# On the Combinatorial Version of the Slepian-Wolf Problem

2 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We study 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 $\alpha n$. 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. For an asymmetric variant of this problem (where one of the Senders transmits the input string to the Receiver without compression) with deterministic encoding a nontrivial lower bound was found by A.Orlitsky and K.Viswanathany. In our paper we prove a new lower bound for the schemes with syndrome coding, where at least one of the Senders uses linear encoding of the input string. For the combinatorial Slepian-Wolf problem with randomized encoding the theoretical optimum of communication complexity was recently found by the first author, though effective protocols with optimal lengths of messages remained unknown. We close this gap and present a polynomial time randomized protocol that achieves the optimal communication complexity.
Type de document :
Pré-publication, Document de travail
2015
Domaine :

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01233020
Contributeur : Andrei Romashchenko <>
Soumis le : mardi 24 novembre 2015 - 12:22:27
Dernière modification le : jeudi 11 janvier 2018 - 06:27:05

### Identifiants

• HAL Id : lirmm-01233020, version 1
• ARXIV : 1511.02899

### Citation

Daniyar Chumbalov, Andrei Romashchenko. On the Combinatorial Version of the Slepian-Wolf Problem. 2015. 〈lirmm-01233020〉

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