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The benefits of coding over routing in a randomized setting (2003)
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| Venue: | In Proceedings of 2003 IEEE International Symposium on Information Theory |
| Citations: | 361 - 44 self |
BibTeX
@INPROCEEDINGS{Ho03thebenefits,
author = {Tracey Ho and Ralf Koetter and Muriel Médard and David R. Karger and Michelle Effros},
title = {The benefits of coding over routing in a randomized setting},
booktitle = {In Proceedings of 2003 IEEE International Symposium on Information Theory},
year = {2003}
}
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Abstract
Abstract — We present a novel randomized coding approach for robust, distributed transmission and compression of information in networks. We give a lower bound on the success probability of a random network code, based on the form of transfer matrix determinant polynomials, that is tighter than the Schwartz-Zippel bound for general polynomials of the same total degree. The corresponding upper bound on failure probability is on the order of the inverse of the size of the finite field, showing that it can be made arbitrarily small by coding in a sufficiently large finite field, and that it decreases exponentially with the number of codeword bits. We demonstrate the advantage of randomized coding over routing for distributed transmission in rectangular grid networks by giving, in terms of the relative grid locations of a source-receiver pair, an upper bound on routing success probability that is exceeded by a corresponding lower bound on coding success probability for sufficiently large finite fields. We also show that our lower bound on the success probability of randomized coding holds for linearly correlated sources. This implies that randomized coding effectively compresses linearly correlated information to the capacity of any network cut in a feasible connection problem. I.
Keyphrases
success probability randomized setting large finite field randomized coding coding approach transfer matrix determinant polynomial finite field distributed transmission schwartz-zippel bound network cut rectangular grid network feasible connection problem failure probability source-receiver pair total degree upper bound general polynomial random network code codeword bit corresponding upper bound relative grid location
