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In a previous paper the structure of the optimal multi-diversity receiver for a fading, noisy diversity channel was determined under the assumption that the memory of the receiver does not extend beyond the time interval of the signal currently being received. The probability of error for such a receiver is determined herein under the following assumptions: the channel is binary and symmetric; the (Gaussian) noises in the various diversity links are white and independent; and the fadings in the various links are Rayleigh distributed and slow, but not necessarily independent. Detailed curves of this probability of error are given for various orders of diversity in the two cases of independent fadings and "exponentially correlated" fadings. Since the optimal receiver may be difficult to implement, a more easily implemented "square-law combining" receiver is also considered, and it is shown that for all practical purposes this simpler receiver behaves optimally. Finally the effect of the assumption that the receiver has a short memory is considered by comparing its performance with that of a longer-memory receiver studied by Pierce and Stein.