A Set Cover Based Efficient Solution for the Complementary Index Coding Problem

The Index Coding problem can be considered as one of the basic problems in information theory. In this problem a relay node needs to deliver a set of packets to a set of client over a broadcast wireless channel. Each client might posses some "side information" related to the transmissions by the relay node. The goal is to minimize number of transmissions from the relay node by taking advantage of the side information. The Index Coding problem has been proven to be NP-hard and NP-hard to approximate. The Complementary Index Coding problem is a complementary problem of the Index Coding problem. In the Complementary Index Coding problem the objective is to maximize number of the saved transmissions, i.e., the number of transmissions that are saved by encoding packets compared to the solution that does not perform coding. This work aims at improving the gains of the Complementary Index Coding problem by proposing a Set Cover based solution that guarantees an approximation ratio of 1/(1-(H_k|S|/n)). Moreover, we propose a scheme for transforming the Index Coding problem in to the Set Cover problem. In addition to this, we compare the proposed algorithm with the current state of the art. The experimental results show that the proposed solution out performs current state of the art both in terms of coding advantage as well as running time.