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

On Decoder Ties for the Binary Symmetric Channel with Arbitrarily Distributed Input