puncturing scheme for polar codes, IEEE Communications Letters, vol. 18, no. 12, pp. 2081–2084, 2014.
V. Miloslavskaya, Shortened polar codes, IEEE Transactions on Information Theory, vol. 61, no. 9, pp. 4852–4865, 2015.
A. Alamdar-Yazdi and F. R. Kschischang, A simplified successive-cancellation decoder for polar codes, IEEE Communications Letters, vol. 15, no. 12, pp. 1378–1380, 2011.
M. Jeong and S. Hong, SC-Fano decoding of polar codes, IEEE Access, vol. 7, pp. 81682–81690, 2019.
I. Tal and A. Vardy, List decoding of polar codes, IEEE Transactions on Information Theory, vol. 61, no. 5, pp. 2213–2226, 2015.
K. Chen, K. Niu, and J. R. Lin, List successive cancellation decoding of polar codes, Electronics Letters, vol. 48, no. 9, pp. 500–501, 2012.
C. Wang, Y. Pan, Y. Lin, and Y. Ueng, Post-processing for CRC-aided successive cancellation list decoding of polar codes, IEEE Communications Letters, vol. 24, no. 7, pp. 1395–1399, 2020.
B. Dai, C. Gao, Z. Yan, and R. Liu, Parity check aided SC-flip decoding algorithms for polar codes, IEEE Transactions on Vehicular Technology, vol. 70, no. 10, pp. 10359–10368, 2021.
Y. Shen, W. Song, Y. Ren, H. Ji, X. You, and C. Zhang, Enhanced belief propagation decoder for 5G polar codes with bit-flipping, IEEE Transactions on Circuits and Systems II:Express Briefs, vol. 67, no. 5, pp. 901–905, 2020.
M. Zhang, Z. Li, and L. Xing, An enhanced belief propagation decoder for polar codes, IEEE Communications Letters, vol. 25, no. 10, pp. 3161–3165, 2021.
J. Hagenauer, Rate-compatible punctured convolutional codes (RCPC codes) and their applications, IEEE Transactions on Communications, vol. 36, no. 4, pp. 389–400, 1988.
K. Chen, K. Niu, and J. Lin, A hybrid ARQ scheme based on polar codes, IEEE Communications Letters, vol. 17, no. 10, pp. 1996–1999, 2013.
J. Gao, P. Fan, and L. Li, Optimized polarizing matrix extension based HARQ scheme for short packet transmission, IEEE Communications Letters, vol. 24, no. 5, pp. 951–955, 2020.
H. Saber and I. Marsland, An incremental redundancy hybrid ARQ scheme via puncturing and extending of polar codes, IEEE Transaction on Communications, vol. 63, no. 11, pp. 3964–3976, 2015.
M. Zhao, G. Zhang, C. Xu, H. Zhang, R. Li, and J. Wang, An adaptive IR-HARQ scheme for polar codes by polarizing matrix extension, IEEE Communications Letters, vol. 22, no. 7, pp. 1306–1309, 2018.
S. Hong and M. Jeong, An efficient construction of rate-compatible punctured polar (RCPP) codes using hierarchical puncturing, IEEE Transactions on Communications, vol. 66, no. 11, pp. 5041–5052, 2018.
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 National Nature Science Foundation of China (Nos. 61761006, 61961004, and 61762011) and the National Nature Science Foundation of Guangxi (Nos. 2017GXNSFAA198263 and 2018GXNSFAA294059).
This work is available under the CC BY-NC-ND 3.0 IGO license: https://creativecommons.org/licenses/by-nc-nd/3.0/igo/