**Finite Field Matrix Channels for Network Coding.** / Blackburn, Simon; Claridge, Jessica.

Research output: Contribution to journal › Article

Forthcoming

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.

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 language | English |
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Number of pages | 21 |

Journal | IEEE Transactions on Information Theory |

State | Accepted/In press - 9 Oct 2018 |

ID: 31384945