Finite-Field Matrix Channels for Network Coding

Simon Blackburn, Jessica Claridge

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In 2010, Silva, Kschischang and Kötter studied certain classes of finite field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced.

In this paper we consider a generalisation of these matrix channels where the number of errors is not required to be constant, indeed the number of errors may follow any distribution. We show that a capacity-achieving input distribution can always be taken to have a very restricted form (the distribution should be uniform given the rank of the input matrix). This result complements, and is inspired by, a paper of Nobrega, Silva and Uchoa-Filho, that establishes a similar result for a class of matrix channels that model network coding with link erasures. Our result shows that the capacity of our channels can be expressed as a maximisation over probability distributions on the set of possible ranks of input matrices: a set of linear rather than exponential size.
Original languageEnglish
Pages (from-to)1614 - 1625
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number3
Publication statusPublished - 12 Oct 2018

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