Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
194 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Fast Successive-Cancellation Decoding of 2 x 2 Kernel Non-Binary Polar Codes: Identification, Decoding and Simplification (2401.07433v1)

Published 15 Jan 2024 in cs.IT and math.IT

Abstract: Non-binary polar codes (NBPCs) decoded by successive cancellation (SC) algorithm have remarkable bit-error-rate performance compared to the binary polar codes (BPCs). Due to the serial nature, SC decoding suffers from large latency. The latency issue in BPCs has been the topic of extensive research and it has been notably resolved by the introduction of fast SC-based decoders. However, the vast majority of research on NBPCs is devoted to issues concerning design and efficient implementation. In this paper, we propose fast SC decoding for NBPCs constructed based on 2 x 2 kernels. In particular, we identify various non-binary special nodes in the SC decoding tree of NBPCs and propose their fast decoding. This way, we avoid traversing the full decoding tree and significantly reduce the decoding delay compared to symbol-by-symbol SC decoding. We also propose a simplified NBPC structure that facilitates the procedure of non-binary fast SC decoding. Using our proposed fast non-binary decoder, we observed an improvement of up to 95% in latency concerning the original SC decoding. This is while our proposed fast SC decoder for NBPCs incurs no error-rate loss.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (28)
  1. E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 3051–3073, Jul. 2009.
  2. A. Alamdar-Yazdi and F. R. Kschischang, “A simplified successivecancellation decoder for polar codes,” IEEE Commun. Lett., vol. 15, no. 12, pp. 1378–1380, Dec. 2011.
  3. G. Sarkis, P. Giard, A. Vardy, C. Thibeault, and W. Gross, “Fast polar decoders: Algorithm and implementation,” IEEE J. Sel. Areas Commun., vol. 32, no. 5, pp. 946–957, May 2014.
  4. S. A. Hashemi, C. Condo, and W. J. Gross, “A fast polar code list decoder architecture based on sphere decoding,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 63, no. 12, pp. 2368–2380, Dec. 2016.
  5. S. A. Hashemi, C. Condo, and W. J. Gross, “Fast and flexible successive-cancellation list decoders for polar codes,” IEEE Trans. Signal Process., vol. 65, no. 21, pp. 5756–5769, Nov. 2017.
  6. M. Hanif and M. Ardakani, “Fast successive-cancellation decoding of polar codes: Identification and decoding of new nodes,” IEEE Commun. Lett., vol. 21, no. 11, pp. 2360–2363, Nov. 2017.
  7. P. Giard, A. Balatsoukas-Stimming, G. Sarkis, C. Thibeault, and W. J. Gross, “Fast low-complexity decoders for low-rate polar codes,” J. Signal Process. Syst., vol. 90, no. 5, pp. 675–685, May 2018.
  8. C. Condo, V. Bioglio, and I. Land, “Generalized fast decoding of polar codes,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Dec. 2018, pp. 1–6.
  9. S. Li, Y. Deng, L. Lu, J. Liu, and T. Huang, “A low-latency simplified successive cancellation decoder for polar codes based on node error probability,” IEEE Commun. Lett., vol. 22, no. 12, pp. 2439–2442, Dec. 2018.
  10. M. H. Ardakani, M. Hanif, M. Ardakani, and C. Tellambura, “Fast successive-cancellation-based decoders of polar codes,” IEEE Trans. Commun., vol. 67, no. 7, pp. 4562–4574, Jul. 2019.
  11. F. Ercan, T. Tonnellier, C. Condo, and W. J. Gross, “Operation merging for hardware implementations of fast polar decoders,” J. Signal Process. Syst., vol. 91, no. 9, pp. 995–1007, Sep. 2019.
  12. S. A. Hashemi, C. Condo, M. Mondelli, and W. J. Gross, “Rate-flexible fast polar decoders,” IEEE Trans. Signal Process., vol. 67, no. 22, pp. 5689–5701, Nov. 2019.
