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Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relativel...

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Autores principales: Tamir (Averbuch), Ran, Merhav, Neri
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7995976/
https://www.ncbi.nlm.nih.gov/pubmed/33668181
http://dx.doi.org/10.3390/e23030265
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author Tamir (Averbuch), Ran
Merhav, Neri
author_facet Tamir (Averbuch), Ran
Merhav, Neri
author_sort Tamir (Averbuch), Ran
collection PubMed
description Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.
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spelling pubmed-79959762021-03-27 Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes Tamir (Averbuch), Ran Merhav, Neri Entropy (Basel) Article Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity. MDPI 2021-02-24 /pmc/articles/PMC7995976/ /pubmed/33668181 http://dx.doi.org/10.3390/e23030265 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Tamir (Averbuch), Ran
Merhav, Neri
Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
title Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
title_full Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
title_fullStr Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
title_full_unstemmed Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
title_short Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
title_sort trade-offs between error exponents and excess-rate exponents of typical slepian–wolf codes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7995976/
https://www.ncbi.nlm.nih.gov/pubmed/33668181
http://dx.doi.org/10.3390/e23030265
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