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

Research output: Contribution to journal › Article › peer-review

Published

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

Research output: Contribution to journal › Article › peer-review

Blackburn, S & Claridge, J 2018, 'Finite-Field Matrix Channels for Network Coding', *IEEE Transactions on Information Theory*, vol. 65, no. 3, pp. 1614 - 1625. https://doi.org/10.1109/TIT.2018.2875763

Blackburn, S., & Claridge, J. (2018). Finite-Field Matrix Channels for Network Coding. *IEEE Transactions on Information Theory*, *65*(3), 1614 - 1625. https://doi.org/10.1109/TIT.2018.2875763

Blackburn S, Claridge J. Finite-Field Matrix Channels for Network Coding. IEEE Transactions on Information Theory. 2018 Oct 12;65(3):1614 - 1625. https://doi.org/10.1109/TIT.2018.2875763

@article{7399d349e00346f6b06696401832ecb8,

title = "Finite-Field Matrix Channels for Network Coding",

abstract = "In 2010, Silva, Kschischang and K{\"o}tter 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.",

author = "Simon Blackburn and Jessica Claridge",

year = "2018",

month = oct,

day = "12",

doi = "10.1109/TIT.2018.2875763",

language = "English",

volume = "65",

pages = "1614 -- 1625",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

}

TY - JOUR

T1 - Finite-Field Matrix Channels for Network Coding

AU - Blackburn, Simon

AU - Claridge, Jessica

PY - 2018/10/12

Y1 - 2018/10/12

N2 - 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.

AB - 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.

U2 - 10.1109/TIT.2018.2875763

DO - 10.1109/TIT.2018.2875763

M3 - Article

VL - 65

SP - 1614

EP - 1625

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 3

ER -