Finite-Field Matrix Channels for Network Coding

DOI10.1109/TIT.2018.2875763zbMATH Open1431.94053arXiv1601.06037OpenAlexW2963779328WikidataQ129098883 ScholiaQ129098883MaRDI QIDQ4629921

Jessica Claridge, Simon R. Blackburn

Publication date: 28 March 2019

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: In 2010, Silva, Kschischang and K"otter 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.

Full work available at URL: https://arxiv.org/abs/1601.06037

Mathematics Subject Classification ID

Channel models (including quantum) in information and communication theory (94A40) Source coding (94A29)

This page was built for publication: Finite-Field Matrix Channels for Network Coding