Representing group codes as permutation codes
نویسندگان
چکیده
منابع مشابه
Representing group codes as permutation codes
Given an abstract group G, an N dimensional orthogonal matrix representation G of G, and an “initial vector” x ∈ R , 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 ...
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There are many analogies between subsets and permutations of a set, and in particular between sets of subsets and sets of permutations. The theories share many features, but there are also big differences. This paper is a survey of old and new results about sets (and groups) of permutations, concentrating on the analogies and on the relations to coding theory. Several open problems are describe...
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A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and space time codes has been used to translate them into the final space time codes. Simulations demonstrate that the performance increases with the block lengths,...
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Let X be a finite set of ‘points’ and d be a metric on X which takes integral values. For any v ∈ X and t ≥ 0, we refer to the set Bt(v) = {u ∈ X : d(u, v) ≤ t} as the ball of radius t centered at v, and we denote the minimum (maximum, respectively) volume of a ball with radius t in X as V min t (V max t ). Let C ⊆ X, C 6= ∅ be a code, i.e. a set of points, which we will refer to as codewords. ...
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Permutation codes are vector quantizers whose codewords are related by permutations and, in one variant, sign changes. Asymptotically, as the vector dimension grows, optimal Variant I permutation code design is identical to optimal entropy-constrained scalar quantizer (ECSQ) design. However, contradicting intuition and previously published assertions, there are finite block length permutation c...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 1999
ISSN: 0018-9448
DOI: 10.1109/18.782174