  13. Y. Ren, A. T. Kristensen, Y. Shen, A. Balatsoukas-Stimming, C. Zhang and A. Burg, “A sequence repetition node-based successive cancellation list decoder for 5G polar codes: algorithm and implementation,” IEEE Trans. Signal Process., vol. 70, pp. 5592–5607, 2022.
  14. I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory, vol. 61, no. 5, pp. 2213–2226, May 2015.
  15. E. Şaşoğlu, E. Telatar and E. Arıkan, “Polarization for arbitrary discrete memoryless channels,” in Proc. IEEE Inf. Theory Workshop, Taormina, Italy, 2009, pp. 144–148
  16. R. Mori and T. Tanaka, “Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes,” in Proc. IEEE Inf. Theory Workshop, Dublin, Ireland, 2010, pp. 1–5.
  17. W. Park and A. Barg, “Polar codes for q-ary channels, q=2r𝑞superscript2𝑟q=2^{r}italic_q = 2 start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT,” IEEE Trans. Inf. Theory, vol. 59, no. 2, pp. 955–969, Feb. 2013.
  18. R. Mori and T. Tanaka, “Source and channel polarization over finite fields and Reed–Solomon matrices,” IEEE Trans. Inf. Theory, vol. 60, no. 5, pp. 2720–2736, May 2014.
  19. N. Cheng, R. Zhang, Y. Ge, W. Shi, Q. Zhang, and X. S. Shen, “Encoder and list decoder of Reed-Solomon kernel based polar codes,” in Proc. 8th Int. Conf. Wireless Commun. Signal Process., 2016, pp. 1–6.
  20. P. Yuan and F. Steiner, “Construction and decoding algorithms for polar codes based on 2 ×\times× 2 non-binary kernels,” in Proc. IEEE 10th Int. Symp. Turbo Codes Iterative Inf. Process., 2018, pp. 1–5.
  21. M. Falk, G. Bauch, and I. Nissen, “Analysis of non-binary polar codes over GF(3) and GF(5) with phase shift keying for short messages,” in Proc. IEEE 92nd Veh. Technol. Conf., 2020, pp. 1–5.
  22. L. Karakchieva and P. Trifonov, “An approximate method for construction of polar codes with kernels over F2tsuperscript2𝑡{}_{2^{t}}start_FLOATSUBSCRIPT 2 start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT end_FLOATSUBSCRIPT,” IEEE Commun. Lett., vol. 24, no. 9, pp. 1857–1860, Sept. 2020.
  23. V. Savin, “Non-binary polar codes for spread-spectrum modulations,” in Proc. 11th Int. Symp. Topics Coding (ISTC), 2021, pp. 1–5
  24. F. Cochachin, L. Luzzi and F. Ghaffari, “Reduced complexity of a successive cancellation based decoder for NB-polar codes,” Proc. 11th Int. Symp. Topics Coding (ISTC), 2021, pp. 1–5
  25. B. Feng, R. Liu, and H. Sun, “Simplified successive-cancellation list decoding of non-binary polar codes with rate-1 node,” in Proc. IEEE Wireless Commun. Netw. Conf., 2020, pp. 1–6.
  26. S. Li, M. Cai, L. Jin, Y. Sun, H. Wu and P. Wang, “An ultra-reliable low-latency non-binary polar coded SCMA scheme,” IEEE Trans. Veh. Technol., vol. 71, no. 6, pp. 6518–6533, June 2022.
  27. P. Chen, B. Bai, and X. Ma, “Non-binary polar coding with low decoding latency and complexity,” J. Intell. Inf. Syst., vol. 1, pp. 36–53, 2023.
  28. A. Voicila, D. Declercq, F. Verdier, M. Fossorier, and P. Urard, “Low-complexity decoding for non-binary LDPC codes in high order fields,” IEEE Trans. Commun., vol. 58, no. 5, pp. 1365––1375, May 2010.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now