Comments on "Effects of Band Limiting on the Detection of Binary Signals"

The analysis presented in a correspondence by Park1 contains a fundamental error in both the integrate-and-dump and the band-limit/sample detectors. In essence, the effect of intersymbol interference is disregarded on the basis that its average effect is not of concern here. It is the average probability of bit error that is important, where the average is taken over the error probabilities resulting from all possible combinations of a string of 2N pulses, N pulses on each side of the pulse under detection, regardless of how large N is. That is to say, if Pe is the average bit-error probability, Pei is the bit-error probability for a specific bit pattem, n is the noise, and Si is the specific pattern, then Pe = Pei(niSi) where x is the expected value of x. But this is definitely not equal to Pe(niSi), as is claimed by Park.