Asymptotic capacity of a random channel

Sutter, Tobias; Sutter, David; Lygeros, John

Asymptotic capacity of a random channel

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Date

2014

Authors

Sutter, Tobias

Sutter, David

Lygeros, John

Publication type

Contribution to a conference collection

Publication status

Published

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

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 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 μ₂ := 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 μ₂ /μ₁ - log μ₁ almost surely and in L² . We further show that the capacity of these random channels converges to this asymptotic value exponentially in n.

Subject (DDC)

004 Computer Science

Conference

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

Cite This

ISO 690

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

BibTex

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

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    <dcterms:abstract xml:lang="eng">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)&lt;sup&gt; 2&lt;/sup&gt; 1 &lt;; ∞, μ &lt;sub&gt;1&lt;/sub&gt; := E[X] and μ&lt;sub&gt; 2&lt;/sub&gt; := 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&lt;sub&gt; 2&lt;/sub&gt; /μ&lt;sub&gt; 1&lt;/sub&gt; - log μ&lt;sub&gt; 1&lt;/sub&gt; almost surely and in L&lt;sup&gt; 2&lt;/sup&gt; . We further show that the capacity of these random channels converges to this asymptotic value exponentially in n.</dcterms:abstract>
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