A lower bound on the probability of error in multihypothesis testing

@article{Poor1995ALB,
  title={A lower bound on the probability of error in multihypothesis testing},
  author={H. Vincent Poor and Sergio Verd{\'u}},
  journal={IEEE Trans. Information Theory},
  year={1995},
  volume={41},
  pages={1992-1994}
}
Consider two random variables X and Y, where X is finitely (or conntably-infinitely) valued, and where Y is arbitrary. Let E denote the minimum probability of error incurred in estimating X from Y. It is shown that where r(X(Y) denotes the posterior probability of X given Y. This bound finds information-theoretic applications in the proof of converse channel coding theorems. It generalizes and strengthens previous lower bounds due to Shannon, and to Verdu and Han. 
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