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Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels

Como, Giacomo

IEEE transactions on information theory, 2010-09, Vol.56 (9), p.4321-4334 [Periódico revisado por pares]

New York, NY: IEEE

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Título:
Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels
Autor: Como, Giacomo
Assuntos: Applied sciences ; Codes ; Coding theory ; Coding, codes ; Computer memory ; Constraint theory ; Control Engineering ; Coset codes ; Electrical Engineering, Electronic Engineering, Information Engineering ; Elektroteknik och elektronik ; Engineering and Technology ; Error analysis ; error exponent ; Exact sciences and technology ; expurgated exponent ; Gaussian channels ; Gilbert-Varshamov bound ; group codes ; Information processing ; Information theory ; Information, signal and communications theory ; Labeling ; Linear code ; linear codes ; Memoryless systems ; minimum distance ; Modulation, demodulation ; Normal distribution ; Parity check codes ; Performance loss ; random codes ; Reglerteknik ; Signal and communications theory ; Systems, networks and services of telecommunications ; Teknik ; Telecommunications ; Telecommunications and information theory ; Transmission and modulation (techniques and equipments) ; Turbo codes
É parte de: IEEE transactions on information theory, 2010-09, Vol.56 (9), p.4321-4334
Descrição: Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity-achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert-Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical-code performance than designing codes whose algebraic structure does not match the channel. This contrasts the well-known fact that the average binary-coset code achieves both the capacity and the random-coding error exponent of any discrete memoryless channel.
Editor: New York, NY: IEEE
Idioma: Inglês

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Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels

Como, Giacomo

New York, NY: IEEE

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