On the Subexponential Decay of Detection Error Probabilities in Long Tandems

  • Authors:

  • W. P. Tay;J. N. Tsitsiklis;M. Z. Win

  • Affiliations:

  • Lab. for Inf. & Decision Syst., MIT, Cambridge, MA;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2008

Quantified Score

Hi-index 754.84

Visualization

Abstract

We consider the problem of Bayesian decentralized binary hypothesis testing in a network of sensors arranged in a tandem. We show that the rate of error probability decay is always subexponential, establishing the validity of a long-standing conjecture. Under the additional assumption of bounded Kullback-Leibler (KL) divergences, we show that for all d > 1/2, the error probability is Omega(e - c nd), where c is a positive constant. Furthermore, the bound Omega(e - c (logn)d) , for all d > 1, holds under an additional mild condition on the distributions. This latter bound is shown to be tight.