Pliable index coding

We propose a new formulation of the index coding problem, where instead of demanding a specific bit (or message), clients are “pliable” and are happy to receive any one bit they do not have. We prove that with this relaxation, although some instances of this problem become simple, in general the problem of finding the optimal linear code remains NP-hard. We also show that if the server has n bits, O(log n log(n/log n)) coded bit transmissions are sufficient to satisfy the clients in the worst case, in contrast to the Ω(n) transmissions required in index coding. We develop several approximation algorithms and evaluate their performance through simulations.