Optimal probabilistic polynomial time compression and the Slepian-Wolf theorem: tighter version and simple proofs

02/02/2018

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by   Bruno Bauwens, et al.

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We give simplify the proofs of the 2 results in Marius Zimand's paper "Kolmogorov complexity version of Slepian-Wolf coding, proceedings of STOC 2017, p22--32". The first is a universal polynomial time compression algorithm: on input ε > 0, a number k and a string x it computes in polynomial time with probability 1-ε a program that outputs x and has length k + O(^2 (|x|/ε)), provided that there exists such a program of length at most k. The second result, is a distributed compression algorithm, in which several parties each send some string to a common receiver. Marius Zimand proved a variant of the Slepian-Wolf theorem using Kolmogorov complexity (in stead of Shannon entropy). With our simpler proof we improve the parameters of Zimand's result.