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Generalized minimum distance decoding in Euclidean space: Performance analysis
Written by:
Dakshi Agrawal
and
Alexander Vardy.
Citation:
Proceedings of IEEE International Symposium on Information Theory,
1997, page 306, June 1997.
Copyright © (1997) by IEEE. Permission to make digital or
hard copies of part or all of this work for personal or classroom use
is granted without fee provided that copies are not made or distributed
for profit. To copy otherwise, to republish, to post on servers, or to
redistribute to lists, requires prior specific permission and/or a fee.
Abstract:
Detailed geometric analysis of decoding regions for GMD decoding is
presented. We show that GMD decoding regions are non-convex in
essentially all cases of interest. We also prove that these regions
are always bounded by hyperplane segments. For d-erasure GMD decoding,
we establish the presence of a large number of bounding hyperplanes at
distance less than (d+1). These results invalidate the estimates of
performance derived from the union bound in the case of (multistage)
GMD decoding. Alternative probabilistic estimates of, and upper bounds
upon, the performance of GMD decoding are developed. Simulation
results, for both low-dimensional and high-dimensional sphere
packings, are in remarkably close agreement with our probabilistic
approximations.
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