Restart Mechanisms for the Successive-Cancellation List-Flip Decoding of Polar Codes
Abstract
:1. Introduction
2. Background
2.1. Construction of Polar Codes
2.2. SC Decoding
2.3. SCL Decoding
2.4. SCF Decoding
2.5. SCLF Decoding
2.6. Dynamic SCLF Decoding
3. Restart Mechanism for the List-Flip Decoder
3.1. Memory Requirements of List-Flip Algorithm
3.2. Generalized Restart Mechanism
3.3. Limited Location Restart Mechanism
3.4. Example of the LLRM
3.5. Memory Model
- the set of restart locations ;
- the path metric information on each restart location ;
- the partial message candidate on each restart location .
4. Obtaining the Restart Locations
4.1. Structural Design
4.2. Design Based on the First Path-Flipping Location
Algorithm 1 Obtaining the distribution of the first path-flipping candidates occurring in SCLF by simulation | |
1: procedure Distr_Bit_Flip_SCLF() | |
2: for do | |
3: | ▹ Initialize |
4: | ▹ Initialize counter |
5: end for | |
6: | ▹ Total number of additional trials performed |
7: for do | |
8: Polar_Encoding | |
9: | ▹ Channel LLRs for the decoding |
10: | ▹ : Set of flipping locations in SCLF, t: Number of additional trials performed |
11: if then | ▹ Initial trial has failed |
12: | ▹ Update the total number of additional trials |
13: for do | |
14: | |
15: | ▹ Extract first bit-flipping |
16: | ▹ Increase by 1 the occurence |
17: end for | |
18: end if | |
19: end for | |
20: for do | |
21: | ▹ Estimate the probability-mass function |
22: end for | |
23: return the distribution | |
24: end procedure |
Algorithm 2 Design of with the distribution of the first path-flipping location | |
1: procedure Design_Restart_with_PMF() | |
2: | |
3: | |
4: for do | |
5: | |
6: if then | ▹ Divide equally with resp. to |
7: | |
8: | ▹ Next restart location |
9: end if | |
10: if then | |
11: return | ▹ Already R restart locations in |
12: end if | |
13: end for | |
14: end procedure |
4.3. Simulation Setup and Results
5. Simulation Results
5.1. Error-Correction Performance
5.2. Memory Estimations
5.3. Average Execution Time Reduction Induced by the LLRM
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
AWGN | additive white Gaussian noise |
BPS | binary phase-shift keying |
CA | CRC-aided |
CRC | cyclic redundancy check |
DSCF | dynamic successive-cancellation flip |
DSCLF | dynamic successive-cancellation list flip |
eMBB | enhanced mobile broadband |
FER | frame-error rate |
GRM | generalized restart mechanism |
LLR | log-likelihood ratio |
LLRM | limited location restart mechanism |
PM | path metric |
PMF | probability-mass function |
PS | partial sum |
PSCLF | successive-cancellation list flip |
RHS | right-hand side |
SC | successive cancellation |
SCL | successive-cancellation list |
SCLF | successive-cancellation list flip |
SCF | successive-cancellation flip |
SCF | simplified restart mechanism |
SNR | signal-to-noise ratio |
References
- Arıkan, E. Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels. IEEE Trans. Inf. Theory 2009, 55, 3051–3073. [Google Scholar] [CrossRef]
- 3GPP. Multiplexing and Channel Coding. Technical Report TS 38.212; Release 16.5. 2018. Available online: https://www.etsi.org/deliver/etsi_ts/138200_138299/138212/16.05.00_60/ts_138212v160500p.pdf (accessed on 9 March 2025).
