Algebraic lower bounds on the free distance of convolutional codes

Lally, K 2006, 'Algebraic lower bounds on the free distance of convolutional codes', IEEE Transactions on Information Theory, vol. 52, no. 5, pp. 2101-2110.

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Title Algebraic lower bounds on the free distance of convolutional codes
Author(s) Lally, K
Year 2006
Journal name IEEE Transactions on Information Theory
Volume number 52
Issue number 5
Start page 2101
End page 2110
Total pages 9
Publisher IEEE
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 F, is shown to be isomorphic to an F-qn[x]-submodule of F-qn[x], where F-qn [x] is the ring of polynomials in indeterminate x over Fn, an extension field of F, 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 F-qn[x]/ < x(L) - 1 >, 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 F-qn 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.
Subject Coding and Information Theory
Keyword(s) convolutional codes
cyclic codes
free distance
lower bound
quasi-cyclic codes
DOI - identifier 10.1109/tit.2006.872980
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ISSN 0018-9448
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