Algebraic lower bounds on the free distance of convolutional codes

Lally, K 2005, 'Algebraic lower bounds on the free distance of convolutional codes', in A. Grant (ed.) Proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, 4-9 September 2005, pp. 2101-2110.


Document type: Conference Paper
Collection: Conference Papers

Attached Files
Name Description MIMEType Size
n2005001369.pdf Published version application/pdf 320.02KB
Title Algebraic lower bounds on the free distance of convolutional codes
Author(s) Lally, K
Year 2005
Conference name 2005 IEEE International Symposium on Information Theory
Conference location Adelaide, Australia
Conference dates 4-9 September 2005
Proceedings title Proceedings of the 2005 IEEE International Symposium on Information Theory
Editor(s) A. Grant
Publisher IEEE
Place of publication Piscataway, USA
Start page 2101
End page 2110
Total pages 10
Abstract A new module structure for convolutional codes is introduced and used to establish further links with quasi-cyclic and cyclic codes. The set of finite weight codewords of an (n,k) convolutional code over Fq is shown to be isomorphic to an Fq[x]-submodule of Fq n[x], where Fq n[x] is the ring of polynomials in indeterminate x over Fq n, an extension field of Fq. Such a module can then be associated with a quasi-cyclic code of index n and block length nL viewed as an Fq[x]-submodule of Fq n[x]/langxL-1rang, for any positive integer L. Using this new module approach algebraic lower bounds on the free distance of a convolutional code are derived which can be read directly from the choice of polynomial generators. Links between convolutional codes and cyclic codes over the field extension Fq n are also developed and Bose-Chaudhuri-Hocquenghem (BCH)-type results are easily established in this setting. Techniques to find the optimal choice of the parameter L are outlined
Subjects Coding and Information Theory
Keyword(s) convolutional codes
cyclic codes
free distance,
lower bound
quasi-cyclic codes
DOI - identifier 10.1109/TIT.2006.872980
Copyright notice © 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Versions
Version Filter Type
Altmetric details:
Access Statistics: 145 Abstract Views, 339 File Downloads  -  Detailed Statistics
Created: Wed, 08 Apr 2009, 09:42:32 EST by Catalyst Administrator
© 2014 RMIT Research Repository • Powered by Fez SoftwareContact us