  In this paper, we establish a new inequality tying together the effective
length and the maximum correlation between the outputs of an arbitrary pair of
Boolean functions which operate on two sequences of correlated random
variables. We derive a new upper-bound on the correlation between the outputs
of these functions. The upper-bound is useful in various disciplines which deal
with common-information. We build upon Witsenhausen's bound on
maximum-correlation. The previous upper-bound did not take the effective length
of the Boolean functions into account.
