DocumentCode :
1538118
Title :
Representing group codes as permutation codes
Author :
Biglieri, Ezio ; Karlof, John K. ; Viterbo, Emanuele
Author_Institution :
Dipt. di Elettronica, Politecnico di Milano, Italy
Volume :
45
Issue :
6
fYear :
1999
fDate :
9/1/1999 12:00:00 AM
Firstpage :
2204
Lastpage :
2207
Abstract :
Given an abstract group 𝒢, an N-dimensional orthogonal matrix representation G of 𝒢, and an “initial vector” x∈R N, Slepian defined the group code generated by the representation G to be the set of vectors Gx. If G is a group of permutation matrices, the set Gx is called a “permutation code”. For permutation codes a “stack algorithm” decoder exists that, in the presence of low noise, produces the maximum-likelihood estimate of the transmitted vector by using far fewer computations than the standard decoder. In this correspondence, a new concept of equivalence of codes of different dimensions is presented which is weaker than the usual definition of equivalent codes. We show that every group code is (weakly) equivalent to a permutation code and we discuss the minimal degree of this permutation code
Keywords :
AWGN channels; group codes; matrix algebra; maximum likelihood decoding; N-dimensional orthogonal matrix representation; abstract group; equivalence of codes; equivalent codes; group codes; maximum-likelihood estimation; minimal degree; permutation codes; permutation matrices; stack algorithm decoder; transmitted vector; Application software; Computer applications; Costs; Decoding; Digital arithmetic; Error correction; Error correction codes; Machine tools; Modulation coding; South America;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.782174
Filename :
782174
Link To Document :
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