Broadcasting with side information

Noga Alon, Avinatan Hassidim, Eyal Lubetzky, Uri Stav, Amit Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 βt be the minimum number of bits that has to be transmitted when each block is of length t, and let β be the limit β= lim →Infin; βt/t. Informally, β is the average communication cost per bit in each block (for long blocks). Finding the coding rate β, 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 βt, and prove that for any constant C there is an explicit broadcast setting in which β= 2 but β1 > C. One of these examples answers a question of [15]. In addition, we provide examples with the following counterintuitive direct-sum phenomena. Consider a union of several mutually independent broadcast settings. The optimal code for the combined setting may yield a significant saving in communication over concatenating optimal encodings for the individual settings. This result also provides new non-linear coding schemes which improve upon the largest known gap between linear and non-linear Network Coding, thus improving the results of [8]. The proofs are based on a relation between this problem and results in the study of Witsenhausen's rate, OR graph products, colorings of Cayley graphs, and the chromatic numbers of Kneser graphs.

Original languageEnglish (US)
Title of host publicationProceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
Pages823-832
Number of pages10
DOIs
StatePublished - 2008
Event49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008 - Philadelphia, PA, United States
Duration: Oct 25 2008Oct 28 2008

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Other

Other49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
CountryUnited States
CityPhiladelphia, PA
Period10/25/0810/28/08

ASJC Scopus subject areas

  • Computer Science(all)

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