  We derive a tight lower bound on equivocation (conditional entropy), or
equivalently a tight upper bound on mutual information between a signal
variable and channel outputs. The bound is in terms of the joint distribution
of the signals and maximum a posteriori decodes (most probable signals given
channel output). As part of our derivation, we describe the key properties of
the distribution of signals, channel outputs and decodes, that minimizes
equivocation and maximizes mutual information. This work addresses a problem in
data analysis, where mutual information between signals and decodes is
sometimes used to lower bound the mutual information between signals and
channel outputs. Our result provides a corresponding upper bound.
