Statistics of a General Class of Avalanche Detectors With Applications to Optical Communication

In a previous paper 1 results on the statistics of two particular avalanche detectors with applications to optical communication were 3075 3076 T H E BELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1971 presented. It was required either t h a t only one carrier suffer collision ionizations in the high-field region (unilateral gain) or t h a t both carriers suffer collision ionizations with equal probability per unit length in t h e high-field region. T h e present work allows for more general unequal ionization probabilities per unit length with the requirement only t h a t the ratio of the two quantities be constant throughout the high-field region. T h e moment-generating function of the random gain is obtained as a function of this ratio and the average gain. T h e results are consistent with unpublished conjectures of R. J. M c l n t y r e . 2 The momentgenerating functions are used to obtain Chernov bounds on t h e error rates of digital optical receivers employing avalanche detectors and using either coherent or incoherent light. Results on avalanche statistics are summarized in Section V. Numerical results on the Chernov bounds are given in Section VI (6.5) and Section V I I .