Geometrical and performance analysis of GMD and Chase decodingalgorithms
Fishler, E.
Amrani, O.
Be'ery, Y.
Dept. of Electr. Eng. Syst., Tel Aviv Univ.;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Jul 1999
Volume: 45,
Issue: 5
On page(s): 1406-1422
ISSN: 0018-9448
References Cited: 12
CODEN: IETTAW
INSPEC Accession Number: 6297665
Digital Object Identifier: 10.1109/18.771143
Current Version Published: 2002-08-06
Abstract
The overall number of nearest neighbors in bounded distance
decoding (BDD) algorithms is given by N0,eff=N0+N
BDD. Where NBDD denotes the number of additional,
non-codeword, neighbors that are generated during the (suboptimal)
decoding process. We identify and enumerate the nearest neighbors
associated with the original generalized minimum distance (GMD) and
Chase (1972) decoding algorithms. After careful examination of the
decision regions of these algorithms, we derive an approximated
probability ratio between the error contribution of a noncodeword
neighbor (one of NBDD points) and a codeword nearest
neighbor. For Chase algorithm 1 it is shown that the contribution to the
error probability of a noncodeword nearest neighbor is a factor of
2d-1 less than the contribution of a codeword, while for
Chase algorithm 2 the factor is 2[d/2]-1, d being the minimum
Hamming distance of the code. For Chase algorithm 3 and GMD, a recursive
procedure for calculating this ratio, which turns out to be
nonexponential in d, is presented. This procedure can also be used for
specifically identifying the error patterns associated with Chase
algorithm 3 and GMD. Utilizing the probability ratio, we propose an
improved approximated upper bound on the probability of error based on
the union bound approach. Simulation results are given to demonstrate
and support the analytical derivations
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