- Tal, I.; Vardy, A. List decoding of polar codes. IEEE Trans. Inf. Theory 2015, 61, 2213–2226. [Google Scholar] [CrossRef]
- Afisiadis, O.; Balatsoukas-Stimming, A.; Burg, A. A low-complexity improved successive cancellation decoder for polar codes. In Proceedings of the 2014 48th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2–5 November 2014; pp. 2116–2120. [Google Scholar] [CrossRef]
- Chandesris, L.; Savin, V.; Declercq, D. Dynamic-SCFlip Decoding of Polar Codes. IEEE Trans. Commun. 2018, 66, 2333–2345. [Google Scholar] [CrossRef]
- Yu, Y.; Pan, Z.; Liu, N.; You, X. Successive Cancellation List Bit-flip Decoder for Polar Codes. In Proceedings of the 2018 10th International Conference on Wireless Communications and Signal Processing (WCSP), Hangzhou, China, 18–20 October 2018; pp. 1–6. [Google Scholar] [CrossRef]
- Cheng, F.; Liu, A.; Zhang, Y.; Ren, J. Bit-Flip Algorithm for Successive Cancellation List Decoder of Polar Codes. IEEE Access 2019, 7, 58346–58352. [Google Scholar] [CrossRef]
- Pan, Y.H.; Wang, C.H.; Ueng, Y.L. Generalized SCL-Flip Decoding of Polar Codes. In Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM), Taipei, Taiwan, 7–11 December 2020; pp. 1–6. [Google Scholar] [CrossRef]
- Shen, Y.; Balatsoukas-Stimming, A.; You, X.; Zhang, C.; Burg, A.P. Dynamic SCL Decoder With Path-Flipping for 5G Polar Codes. IEEE Wireless Commun. Lett. 2022, 11, 391–395. [Google Scholar] [CrossRef]
- Lv, H.; Yin, H.; Yang, Z.; Wang, Y.; Dai, J. Adaptive List Flip Decoder for Polar Codes with High-Order Error Correction Capability and a Simplified Flip Metric. Entropy 2022, 24, 1806. [Google Scholar] [CrossRef] [PubMed]
- Li, J.; Zhou, L.; Li, Z.; Gao, W.; Ji, R.; Zhu, J.; Liu, Z. Deep Learning-Assisted Adaptive Dynamic-SCLF Decoding of Polar Codes. IEEE Trans. Cogn. Commun. Netw. 2024, 10, 836–851. [Google Scholar] [CrossRef]
- Ivanov, F.; Morishnik, V.; Krouk, E. Improved generalized successive cancellation list flip decoder of polar codes with fast decoding of special nodes. J. Commun. Netw. 2021, 23, 417–432. [Google Scholar] [CrossRef]
- Doan, N.; Hashemi, S.; Gross, W. Fast Successive-Cancellation List Flip Decoding of Polar Codes. IEEE Access 2022, 10, 5568–5584. [Google Scholar] [CrossRef]
- Wang, Y.; Qiu, S.; Chen, L.; Wang, Q.; Zhang, Y.; Liu, C.; Xing, Z. A Low-Latency Successive Cancellation Hybrid Decoder for Convolutional Polar Codes. In Proceedings of the 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain, 4–8 May 2020; pp. 5105–5109. [Google Scholar] [CrossRef]
- Pillet, C.; Sagitov, I.; Domer, G.; Giard, P. Partitioned Successive-Cancellation List Flip Decoding of Polar Codes. In Proceedings of the 2024 IEEE Workshop on Signal Processing Systems (SiPS), Cambridge, MA, USA, 4–6 November 2024; pp. 19–24. [Google Scholar] [CrossRef]
- Sagitov, I.; Pillet, C.; Balatsoukas-Stimming, A.; Giard, P. Successive-Cancellation Flip Decoding of Polar Code with a Simplified Restart Mechanism. In Proceedings of the 2023 IEEE Wireless Communications and Networking Conference (WCNC), Glasgow, Scotland, 26–29 March 2023; pp. 1–6. [Google Scholar] [CrossRef]
- Sagitov, I.; Pillet, C.; Balatsoukas-Stimming, A.; Giard, P. Generalized Restart Mechanism for Successive-Cancellation Flip Decoding of Polar Codes. J. Signal Process. Syst. 2025. [Google Scholar] [CrossRef]
- Tal, I.; Vardy, A. How to Construct Polar Codes. IEEE Trans. Inf. Theory 2013, 59, 6562–6582. [Google Scholar] [CrossRef]
- Alamdar-Yazdi, A.; Kschischang, F.R. A Simplified Successive-Cancellation Decoder for Polar Codes. IEEE Commun. Lett. 2011, 15, 1378–1380. [Google Scholar] [CrossRef]
- Leroux, C.; Tal, I.; Vardy, A.; Gross, W.J. Hardware architectures for successive cancellation decoding of polar codes. In Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, 22–27 May 2011; pp. 1665–1668. [Google Scholar] [CrossRef]
