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The generalized Poor-Verdu error lower bound established in [1] formultihypothesis testing is studied in the classical channel coding context. Itis proved that for any sequence of block codes sent over the memoryless binarysymmetric channel (BSC), the minimum probability of error (under maximumlikelihood decoding) has a relative deviation from the generalized bound thatgrows at most linearly in blocklength. This result directly implies that forarbitrary codes used over the BSC, decoder ties can only affect thesubexponential behavior of the minimum probability of error.

Decoder Ties Do Not Affect the Error Exponent of the Memoryless Binary Symmetric Channel