Randomized Polynomial Time Protocol for Combinatorial Slepian-Wolf Problem

Daniyar Chumbalov

Abstract:

We consider the following combinatorial version of the Slepian–Wolf
coding scheme. Two isolated Senders are given binary strings X and Y respectively; the length of each string is equal to n, and the Hamming distance between
the strings is at most αn. The Senders compress their strings and communicate
the results to the Receiver. Then the Receiver must reconstruct both strings X
and Y . The aim is to minimise the lengths of the transmitted messages.
The theoretical optimum of communication complexity for this scheme (with
randomised parties) was found in [8], though effective protocols with optimal
lengths of messages remained unknown. We close this gap and present for this
communication problem a polynomial time randomised protocol that achieves
the optimal communication complexity