Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more...

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Autores: Lim, SH, Feng, C, Pastore, A, Nazer, B, Gastpar, M
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
Repositorio:r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
OAI Identifier:oai:cttc.fundanetsuite.com:p3073
Acceso en línea:https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3073
Access Level:acceso abierto
Palabra clave:Decoding
Lattices
Linear codes
Receivers
Relay networks (telecommunications)
Random variables
Compute-forward
joint decoding
linear codes
multiple-access channel
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spelling Compute-Forward for DMCs: Simultaneous Decoding of Multiple CombinationsLim, SHFeng, CPastore, ANazer, BGastpar, MDecodingLatticesLinear codesReceiversRelay networks (telecommunications)Random variablesCompute-forwardjoint decodinglinear codesmultiple-access channelAlgebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering L <= K linear combinations of transmitted codewords over a K-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. This paper develops bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and applies them to obtain a larger achievable region for compute-forward over a K-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.Institute of Electrical and Electronics Engineers Inc.2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3073IEEE TRANSACTIONS ON INFORMATION THEORYISSN: 00189448ISSNe: 15579654reponame:r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)instname:Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)Inglésinfo:eu-repo/semantics/openAccessoai:cttc.fundanetsuite.com:p30732026-06-17T11:44:47Z
dc.title.none.fl_str_mv Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
title Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
spellingShingle Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
Lim, SH
Decoding
Lattices
Linear codes
Receivers
Relay networks (telecommunications)
Random variables
Compute-forward
joint decoding
linear codes
multiple-access channel
title_short Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
title_full Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
title_fullStr Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
title_full_unstemmed Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
title_sort Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
dc.creator.none.fl_str_mv Lim, SH
Feng, C
Pastore, A
Nazer, B
Gastpar, M
author Lim, SH
author_facet Lim, SH
Feng, C
Pastore, A
Nazer, B
Gastpar, M
author_role author
author2 Feng, C
Pastore, A
Nazer, B
Gastpar, M
author2_role author
author
author
author
dc.subject.none.fl_str_mv Decoding
Lattices
Linear codes
Receivers
Relay networks (telecommunications)
Random variables
Compute-forward
joint decoding
linear codes
multiple-access channel
topic Decoding
Lattices
Linear codes
Receivers
Relay networks (telecommunications)
Random variables
Compute-forward
joint decoding
linear codes
multiple-access channel
description Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering L <= K linear combinations of transmitted codewords over a K-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. This paper develops bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and applies them to obtain a larger achievable region for compute-forward over a K-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3073
url https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3073
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
dc.source.none.fl_str_mv IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN: 00189448
ISSNe: 15579654
reponame:r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
instname:Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
instname_str Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
reponame_str r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
collection r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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