Bounds on Error-Pattern Probabilities for Digital Communications Systems

An upper bound is obtained on the probability that a specified pattern of errors, caused by a combination of intersymbol interference and additive Gaussian noise, occurs in an amplitudemodulated digital data transmission system. The bound, which is a generalization of Saltzberg\´s upper bound for the probability of a single error, behaves as an exponential function of the signal-to-noise ratio and the overall channel impulse response. The exponent of the bound for a pair of errors is calculated for two "typical" channels and in each case is fairly close to twice the corresponding Saltzberg exponent for a single error.