TY - GEN

T1 - On the complementary Index Coding problem

AU - Chaudhry, M. A.R.

AU - Asad, Z.

AU - Sprintson, A.

AU - Langberg, Michael

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80054818961&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6034005

DO - 10.1109/ISIT.2011.6034005

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AN - SCOPUS:80054818961

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 244

EP - 248

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -