Relationship between the saddlepoint approximation and the modified Chernoff bound [optical communication]

A comparison is made of two methods for the computation of the probability that the sum of a Gaussian and a nonGaussian random variable exceeds a certain threshold value. The two methods, the saddlepoint approximation (SAP) and the modified Chernoff bound, are closely related to one another. For the computation of error probabilities in digital optical communications where both methods can be applied, the modified Chernoff bound is found to lie close above the saddlepoint approximation for all cases of practical interest. The ratio of signal-dependent to additive noise has been established as the parameter dominating the bound tightness. Since the SAP has been reported to be extremely precise, this result indicates that the more versatile upper bound can be used with confidence both for performance evaluation and for optimization of optical communication systems