Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 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

On Streaming Codes for Simultaneously Correcting Burst and Random Erasures (2405.06621v1)

Published 10 May 2024 in cs.IT and math.IT

Abstract: Streaming codes are packet-level codes that recover dropped packets within a strict decoding-delay constraint. We study streaming codes over a sliding-window (SW) channel model which admits only those erasure patterns which allow either a single burst erasure of $\le b$ packets along with $\le e$ random packet erasures, or else, $\le a$ random packet erasures, in any sliding-window of $w$ time slots. We determine the optimal rate of a streaming code constructed via the popular diagonal embedding (DE) technique over such a SW channel under delay constraint $\tau=(w-1)$ and provide an $O(w)$ field size code construction. For the case $e>1$, we show that it is not possible to significantly reduce this field size requirement, assuming the well-known MDS conjecture. We then provide a block code construction whose DE yields a streaming code achieving the rate derived above, over a field of size sub-linear in $w,$ for a family of parameters having $e=1.$ We show the field size optimality of this construction for some parameters, and near-optimality for others under a sparsity constraint. Additionally, we derive an upper-bound on the $d_{\text{min}}$ of a cyclic code and characterize cyclic codes which achieve this bound via their ability to simultaneously recover from burst and random erasures.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (25)
  1. E. Martinian and C. W. Sundberg, “Burst erasure correction codes with low decoding delay,” IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2494–2502, 2004.
  2. E. Martinian and M. Trott, “Delay-Optimal Burst Erasure Code Construction,” in Proc. IEEE Int. Symp. Inf. Theory, Nice, France, June 24-29, 2007, pp. 1006–1010.
  3. A. Badr, P. Patil, A. Khisti, W. Tan, and J. G. Apostolopoulos, “Layered Constructions for Low-Delay Streaming Codes,” IEEE Trans. Inf. Theory, vol. 63, no. 1, pp. 111–141, 2017.
  4. M. N. Krishnan, D. Shukla, and P. V. Kumar, “Rate-optimal streaming codes for channels with burst and random erasures,” IEEE Trans. Inf. Theory, vol. 66, no. 8, pp. 4869–4891, 2020.
  5. E. Domanovitz, S. L. Fong, and A. Khisti, “An explicit rate-optimal streaming code for channels with burst and arbitrary erasures,” IEEE Trans. Inf. Theory, vol. 68, no. 1, pp. 47–65, 2022.
  6. A. Badr, A. Khisti, W.-t. Tan, and J. Apostolopoulos, “Streaming codes with partial recovery over channels with burst and isolated erasures,” IEEE Journal of Selected Topics in Signal Processing, vol. 9, no. 3, pp. 501–516, 2015.
  7. S. Bhatnagar, B. Chakraborti, and P. V. Kumar, “Streaming codes for handling a combination of burst and random erasures,” in 2021 IEEE Information Theory Workshop (ITW), 2021, pp. 1–6.
  8. M. Rudow and K. V. Rashmi, “Learning-augmented streaming codes for variable-size messages under partial burst losses,” in 2023 IEEE International Symposium on Information Theory (ISIT), June 2023, pp. 1101–1106.
  9. V. Ramkumar, S. Bhatnagar, and P. V. Kumar, “Near-optimal streaming codes with linear field size,” in 2023 IEEE International Symposium on Information Theory (ISIT), 2023, pp. 1118–1123.
  10. J. Cloud and M. Médard, “Multi-path low delay network codes,” in Proc. IEEE Global Communications Conference, GLOBECOM 2016, Washington, DC, USA, December 4-8, 2016.   IEEE, 2016, pp. 1–7.
  11. S. L. Fong, A. Khisti, B. Li, W. Tan, X. Zhu, and J. G. Apostolopoulos, “Optimal streaming erasure codes over the three-node relay network,” IEEE Trans. Inf. Theory, vol. 66, no. 5, pp. 2696–2712, 2020.
  12. M. Rudow and K. V. Rashmi, “Online versus offline rate in streaming codes for variable-size messages,” in 2020 IEEE International Symposium on Information Theory (ISIT), 2020, pp. 509–514.
  13. N. Adler and Y. Cassuto, “Burst-Erasure Correcting Codes With Optimal Average Delay,” IEEE Trans. Inf. Theory, vol. 63, no. 5, pp. 2848–2865, 2017.
  14. M. Haghifam, M. N. Krishnan, A. Khisti, X. Zhu, W. Tan, and J. G. Apostolopoulos, “On streaming codes with unequal error protection,” IEEE J. Sel. Areas Inf. Theory, vol. 2, no. 4, pp. 1165–1179, 2021.
  15. P. Su, Y. Huang, S. Lin, I. Wang, and C. Wang, “Random linear streaming codes in the finite memory length and decoding deadline regime,” in Proc. IEEE International Symposium on Information Theory, ISIT 2021, Melbourne, Australia, July 12-20, 2021.   IEEE, 2021, pp. 730–735.
  16. M. N. Krishnan, G. K. Facenda, E. Domanovitz, A. Khisti, W. Tan, and J. G. Apostolopoulos, “High rate streaming codes over the three-node relay network,” in Proc. IEEE Information Theory Workshop, ITW 2021, Kanazawa, Japan, October 17-21, 2021.   IEEE, 2021, pp. 1–6.
  17. V. Ramkumar, M. Vajha, and P. V. Kumar, “Locally recoverable streaming codes for packet-erasure recovery,” in Proc. IEEE Information Theory Workshop, ITW 2021, Kanazawa, Japan, October 17-21, 2021.   IEEE, 2021, pp. 1–6.
  18. M. Rudow and K. Rashmi, “Learning-augmented streaming codes are approximately optimal for variable-size messages,” in 2022 IEEE International Symposium on Information Theory (ISIT), 2022, pp. 474–479.
  19. A. Frank, “Delay-optimal coding for secure transmission over parallel burst erasure channels with an eavesdropper,” in 2020 IEEE International Symposium on Information Theory (ISIT), 2020, pp. 960–965.
  20. A. Frank, H. Aydinian, and H. Boche, “Delay optimal coding for secure transmission over a burst erasure wiretap channel,” in 2019 IEEE Wireless Communications and Networking Conference (WCNC), 2019, pp. 1–7.
  21. A. Badr, D. Lui, and A. Khisti, “Streaming codes for multicast over burst erasure channels,” IEEE Transactions on Information Theory, vol. 61, no. 8, pp. 4181–4208, 2015.
  22. R. Mahmood, A. Badr, and A. Khisti, “Streaming codes for multiplicative-matrix channels with burst rank loss,” IEEE Transactions on Information Theory, vol. 64, no. 7, pp. 5296–5311, 2018.
  23. M. Vajha, V. Ramkumar, M. N. Krishnan, and P. V. Kumar, “Explicit rate-optimal streaming codes with smaller field size,” in Proc. IEEE International Symposium on Information Theory, ISIT 2021, Melbourne, Australia, July 12-20, 2021.   IEEE, 2021, pp. 736–741.
  24. M. Nikhil Krishnan, V. Ramkumar, M. Vajha, and P. Vijay Kumar, “Simple streaming codes for reliable, low-latency communication,” IEEE Communications Letters, vol. 24, no. 2, pp. 249–253, 2020.
  25. Z. Li, A. Khisti, and B. Girod, “Correcting erasure bursts with minimum decoding delay,” in 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2011, pp. 33–39.

Summary

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

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