Error Exponents for Neyman-Pearson Detection of Markov Chains in Noise

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 behaviour of the error exponent as the transition parameters of the Markov chain and the signal-to-noise ratio are varied. Comparisons between the high SNR asymptotics for the time-invariant and fading situations will also be made.

[1]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[2]  Venugopal V. Veeravalli,et al.  Decentralized detection in sensor networks , 2003, IEEE Trans. Signal Process..

[3]  Stéphane Boucheron,et al.  Optimal error exponents in hidden Markov models order estimation , 2003, IEEE Trans. Inf. Theory.

[4]  Shlomo Shamai,et al.  Information theoretic considerations for cellular mobile radio , 1994 .

[5]  Gerald R. Benitz,et al.  Large deviation rate calculations for nonlinear detectors in Gaussian noise , 1990, IEEE Trans. Inf. Theory.

[6]  LOUIS L. SCHARF,et al.  Likelihood ratios for sequential hypothesis testing on Markov sequences , 1977, IEEE Trans. Inf. Theory.

[7]  W. Hackbusch.  Integral Equations: Theory and Numerical Treatment , 1995 .

[8]  H. Vincent Poor,et al.  Neyman-Pearson Detection of Gauss-Markov Signals in Noise: Closed-Form Error Exponent and Properties , 2005, ISIT.

[9]  Neri Merhav,et al.  Universal classification for hidden Markov models , 1991, IEEE Trans. Inf. Theory.

[10]  Ofer Zeitouni,et al.  Asymptotic filtering for finite state Markov chains , 1996 .

[11]  Neri Merhav,et al.  Hidden Markov processes , 2002, IEEE Trans. Inf. Theory.

[12]  Randall K. Bahr.  Asymptotic analysis of error probabilities for the nonzero-mean Gaussian hypothesis testing problem , 1990, IEEE Trans. Inf. Theory.

[13]  Pramod K. Varshney,et al.  Channel aware decision fusion in wireless sensor networks , 2004, IEEE Transactions on Signal Processing.

[14]  M. A. Wolfe.  A first course in numerical analysis , 1972 .

[15]  L. Mevel,et al.  Asymptotic properties of the MLE in hidden Markov models , 1997, 1997 European Control Conference (ECC).

[16]  Biao Chen,et al.  Fusion of censored decisions in wireless sensor networks , 2005, IEEE Transactions on Wireless Communications.

[17]  Laurent Mevel,et al.  Exponential Forgetting and Geometric Ergodicity in Hidden Markov Models , 2000, Math. Control. Signals Syst..

[18]  John B. Thomas,et al.  Detectors for discrete-time signals in non-Gaussian noise , 1972, IEEE Trans. Inf. Theory.

[19]  Pramod K. Varshney,et al.  Fusion of decisions transmitted over Rayleigh fading channels in wireless sensor networks , 2006, IEEE Transactions on Signal Processing.

[20]  James A. Bucklew,et al.  Optimal sampling schemes for the Gaussian hypothesis testing problem , 1990, IEEE Trans. Acoust. Speech Signal Process..

[21]  F. Olver.  Asymptotics and Special Functions , 1974 .

[22]  Jamie S. Evans,et al.  Probability of Error Analysis for Hidden Markov Model Filtering With Random Packet Loss , 2007, IEEE Transactions on Signal Processing.

[23]  Brian D. O. Anderson,et al.  On state-estimation of a two-state hidden Markov model with quantization , 2001, IEEE Trans. Signal Process..

[24]  H. Vincent Poor,et al.  Neyman-pearson detection of gauss-Markov signals in noise: closed-form error exponentand properties , 2005, IEEE Transactions on Information Theory.

[25]  Lang Tong,et al.  Asymptotic Detection Performance of Type-Based Multiple Access Over Multiaccess Fading Channels , 2007, IEEE Transactions on Signal Processing.

[26]  K. Atkinson.  The Numerical Solution of Integral Equations of the Second Kind , 1997 .

[27]  Prakash Narayan,et al.  Order estimation and sequential universal data compression of a hidden Markov source by the method of mixtures , 1994, IEEE Trans. Inf. Theory.