Finite-Field Matrix Channels for Network Coding. / Blackburn, Simon; Claridge, Jessica.
In: IEEE Transactions on Information Theory, Vol. 65, No. 3, 12.10.2018, p. 1614 - 1625.Research output: Contribution to journal › Article › peer-review
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Finite-Field Matrix Channels for Network Coding. / Blackburn, Simon; Claridge, Jessica.
In: IEEE Transactions on Information Theory, Vol. 65, No. 3, 12.10.2018, p. 1614 - 1625.Research output: Contribution to journal › Article › peer-review
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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 -