An Equivalence Between Network Coding and Index Coding

Michelle Effros, Salim El Rouayheb, Michael Langberg

Research output: Contribution to journalArticlepeer-review


We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and nonlinear codes. Specifically, we present a reduction that maps a network coding instance to an index coding instance while preserving feasibility, i.e., the network coding instance has a feasible solution if and only if the corresponding index coding instance is feasible. In addition, we show that one can determine the capacity region of a given network coding instance with colocated sources by studying the capacity region of a corresponding index coding instance. Previous connections between network and index coding were restricted to the linear case.

Original languageEnglish
Article number7064720
Pages (from-to)2478-2487
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 1 May 2015

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  • Communication networks
  • network coding


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