Asymptotic capacity of a random channel

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SUTTER, Tobias, David SUTTER, John LYGEROS, 2014. Asymptotic capacity of a random channel. 52nd Annual Allerton Conference on Communication, Control, and Computing. Monticello, IL, USA, Sep 30, 2014 - Oct 3, 2014. In: 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton). Piscataway, NJ:IEEE, pp. 771-778. ISBN 978-1-4799-8009-3. Available under: doi: 10.1109/ALLERTON.2014.7028532

@inproceedings{Sutter2014Asymp-55741, title={Asymptotic capacity of a random channel}, year={2014}, doi={10.1109/ALLERTON.2014.7028532}, isbn={978-1-4799-8009-3}, address={Piscataway, NJ}, publisher={IEEE}, booktitle={2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)}, pages={771--778}, author={Sutter, Tobias and Sutter, David and Lygeros, John} }

Asymptotic capacity of a random channel 2021-12-02T12:55:58Z terms-of-use Sutter, David 2014 Sutter, Tobias 2021-12-02T12:55:58Z 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 v on (R≥0, B(R≥0)) before being normalized, where v is such that E[X log X)<sup> 2</sup> 1 <; ∞, μ <sub>1</sub> := E[X] and μ<sub> 2</sub> := E[X log X] for a random variable X with distribution v. We prove that in the limit as n → ∞, the capacity of such a channel converges to μ<sub> 2</sub> /μ<sub> 1</sub> - log μ<sub> 1</sub> almost surely and in L<sup> 2</sup> . We further show that the capacity of these random channels converges to this asymptotic value exponentially in n. eng Lygeros, John Sutter, David Sutter, Tobias Lygeros, John

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