Download Computing and Combinatorics: 15th Annual International by S. Muthukrishnan (auth.), Hung Q. Ngo (eds.) PDF

By S. Muthukrishnan (auth.), Hung Q. Ngo (eds.)

This quantity constitutes the refereed lawsuits of the fifteenth foreign Computing and Combinatorics convention, COCOON 2009, held in big apple, manhattan, united states in July 2009. The fifty one revised prolonged abstracts awarded have been conscientiously reviewed and chosen from a hundred twenty five submissions. The papers are geared up in topical sections on algorithmic video game concept and coding conception, algorithms and information buildings, graph drawing, algorithms and knowledge constructions, cryptography and protection, algorithms, computational geometry, approximation algorithms, computational biology and bioinformatics, sampling and studying, complexity and computability, probabilistic research, and algorithms and knowledge structures.

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Read Online or Download Computing and Combinatorics: 15th Annual International Conference, COCOON 2009 Niagara Falls, NY, USA, July 13-15, 2009 Proceedings PDF

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Additional resources for Computing and Combinatorics: 15th Annual International Conference, COCOON 2009 Niagara Falls, NY, USA, July 13-15, 2009 Proceedings

Sample text

It has been known since [Zyablov and Pinsker 1982] that a random q-ary code of rate 1−Hq (ρ)−ε (where 0 < ρ < 1−1/q, ε > 0 and Hq (·) is the q-ary entropy function) with high probability is a (ρ, 1/ε)-list decodable code. ) In this paper we prove the “converse” result. In particular, we prove that for every 0 < ρ < 1 − 1/q, a random code of rate 1 − Hq (ρ) − ε, with high probability, is not a (ρ, L)-list decodable c , where c is a constant that depends only on ρ and q. code for any L ε We also prove a similar lower bound for random linear codes.

5369, pp. 148–158. edu Abstract. It has been known since [Zyablov and Pinsker 1982] that a random q-ary code of rate 1−Hq (ρ)−ε (where 0 < ρ < 1−1/q, ε > 0 and Hq (·) is the q-ary entropy function) with high probability is a (ρ, 1/ε)-list decodable code. ) In this paper we prove the “converse” result. In particular, we prove that for every 0 < ρ < 1 − 1/q, a random code of rate 1 − Hq (ρ) − ε, with high probability, is not a (ρ, L)-list decodable c , where c is a constant that depends only on ρ and q.

Thus, for some code, there exists some received word for which the output list size needs to be at least L. To convert this into a high probability event, we bound the variance of these events (again the notion of disjointness discussed above helps) and then appeal to Chebyschev’s inequality. The drawback of the approach above is that one can only prove the required tight lower bound on the list size for ρ < 1/2(1 − 1/q). To push up ρ close to 1 − 1/q, we will need the following idea. Instead of carving the space of received words into (exponentially many) Hamming balls of relative radius 2ρ, we will carve the space into exponentially many disjoint clusters with the following properties.

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