Refined coding bounds and code constructions for coherent network error correction

IEEE Transactions on Information Theory

Volumn 57, Issue 3, 2011, Pages 1409-1424

  Yang, Shenghao ^a   Yeung, Raymond W ^a   Ngai, Chi Kin ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

GilbertVarshamov bound; Hamming bound; network code construction; network coding; network error correction; Singleton bound

Indexed keywords

GILBERT-VARSHAMOV BOUND; HAMMING BOUND; NETWORK CODE CONSTRUCTION; NETWORK ERROR CORRECTION; SINGLETON BOUND;

ALGORITHMS; ENCODING (SYMBOLS); INFORMATION THEORY; LINEAR NETWORKS; REFINING;

NETWORK CODING;

EID: 79951931376     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2106930     Document Type: Article

References (29)

1. R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1204-1216, Jul. 2000.
2. S.-Y. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 371-381, Feb. 2003.
3. R.Koetter and M. Medard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol. 11, no. 5, pp. 782-795, Oct. 2003.
4. S. Jaggi, P. Sanders, P. A. Chou, M. Effros, S. Egner, K. Jain, and L. Tolhuizen, "Polynomial time algorithms for multicast network code construction," IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1973-1982, Jun. 2005. (Pubitemid 40843620)
5. T. Ho, M. Medard, R. Koetter, D. R. Karger, M. Effros, J. Shi, and B. Leong, "A random linear network coding approach to multicast," IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4413-4430, Oct. 2006. (Pubitemid 46445282)
6. N. Cai and R. W. Yeung, "Network coding and error correction," presented at the IEEE Information Theory Workshop, Bangalore, India, Oct. 2002.
7. S. Jaggi, M. Langberg, S. Katti, T. Ho, D. Katabi, M. Médard, and M. Effros, "Resilient network coding in the presence of byzantine adversaries," IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2596-2603, Jun. 2008.
8. F. MacWilliams and N. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1978.
9. S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, 2nd ed. Upper Saddle River, NJ: Pearson Prentice-Hall, 2004.
10. R. W. Yeung and N. Cai, "Network error correction, part I: basic concepts and upper bounds," Commun. Inf. Syst., vol. 6, no. 1, pp. 19-36, 2006.
11. N. Cai and R. W. Yeung, "Network error correction, part II: Lower bounds," Commun. Inf. Syst., vol. 6, no. 1, pp. 37-54, 2006.
12. Z. Zhang, "Linear network error correction codes in packet networks," IEEE Trans. Inf. Theory, vol. 54, no. 1, pp. 209-218, Jan. 2008.
13. R. C. Singleton, "Maximum distance q-nary code," IEEE Trans. Inf. Theory, vol. IT-10, pp. 116-118, 1964.
14. R. W. Yeung, S.-Y. R. Li, N. Cai, and Z. Zhang, "Network coding theory," Found. Trends Commun. Inf. Theory, vol. 2, no. 4 and 5, pp. 241-381, 2005.
15. S. Yang, R. W. Yeung, and Z. Zhang, "Weight properties of network codes," Eur. Trans. Telecommun., vol. 19, no. 4, pp. 371-383, 2008.
16. S. Jaggi, M. Langberg, T. Ho, and M. Effros, "Correction of adversarial errors in networks," presented at the IEEE Int. Symp. Information Technology, Jul. 2005.
17. S. Yang and R. W. Yeung, "Characterizations of network error correction/ detection and erasure correction," presented at the Netcod Workshop, Jan. 2007.
18. T. Ho, B. Leong, R. Koetter, M. Medard, M. Effros, and D. R. Karger, "Byzantine modification detection in multicast networks using randomized network coding," presented at the IEEE Int. Symp. Information Theory, Jun. 2004.
19. S. Jaggi and M. Langberg, "Resilient network codes in the presence of eavesdropping Byzantine adversaries," presented at the IEEE Int. Symp. Information Theory, Jun. 2007.
20. H. Balli, X. Yan, and Z. Zhang, "Error correction capability of random network error correction codes," presented at the IEEE Int. Symp. Information Theory, Jun. 2007.
21. X. Yan, H. Balli, and Z. Zhang, "Decoding beyond error correction capability for random network error correction codes," IEEE Trans. Inf. Theory, submitted for publication.
22. R. Koetter and F. R. Kschischang, "Coding for errors and erasures in random network coding," IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3579-3591, Aug. 2008.
23. D. Silva, F. Kschischang, and R. Koetter, "A rank-metric approach to error control in random network coding," IEEE Trans. Inf. Theory, vol. 54, no. 9, pp. 3951-3967, Sep. 2008.
24. S. Yang, C. K. Ngai, and R. W. Yeung, "Construction of linear network codes that achieve a refined Singleton bound," presented at the IEEE Int. Symp. Information Theory, Jun. 2007.
25. S. Yang and R. W. Yeung, "Refined coding bounds for network error correction," presented at the IEEE Int. Symp. Information Theory, Bergen, Norway, 2007.
26. R. Matsumoto, "Construction algorithm for network error-correcting codes attaining the Singleton bound," IEICE Trans. Fundam., vol. E90-A, no. 9, pp. 1729-1735, Sep. 2007.
27. Wikipedia [Online]. Available: http://en.wikipedia.org/wiki/directed- acyclic-graph, online
28. S. Yang, "Network Coding and Error Correction," Ph.D. dissertation, The Chinese University of Hong Kong, Hong Kong, 2008.
29. R. W. Yeung, Information Theory and Network Coding. New York: Springer, 2008.