On the optimal block length for joint channel and network coding

Christian Koller, Martin Haenggi, Jörg Kliewer, Daniel J. Costello

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

12 Scopus citations

Abstract

Channel coding alone is not sufficient to reliably transmit a message of finite length from a source to one or more destinations. To ensure that no data is lost, channel coding on the physical layer needs to be combined with rateless erasure correcting schemes such as automatic repeat request (ARQ) or random linear network coding (RLNC) on a higher layer. In this paper we consider channel coding on a binary symmetric channel and random linear network coding for erasure correction. Given a message of length K and network coding over a finite Galois field of size q, we obtain the optimal number of blocks for network coding that minimizes the expected number of transmissions. We consider both a single link and broadcast to n destinations. As the field size of network coding gets large and the expected coding overhead in blocks becomes small, we show that, given our assumptions, the benefit of using a larger channel coded block outweighs the advantage of employing network coding over many blocks and the optimal number of number of blocks tends to one, making RLNC equivalent to simple ARQ.

Original languageEnglish (US)
Title of host publication2011 IEEE Information Theory Workshop, ITW 2011
Pages528-532
Number of pages5
DOIs
StatePublished - Dec 21 2011
Externally publishedYes
Event2011 IEEE Information Theory Workshop, ITW 2011 - Paraty, Brazil
Duration: Oct 16 2011Oct 20 2011

Publication series

Name2011 IEEE Information Theory Workshop, ITW 2011

Other

Other2011 IEEE Information Theory Workshop, ITW 2011
Country/TerritoryBrazil
CityParaty
Period10/16/1110/20/11

All Science Journal Classification (ASJC) codes

  • Information Systems

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