DocumentCode :
1316472
Title :
The trellis structure of maximal fixed-cost codes
Author :
Kschischang, Frank R.
Author_Institution :
Dept. of Electr. & Comput. Eng., Toronto Univ., Ont., Canada
Volume :
42
Issue :
6
fYear :
1996
fDate :
11/1/1996 12:00:00 AM
Firstpage :
1828
Lastpage :
1838
Abstract :
We show that the family of maximal fixed-cost (MFC) codes, with codeword costs defined in a right-cancellative semigroup, are rectangular, and hence admit biproper trellis presentations. Among all possible trellis presentations for a rectangular code, biproper trellises minimize a wide variety of complexity measures, including the Viterbi decoding complexity. Examples of MFC codes include such “nonlinear” codes as permutation codes and shells of constant norm in the integer lattice, as well as linear codes over a finite field. The intersection of two rectangular codes is another rectangular code; therefore, “nonlinear” codes such as lattice shells or words of constant weight in a linear code have biproper trellis presentations. We show that every rectangular code can be interpreted as an MFC code. Applications of these results include error detection, trellis-based indexing, and soft-decision decoding
Keywords :
Viterbi decoding; block codes; error detection codes; linear codes; Viterbi decoding complexity; biproper trellis presentations; block code; codeword costs; complexity measures; constant norm shells; constant weight words; error detection; finite field; integer lattice; linear codes; maximal fixed cost codes; nonlinear codes; permutation codes; rectangular biproper trellises; rectangular codes intersection; right cancellative semigroup; soft decision decoding; trellis based indexing; trellis structure; Block codes; Convolutional codes; Costs; Decoding; Galois fields; Indexing; Information theory; Lattices; Linear code; Viterbi algorithm;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.556678
Filename :
556678
Link To Document :
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