Shortened PAC Codes and List Decoding

doi:10.12142/ZTECOM.202504010

ZTE Communications ›› 2025, Vol. 23 ›› Issue (4): 86-96.DOI: 10.12142/ZTECOM.202504010

• Research Papers • Previous Articles Next Articles

Shortened PAC Codes and List Decoding

LIU Aolin¹^,², FENG Bowen¹(), LIANG Chulong³, XU Jin³, ZHANG Qinyu¹^,²

^1.Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
^2.Pengcheng Laboratory, Shenzhen 518055, China
^3.ZTE Corporation, Shenzhen 518057, China

Received:2024-08-14 Online:2025-12-25 Published:2025-12-22
About author:LIU Aolin received his BS degree in communication engineering from Harbin Institute of Technology (Shenzhen), China in 2023, where he is currently pursuing the PhD degree in information and communication engineering. He is also affiliated with Pengcheng Laboratory, China. His research interests include coding theory, error control codes, and satellite communications.
FENG Bowen (fengbowen@hit.edu.cn) received his BS, MS, and PhD degrees in information and communication engineering from the Harbin Institute of Technology, China in 2014, 2016, and 2021, respectively. From 2021 to 2024, he was a postdoctoral research fellow with Harbin Institute of Technology (Shenzhen) (HITSZ), China. He is currently an associate professor with the Guangdong Provincial Key Laboratory of Aerospace Communication and Networking Technology, HITSZ. His research interests include error control codes, satellite communications, and machine-to-machine communications.
LIANG Chulong received his BE degree in communication engineering and PhD degree in communication and information systems from Sun Yat-sen University, China in 2010 and 2015, respectively. He was a post-doctoral fellow with the Department of Electronic Engineering, City University of Hong Kong, China from July 2015 to June 2018, where he was a research fellow, from June 2018 to May 2019. He is currently a senior engineer with the Algorithm Department, ZTE Corporation. His current research interests include channel coding theory and its applications to communication systems.
XU Jin received his PhD degree from the School of Electronic Information, Wuhan University, China. He is currently a senior pre-research engineer with ZTE Corporation. His research interests include error correction codes, digital signal processing, semantic communication, and machine learning.
ZHANG Qinyu received his bachelor’s degree in communication engineering from the Harbin Institute of Technology (HIT)， China in 1994 and PhD degree in biomedical and electrical engineering from the University of Tokushima, Japan in 2003. From 1999 to 2003, he was an assistant professor with the University of Tokushima. He has been with Harbin Institute of Technology (Shenzhen) (HITSZ), China since 2003; he is currently a full professor and and serves as the Vice President of HITSZ. He has received the National Science Fund for Distinguished Young Scholars, and been recognized as a Young and Middle-Aged Leading Scientist of China and a Chinese New Century Excellent Talent in University, among other honors. He has also obtained three scientific and technological awards from government authorities. His research interests include aerospace communications and networks, and wireless communications and networks.
Supported by:
the National Natural Sciences Foundation of China (NSFC)(62301185);the National Natural Sciences Foundation of China (NSFC)(62027802);ZTE Industry?University-Institute Cooperation Funds, and in part by The Major Key Project of PCL(PCL2024A01)

Abstract

Abstract:

Shortening is a standard rate-matching method for polar codes in wireless communications. Since polarization-adjusted convolutional (PAC) codes also have a block length limited to the integer powers of two, they also require rate-matching. To this end, we first analyze the limitations of existing shortening patterns for PAC codes and explore their feasibility. Subsequently, we propose a novel shortening scheme for PAC codes based on list decoding, where the receiver is allowed to treat the values of the deleted bits as undetermined. This approach uses a specialized PAC codeword and activates multiple decoding paths during the initialization of list decoding, enabling it to achieve the desired reliability.

Key words: polarization-adjusted convolutional codes, rate-matching, shortened codes, list decoding

LIU Aolin, FENG Bowen, LIANG Chulong, XU Jin, ZHANG Qinyu. Shortened PAC Codes and List Decoding[J]. ZTE Communications, 2025, 23(4): 86-96.

