By Topic

Geometrical and performance analysis of GMD and Chase decoding algorithms

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
E. Fishler ; Dept. of Electr. Eng. Syst., Tel Aviv Univ., Israel ; O. Amrani ; Y. Be'ery

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

Published in:

IEEE Transactions on Information Theory  (Volume:45 ,  Issue: 5 )