Asymptotic capacity of a random channel

Sutter, Tobias; Sutter, David; Lygeros, John

Asymptotic capacity of a random channel

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2014

Autor:innen

Sutter, Tobias

Sutter, David

Lygeros, John

DOI (zitierfähiger Link)

https://doi.org/10.1109/ALLERTON.2014.7028532

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Beitrag zu einem Konferenzband

Publikationsstatus

Published

Erschienen 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. Available under: doi: 10.1109/ALLERTON.2014.7028532

Zusammenfassung

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.

Fachgebiet (DDC)

004 Informatik

Konferenz

52nd Annual Allerton Conference on Communication, Control, and Computing, 30. Sept. 2014 - 3. Okt. 2014, Monticello, IL, USA

Zitieren

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, 30. Sept. 2014 - 3. Okt. 2014. 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. 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}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/55741">
    <dc:creator>Sutter, David</dc:creator>
    <dc:creator>Lygeros, John</dc:creator>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Sutter, Tobias</dc:contributor>
    <dc:language>eng</dc:language>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <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>
    <dc:creator>Sutter, Tobias</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-12-02T12:55:58Z</dc:date>
    <dc:contributor>Lygeros, John</dc:contributor>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
    <dc:contributor>Sutter, David</dc:contributor>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:issued>2014</dcterms:issued>
    <dcterms:title>Asymptotic capacity of a random channel</dcterms:title>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-12-02T12:55:58Z</dcterms:available>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55741"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Nein