Correspondence Error Exponents for Neyman–Pearson Detection of Markov Chains in Noise

Abstract—A numerical method for computing the error exponent for Neyman–Pearson detection of two-state Markov chains in noise is presented, for both time-invariant and fading channels. We give numerical studies showing the behavior of the error exponent as the transition parameters of the Markov chain and the signal-to-noise ratio (SNR) are varied. Comparisons between the high-SNR asymptotics in Gaussian noise for the time-invariant and fading situations will also be made. Index Terms—Error exponent, fading channel, hidden Markov model (HMM), Neyman–Pearson detection