  The error probability of block codes sent under a non-uniform input
distribution over the memoryless binary symmetric channel (BSC) and decoded via
the maximum a posteriori (MAP) decoding rule is investigated. It is proved that
the ratio of the probability of MAP decoder ties to the probability of error
when no MAP decoding ties occur grows at most linearly in blocklength, thus
showing that decoder ties do not affect the code's error exponent. This result
generalizes a similar recent result shown for the case of block codes
transmitted over the BSC under a uniform input distribution.
