Asymptotic performance analysis for minimum-hamming-distance fusion

Abstract

Distributed (M-ary) detection and fault-tolerance have been considered as two fundamental functions in the context of large-scale sensor networks. Distributed multiclass classification fusion using error correcting codes (DCFECC) has been proposed to provide good fault-tolerance capability in wireless sensor networks. Minimum Hamming distance fusion is an essential part of the DCFECC approach. In this paper, we study the asymptotic performance of minimum Hamming distance fusion for both fault-free and faulty situations when the number of sensors tends to infinity. We conclude that the error probability vanishes asymptotically as long as the minimum Hamming distance d(min) of the DCFECC code approaches infinity, and the probabilities of correct local classification for all hypotheses are greater than one half. In case d(min)/2, normalized by the number of sensors, can be made larger than the largest local classification error, an explicit expression for the error exponent of the DCFECC system in terms of the Kullback-Leibler divergence can be established. A converse where the DCFECC decoding error is bounded away from zero is also addressed.