Index coding with side information

Ziv Bar-Yossef, Yitzhak Birk, T. S. Jayram, Tomer Kol

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by a problem of transmitting supplemental data over broadcast channels (Birk and Kol, INFOCOM 1998), we study the following coding problem: a sender communicates with n receivers R1, ⋯ Rn. He holds an input x ∈ {0,1}n and wishes to broadcast a single message so that each receiver Ri can recover the bit xi. Each Ri has prior side information about x, induced by a directed graph G; on n nodes; Ri knows the bits of x in the positions {j Ι (i,j) is an edge of G}. G is known to the sender and to the receivers. We call encoding schemes that achieve this goal indexcodes for { 0,1 }n with side information graph G. In this paper we identify a measure on graphs, the minrank, which exactly characterizes the minimum length of linear and certain types of nonlinear index codes. We show that for natural classes of side information graphs, including directed acyclic graphs, perfect graphs, odd holes, and odd anti-holes, minrank is the optimal length of arbitrary index codes. For arbitrary index codes and arbitrary graphs, we obtain a lower bound in terms of the size of the maximum acyclic induced subgraph. This bound holds even for randomized codes, but has been shown not to be tight.

Original languageEnglish
Article number5714242
Pages (from-to)1479-1494
Number of pages16
JournalIEEE Transactions on Information Theory
Volume57
Issue number3
DOIs
StatePublished - Mar 2011

Keywords

  • Broadcast channels
  • code length
  • error correction coding
  • information cost

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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