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# Asymptotic capacity of a random channel

Type of Publication: | Contribution to a conference collection |

Publication status: | Published |

Author: | Sutter, Tobias; Sutter, David; Lygeros, John |

Year of publication: | 2014 |

Conference: | 52nd Annual Allerton Conference on Communication, Control, and Computing, Sep 30, 2014 - Oct 3, 2014, Monticello, IL, USA |

Published in: | 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton). - Piscataway, NJ : IEEE, 2014. - pp. 771-778. - ISBN 978-1-4799-8009-3 |

DOI (citable link): | https://dx.doi.org/10.1109/ALLERTON.2014.7028532 |

Summary: |
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)
^{ 2} 1 <; ∞, μ _{1} := E[X] and μ_{ 2} := 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_{ 2} /μ_{ 1} - log μ_{ 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. |

Subject (DDC): | 004 Computer Science |

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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} }