Figures/Tables 1

References 23

[1]	ARIKAN E. Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels [J]. IEEE transactions on information theory, 2009, 55(7): 3051–3073. DOI: 10.1109/TIT.2009.2021379
[2]	3GPP. 3rd generation partnership project; technical specification group radio access network; NR; multiplexing and channel coding (release 17): TS 38.212 [S]. 2022
[3]	NIU K, DAI J, CHEN K, et al. Rate-compatible punctured polar codes: optimal construction based on polar spectra [EB/OL]. [2024-12-03].
[4]	ARIKAN E. From sequential decoding to channel polarization and back again [EB/OL]. [2024-09-09].
[5]	ROWSHAN M, BURG A, VITERBO E. Polarization-adjusted convolutional (PAC) codes: sequential decoding vs list decoding [J]. IEEE transactions on vehicular technology, 2021, 70(2): 1434–1447. DOI: 10.1109/TVT.2021.3052550
[6]	LIU W X, CHEN L, LIU X C. A weighted sum based construction of PAC codes [J]. IEEE communications letters, 2023, 27(1): 28–31. DOI: 10.1109/LCOMM.2022.3209082
[7]	NIU K, CHEN K, LIN J R. Beyond turbo codes: rate-compatible punctured polar codes [C]//Proc. IEEE International Conference on Communications (ICC). IEEE, 2013: 3423–3427. DOI: 10.1109/ICC.2013.6655078
[8]	LI L P, SONG W, NIU K. Optimal puncturing of polar codes with a fixed information set [J]. IEEE access, 2019, 7: 65965–65972. DOI: 10.1109/ACCESS.2019.2918346
[9]	SOLIMAN T, YANG F. Cooperative punctured polar coding (CPPC) scheme based on plotkin's construction [J]. Radioengineering, 2016, 25(3): 482–489. DOI: 10.13164/re.2016.0482
[10]	BIOGLIO V, GABRY F, LAND I. Low-complexity puncturing and shortening of polar codes [C]//Proc. IEEE Wireless Communications and Networking Conference Workshops (WCNCW). IEEE, 2017: 1–6. DOI: 10.1109/WCNCW.2017.7919040
[11]	ZHAO J H, ZHANG W, LIU Y Y. A novel puncturing scheme of low rate polar codes based on fixed information set [J]. IEEE communications letters, 2021, 25(7): 2104–2108. DOI: 10.1109/LCOMM.2021.3072050
[12]	HAN S, KIM B, HA J. Rate-compatible punctured polar codes [J]. IEEE communications letters, 2022, 26(4): 753–757. DOI: 10.1109/LCOMM.2022.3144695
[13]	WANG R X, LIU R K. A novel puncturing scheme for polar codes [J]. IEEE communications letters, 2014, 18(12): 2081–2084. DOI: 10.1109/LCOMM.2014.2364845
[14]	ARIKAN E. Systematic encoding and shortening of PAC codes [J]. Entropy, 2020, 22(11): 1301. DOI: 10.3390/e22111301
[15]	MILOSLAVSKAYA V. Shortened polar codes [J]. IEEE transactions on information theory, 2015, 61(9): 4852–4865. DOI: 10.1109/TIT.2015.2453312
[16]	CHAKI P, KAMIYA N. On the properties of bit-reversal shortening in polar codes [C]//Proc. International Symposium on Information Theory and Its Applications (ISITA). IEEE, 2018: 437–441. DOI: 10.23919/ISITA.2018.8664298
[17]	OLIVEIRA R M, DE LAMARE R C. Rate-compatible polar codes based on polarization-driven shortening [J]. IEEE communications letters, 2018, 22(10): 1984–1987. DOI: 10.1109/LCOMM.2018.2863375
[18]	OLIVEIRA R M, DE LAMARE R C. Design of rate-compatible polar codes based on non-uniform channel polarization [J]. IEEE access, 2021, 9: 41902–41912. DOI: 10.1109/ACCESS.2021.3065816
[19]	JANG M, AHN S K, JEONG H, et al. Rate matching for polar codes based on binary domination [J]. IEEE transactions on communications, 2019, 67(10): 6668–6681. DOI: 10.1109/TCOMM.2019.2930502
[20]	ROWSHAN M, VITERBO E. On convolutional precoding in PAC codes [C]//Proceedings of IEEE Globecom Workshops (GC Wkshps). IEEE, 2021: 1–6. DOI: 10.1109/gcwkshps52748.2021.9681987
[21]	SUN H, VITERBO E, LIU R K. Analysis of polarization-adjusted convolutional codes (PAC): a source-channel coding method [C]//Proc. IEEE Globecom Workshops (GC Wkshps). IEEE, 2021: 1–6. DOI: 10.1109/gcwkshps52748.2021.9682079
[22]	FENG B W, YANG Y, JIAO J, et al. On tail-biting polarization-adjusted convolutional (TB-PAC) codes and small-sizes list decoding [J]. IEEE communications letters, 2023, 27(2): 433–437. DOI: 10.1109/LCOMM.2022.3225177
[23]	ROWSHAN M, DAU S H, VITERBO E. On the formation of min-weight codewords of polar/PAC codes and its applications [J]. IEEE transactions on information theory, 2023, 69(12): 7627–7649. DOI: 10.1109/TIT.2023.3319015

Shortened PAC Codes and List Decoding

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 1

References 23

Related Articles 0

Recommended Articles

Metrics