 
Summary: Broadcasting with side information
Noga Alon
Avinatan Hassidim
Eyal Lubetzky
Uri Stav§
Amit Weinstein¶
Abstract
A sender holds a word x consisting of n blocks xi, each of t bits, and wishes to broadcast
a codeword to m receivers, R1, ..., Rm. Each receiver Ri is interested in one block, and has
prior side information consisting of some subset of the other blocks. Let t be the minimum
number of bits that has to be transmitted when each block is of length t, and let be the limit
= limt t/t. In words, is the average communication cost per bit in each block (for long
blocks). Finding the coding rate , for such an informed broadcast setting, generalizes several
coding theoretic parameters related to Informed Source Coding on Demand, Index Coding and
Network Coding.
In this work we show that usage of large data blocks may strictly improve upon the trivial
encoding which treats each bit in the block independently. To this end, we provide general
bounds on t, and prove that for any constant C there is an explicit broadcast setting in which
= 2 but 1 > C. One of these examples answers a question of [15].
In addition, we provide examples with the following counterintuitive directsum phenomena.
