Bounds on the symmetric binary cutoff rate for dispersive Gaussian channels

Bounds on the symmetric binary cutoff rate for a pulse amplitude modulated (PAM) signaling over dispersive Gaussian channels are evaluated and discussed. These easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary (two-level) PAM schemes, operating through a prefiltered additive white Gaussian channel, the memory of which is long enough to make the exact evaluation of the cutoff rate formidable. The core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory, regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix, commonly applied in large deviation problems. These bounds are calculated for some examples and their respective tightness is considered. Further potential applications of the proposed bounding technique are pointed out