On polarization for the linear operator channel

César Brito, Jörg Kliewer

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

Abstract

We address the problem of reliably transmitting information through a network where the nodes perform random linear network coding and where an adversary potentially injects malicious packets into the network. A good model for such a channel is a linear operator channel, where in this work we employ a combined multiplicative and additive matrix channel. We show that this adversarial channel behaves like a subspace-based symmetric discrete memoryless channel (DMC) under subspace insertions and deletions and typically has an input alphabet with non-prime cardinality. This facilitates the recent application of channel polarization results for DMCs with arbitrary input alphabets by providing a suitable one-to-one mapping from input matrices to subspaces. As a consequence, we show that polarization for this adversarial linear operator channel can be obtained via an element-wise encoder mapping for the input matrices, which replaces the finite field summation in the channel combining step for Arikan's classical polar codes.

Original languageEnglish (US)
Title of host publication2013 IEEE Information Theory Workshop, ITW 2013
DOIs
StatePublished - Dec 1 2013
Externally publishedYes
Event2013 IEEE Information Theory Workshop, ITW 2013 - Seville, Spain
Duration: Sep 9 2013Sep 13 2013

Publication series

Name2013 IEEE Information Theory Workshop, ITW 2013

Other

Other2013 IEEE Information Theory Workshop, ITW 2013
CountrySpain
CitySeville
Period9/9/139/13/13

All Science Journal Classification (ASJC) codes

  • Information Systems

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