On doubly-cyclic convolutional codes

Heide Gluesing-Luerssen; Wiland Schmale

doi:10.1007/s00200-006-0014-9

On doubly-cyclic convolutional codes

Heide Gluesing-Luerssen, Wiland Schmale

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra [x]/(xⁿ-1), where is a finite field. A particular choice of the data leads to the class of doubly-cyclic CC's. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC's basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.

Original language	English
Pages (from-to)	151-170
Number of pages	20
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s00200-006-0014-9
State	Published - Jun 2006

Keywords

Convolutional coding theory
Cyclic codes
Skew polynomial rings

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1007/s00200-006-0014-9

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AU - Schmale, Wiland

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AB - Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra [x]/(xn-1), where is a finite field. A particular choice of the data leads to the class of doubly-cyclic CC's. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC's basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.

KW - Convolutional coding theory

KW - Cyclic codes

KW - Skew polynomial rings

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JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

IS - 2

ER -

On doubly-cyclic convolutional codes

Abstract

Keywords

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