DocumentCode :
918953
Title :
Algebraic lower bounds on the free distance of convolutional codes
Author :
Lally, Kristine
Author_Institution :
Dept. of Math. & Stat., RMIT Univ., Melbourne, Vic.
Volume :
52
Issue :
5
fYear :
2006
fDate :
5/1/2006 12:00:00 AM
Firstpage :
2101
Lastpage :
2110
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
Keywords :
BCH codes; algebraic codes; block codes; convolutional codes; cyclic codes; polynomials; BCH; Bose-Chaudhuri-Hocquenghem; algebraic lower bound; block length; convolutional code; polynomial generator; quasicyclic code; Australia; Block codes; Convolutional codes; Error correction codes; Information theory; Mathematics; Statistics; Transfer functions; Vectors; Convolutional codes; cyclic codes; free distance; lower bound; quasi-cyclic codes;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2006.872980
Filename :
1624643
Link To Document :
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