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60 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 1, JANUARY 2000 Generalized Minimum Distance Decoding in
 

Summary: 60 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 1, JANUARY 2000
Generalized Minimum Distance Decoding in
Euclidean Space: Performance Analysis
Dakshi Agrawal, Member, IEEE, and Alexander Vardy, Fellow, IEEE
Abstract--We present a detailed analysis of generalized min-
imum distance (GMD) decoding algorithms for Euclidean-space
codes. In particular, we completely characterize GMD decoding
regions in terms of receiver front-end properties. This char-
acterization is used to show that GMD decoding regions have
intricate geometry. We prove that although these decoding re-
gions 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 de-
coding 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

  

Source: Agrawal, Rakesh - IBM T.J. Watson Research Center

 

Collections: Computer Technologies and Information Sciences