  This paper investigates the error probability of a stochastic decision and
the way in which it differs from the error probability of an optimal decision,
i.e., the maximum a posteriori decision. This paper calls attention to the fact
that the error probability of a stochastic decision with the a posteriori
distribution is at most twice the error probability of the maximum a posteriori
decision. It is shown that, by generating an independent identically
distributed random sequence subject to the a posteriori distribution and making
a decision that maximizes the a posteriori probability over the sequence, the
error probability approaches exponentially the error probability of the maximum
a posteriori decision as the sequence length increases. Using these ideas as a
basis, we can construct stochastic decoders for source/channel codes.
