# Asymptotic Capacity of a Random Channel

Author(s):T. Sutter, D. Sutter, J. Lygeros |
Conference/Journal:Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA |

Abstract:We consider discrete memoryless channels with input and output alphabet size n whose channel transition matrix consists of entries that are independent and identically distributed according to some probability distribution \nu on (\R_+,\Borelsigalg{\R_+}) before being normalized, where \nu is such that E[(X \log X)^2]<\infty, \mu_1:=E[X] and \mu_2:=E[X \log X] for a random variable X with distribution \nu. We prove that in the limit as n goes to infinity, the capacity of such a channel converges to \mu_2 / \mu_1 - log \mu_1 almost surely and in L^2. We further show that the capacity of these random channels converges to this asymptotic value exponentially in n. Further Information |
Year:2014 |

Type of Publication:(01)Article | |

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% Autogenerated BibTeX entry @InProceedings { SutSut:2014:IFA_4830, author={T. Sutter and D. Sutter and J. Lygeros}, title={{Asymptotic Capacity of a Random Channel}}, booktitle={Allerton Conference on Communication, Control, and Computing}, pages={}, year={2014}, address={Monticello, IL, USA}, month=oct, url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=4830} } | |

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