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Dynamical systems, curves and coding for continuous alphabet sources | IEEE Conference Publication | IEEE Xplore

Dynamical systems, curves and coding for continuous alphabet sources


Abstract:

Good codes for transmitting a continuous-alphabet source over an AWGN channel can be constructed using simple dynamical systems. The trajectories of the dynamical systems...Show More

Abstract:

Good codes for transmitting a continuous-alphabet source over an AWGN channel can be constructed using simple dynamical systems. The trajectories of the dynamical systems that we consider are curves in /spl Ropf//sup N/, and we use these curves as signal sets for a modulation system. In this paper we consider the problem of choosing the parameters of the dynamical system such that the length of its trajectory is maximized subject to a constraint on the minimum distance between its "folds". We provide some general results on the construction of such curves and show how to select the parameters optimally in the case N=6. This is done by reducing the problem to one of choosing a vector (1, a, b) in /spl Zopf//sup 3/ for which a high packing density is obtained for the lattice /spl Lambda//sub p/ obtained by projecting /spl Zopf//sup 3/ into the plane orthogonal to (1, a, b). Two approaches are used to prove the central result of the paper.
Date of Conference: 25-25 October 2002
Date Added to IEEE Xplore: 06 January 2003
Print ISBN:0-7803-7629-3
Conference Location: Bangalore, India

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