Random coding bound for the second moment of multidimensional lattices

Authors:
B. D. Kudryashov;K. V. Yurkov
Affiliations:
St. Petersburg State University of Aerospace Instrumentation, Russia;St. Petersburg State University of Aerospace Instrumentation, Russia
Venue:
Problems of Information Transmission
Year:
2007

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Sphere-packings, lattices, and groups

Sphere-packings, lattices, and groups
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IEEE Transactions on Information Theory
Lattices which are good for (almost) everything

IEEE Transactions on Information Theory

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Abstract

Efficiency of lattice quantization depends on the parameter of a lattice called the normalized second moment of the Voronoi polyhedron. We apply random-coding methods to study lattices generated by q-ary linear codes. We prove that in this class there are lattices with the normalized second moment close to the theoretically attainable limit.