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A fast encoding method for lattice codes and quantizers
John H. Conway,Neil J. A. Sloane +1 more
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A solution to the inverse problem for the same lattices, namely, given an integer k, to find the kth code vector, and to the closely related problem of finding the index k of a given code vector.Abstract:
In an earlier paper the authors described a very fast method which, for the root lattices A_{n}, D_{n}, E_{n} , their duals and certain other lattices, finds the closest lattice point to an arbitrary point of the underlying space. If the lattices are used as codes for a Gaussian channel, the algorithm provides a fast decoding procedure, or if they are used as vector quantizers the algorithm performs the analog-to-digital conversion efficiently. The present paper offers a solution to the inverse problem for the same lattices (the encoding problem for channel codes or the digital-to-analog part of quantizing), namely, given an integer k , to find the kth code vector, and to the closely related problem of finding the index k of a given code vector.read more
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References
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Journal ArticleDOI
Fast quantizing and decoding and algorithms for lattice quantizers and codes
John H. Conway,Neil J. A. Sloane +1 more
TL;DR: A very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data.
Journal ArticleDOI
Optimization of Two-Dimensional Signal Constellations in the Presence of Gaussian Noise
TL;DR: In this paper an asymptotic (large signal-to-noise ratio) expression is derived for the error rate and it is rigorously proved in the Appendix that the optimum constellations tend toward an equilateral structure, and become uniformly distributed in a circle.
Journal ArticleDOI
Voronoi regions of lattices, second moments of polytopes, and quantization
John H. Conway,Neil J. A. Sloane +1 more
TL;DR: The answers to the squared distance questions and a description of the Voronoi (or nearest neighbor) regions of these lattices have applications to quantization and to the design of signals for the Gaussian channel.