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In this paper we show that the Index Coding problem captures severalimportant properties of the more general Network Coding problem. An instance ofthe Index Coding problem includes a server that holds a set of informationmessages $X=\{x_1,...,x_k\}$ and a set of receivers $R$. Each receiver has someside information, known to the server, represented by a subset of $X$ anddemands another subset of $X$. The server uses a noiseless communicationchannel to broadcast encodings of messages in $X$ to satisfy the receivers'demands. The goal of the server is to find an encoding scheme that requires theminimum number of transmissions.  We show that any instance of the Network Coding problem can be efficientlyreduced to an instance of the Index Coding problem. Our reduction shows thatseveral important properties of the Network Coding problem carry over to theIndex Coding problem. In particular, we prove that both scalar linear andvector linear codes are insufficient for achieving the minimal number oftransmissions.

On the Relation Between the Index Coding and the Network Coding Problems