- Balatsoukas-Stimming, A.; Parizi, M.; Burg, A. LLR-Based Successive Cancellation List Decoding of Polar Codes. IEEE Trans. Signal Process. 2015, 63, 5165–5179. [Google Scholar] [CrossRef]
- Sarkis, G.; Giard, P.; Vardy, A.; Thibeault, C.; Gross, W.J. Fast Polar Decoders: Algorithm and Implementation. IEEE J. Sel. Areas Commun. 2014, 32, 946–957. [Google Scholar] [CrossRef]
- Ercan, F.; Tonnellier, T.; Doan, N.; Gross, W.J. Practical Dynamic SC-Flip Polar Decoders: Algorithm and Implementation. IEEE Trans. Signal Process. 2020, 68, 5441–5456. [Google Scholar] [CrossRef]
- Xiyue, X.; Meilin, H.; Rui, G. Flexible Restart Mechanism for Successive Cancellation Flip Decoding of Polar Codes. IEEE Commun. Lett. 2024, 28, 2459–2463. [Google Scholar] [CrossRef]
- Giard, P.; Balatsoukas-Stimming, A.; Müller, T.C.; Bonetti, A.; Thibeault, C.; Gross, W.J.; Flatresse, P.; Burg, A. PolarBear: A 28-nm FD-SOI ASIC for Decoding of Polar Codes. IEEE J. Emerg. Sel. Top. Circuits Syst. 2017, 7, 616–629. [Google Scholar] [CrossRef]
N | ||||||||
---|---|---|---|---|---|---|---|---|
bits | % | % | % | % | ||||
1024 | 1 | 30 | 32,270 | ¼ | 1.8 | 5.5 | 2.1 | 235.0 |
½ | 7.7 | 10.3 | 6.1 | 875.1 | ||||
¾ | 4.6 | 15.0 | 12.0 | 1921.5 | ||||
1024 | 2 | 50 | 33,110 | ¼ | 2.2 | 5.5 | 2.1 | |
½ | 2.2 | 10.0 | 6.0 | |||||
¾ | 2.7 | 14.7 | 11.7 | |||||
1024 | 3 | 300 | 42,860 | ¼ | 1.5 | 4.2 | 1.6 | |
½ | 1.4 | 7.7 | 4.6 | |||||
¾ | 1.8 | 11.3 | 11.7 | |||||
512 | 3 | 300 | 21,682 | ¼ | 1.7 | 3.9 | 1.7 | 83.1 |
½ | 2.4 | 6.8 | 4.2 | 290.7 | ||||
¾ | 1.8 | 9.8 | 7.6 | 623.8 | ||||
2048 | 3 | 300 | 75,504 | ¼ | 1.5 | 4.4 | 1.6 | 374.0 |
½ | 1.6 | 8.5 | 4.9 | 1442.1 | ||||
¾ | 1.1 | 12.5 | 13.0 | 3204.5 |
N | (%) | (%) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
dB | (%) | (%) | ||||||||||
1024 | 1 | 30 | ¼ | 1.34 | 18.5 | 16.9 | 12.3 | 14.3 | 51.9 | 47.4 | 34.6 | 40.1 |
½ | 1.87 | 12.8 | 9.9 | 7.9 | 8.1 | 35.8 | 27.7 | 22.1 | 22.7 | |||
¾ | 3.03 | 10.4 | 7.8 | 7.1 | 5.9 | 28.3 | 21.0 | 19.1 | 16.1 | |||
1024 | 2 | 50 | ¼ | 1.21 | 25.4 | 23.1 | 18.2 | 18.9 | 56.7 | 51.7 | 40.7 | 42.1 |
½ | 1.78 | 19.1 | 14.8 | 12.5 | 12.2 | 36.0 | 27.9 | 23.5 | 22.9 | |||
¾ | 3.00 | 9.8 | 7.0 | 5.8 | 5.1 | 23.1 | 16.5 | 13.7 | 12.0 | |||
1024 | 3 | 300 | ¼ | 1.06 | 45.5 | 41.7 | 31.0 | 33.2 | 52.0 | 47.6 | 35.4 | 37.9 |
½ | 1.66 | 27.8 | 22.2 | 16.7 | 17.2 | 32.2 | 25.7 | 19.3 | 19.9 | |||
¾ | 2.86 | 15.3 | 11.7 | 7.1 | 7.5 | 18.7 | 14.3 | 8.7 | 9.2 | |||
512 | 3 | 300 | ¼ | 1.39 | 47.3 | 43.3 | 34.4 | 35.5 | 55.7 | 51.0 | 40.5 | 41.9 |
½ | 1.92 | 30.8 | 28.1 | 20.0 | 20.3 | 35.5 | 32.4 | 23.1 | 23.4 | |||
¾ | 3.08 | 14.5 | 11.5 | 6.6 | 6.8 | 18.2 | 14.4 | 8.2 | 8.5 | |||
2048 | 3 | 300 | ¼ | 0.84 | 44.1 | 38.0 | 31.8 | 26.7 | 55.2 | 47.6 | 39.8 | 33.4 |
½ | 1.49 | 27.8 | 21.8 | 17.2 | 17.7 | 33.7 | 26.5 | 20.8 | 21.5 | |||
¾ | 2.73 | 12.5 | 8.9 | 4.7 | 4.8 | 15.5 | 11.0 | 5.8 | 6.0 |
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Pillet, C.; Sagitov, I.; Balatsoukas-Stimming, A.; Giard, P. Restart Mechanisms for the Successive-Cancellation List-Flip Decoding of Polar Codes. Entropy 2025, 27, 309. https://doi.org/10.3390/e27030309
Pillet C, Sagitov I, Balatsoukas-Stimming A, Giard P. Restart Mechanisms for the Successive-Cancellation List-Flip Decoding of Polar Codes. Entropy. 2025; 27(3):309. https://doi.org/10.3390/e27030309
Chicago/Turabian StylePillet, Charles, Ilshat Sagitov, Alexios Balatsoukas-Stimming, and Pascal Giard. 2025. "Restart Mechanisms for the Successive-Cancellation List-Flip Decoding of Polar Codes" Entropy 27, no. 3: 309. https://doi.org/10.3390/e27030309
APA StylePillet, C., Sagitov, I., Balatsoukas-Stimming, A., & Giard, P. (2025). Restart Mechanisms for the Successive-Cancellation List-Flip Decoding of Polar Codes. Entropy, 27(3), 309. https://doi.org/10.3390/e27030309