|
 |
Generalized minimum distance decoding in Euclidean space: Performance analysis
Written by:
Dakshi Agrawal
and
Alexander Vardy.
Citation:
IEEE Transaction on Information Theory, 46:60-83, January 2000.
Copyright © (2000) 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:
We present a detailed analysis of generalized minimum distance
(GMD) decoding algorithms for Euclidean space codes. In particular,
we completely characterize GMD decoding regions in terms of receiver
front-end properties. This characterization is used to show that GMD
decoding regions have intricate geometry. We prove that although these
decoding regions are polyhedral, they are essentially always nonconvex. We
furthermore show that conventional performance parameters, such as
error-correction radius and effective error coefficient, do not capture
the essential geometric features of a GMD decoding region, and thus
do not provide a meaningful measure of performance. As an alternative,
probabilistic estimates of, and upper bounds upon, the performance of
GMD decoding are developed. Furthermore, extensive simulation results,
for both low-dimensional and high-dimensional sphere-packings, are
presented. These simulations show that multilevel codes in conjunction
with multistage GMD decoding provide significant coding gains at a very
low complexity. Simulated performance, in both cases, is in remarkably
close agreement with our probabilistic approximations.
|
|
United States
