On the complementary Index Coding problem

M. A.R. Chaudhry, Z. Asad, A. Sprintson, M. Langberg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The Index Coding problem is one of the basic problems in wireless network coding. In this problem, a server needs to deliver a set P of packets to several clients through a noiseless broadcast channel. Each client needs to obtain a certain subset of P and has prior side information about a different subset of P. The objective is to satisfy the requirements of all clients with the minimum number of transmissions. Recently, it was shown that the Index Coding problem is NP-hard. Furthermore, this problem was shown to be hard to approximate under a widely accepted complexity assumption. In this paper, we consider a complementary problem whose goal is to maximize the number of saved transmissions, i.e., the number of transmissions that are saved by combining packets compared to the solution that does not involve coding. We refer to this problem as the the Complementary Index Coding problem. It turns out that the complementary problem can be approximated in certain cases of practical importance. We consider the multiple unicast and multiple multicast scenarios. In the multiple unicast scenario, each packet is requested by a single client; while in the multiple multicast scenario, each packet can be requested by several clients. For the multiple unicast scenario, we present approximation algorithms for finding scalar and vector linear solutions. For the multiple multicast scenario, we show that finding an approximation solution is NP-hard.

Original languageEnglish
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Number of pages5
StatePublished - 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: 31 Jul 20115 Aug 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104


Conference2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Country/TerritoryRussian Federation
CitySt. Petersburg


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