Abstract
A number of problems are considered relevant to understanding the performance of optical-fiber communication systems that use pulse transmission. The methods used are typically exact solutions or bounds, and we concentrate on simple examples that aid our understanding. Some of our work makes contact with previous studies, particularly by Personick and Hubbard. The major results are: (i) Presentation of an integral equation for the output density for single-pulse detection with arbitrary avalanche gain (ii) Exact solution for the probability distribution for gains in physical avalanche diodes (iii) Bounds on performance when intersymbol interference is present (but no avalanche gain) which suggest that an optimum-bit detector can perform, under practical conditions, only two or three dB better than a simple integrate-and-dump filter, yielding results still many dB from the quantum limit. Thus, in particular, little performance gain is to be expected from equalization techniques.
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