The A Posteriori Theory of Reception

In the a posteriori theory of reception, a posteriori probabilities and probability densities provide a complete description of the results of the receiving process. An ideal receiver, by definition, calculates and presents the a posteriori distribution of a desired quantity or quantities to an observer. Owing to the dependence of the a posteriori distribution on a priori information, which may not always be available, the concept of a sufficient receiver was introduced. A sufficient receiver calculates and presents to the observer a sufficient statistic; this statistic contains the essential information in the received waveform and permits the a posteriori distribution to be computed when the a priori statistics are known. When reception occurs in additive Gaussian noise, the a posteriori theory leads to sufficient receivers that employ matched filters. However, the theory has been found to be useful in many situations where the optimum receiver structure is not obvious.