多假设检验的广义Poor-Verdu误差界和信道可靠性函数
A Generalized Poor-Verdu Error Bound for Multihypothesis Testing and the Channel Reliability Function
摘要：
给出了多假设检验的最小错误概率的一个下界。在倾斜参数θ大于或等于1的情况下，该界限用倾斜后验假设分布的累积分布函数表示，推广了Poor和Verdu（1995）的早期界限。一个充分的条件下，新的界限（减去乘法因子）提供了确切的错误概率在极限θ走向无穷大。还提供了说明新的界限的例子。这个广义的Poor-Verdu界的信道可靠性函数的应用程序进行，从而在两个信息谱上界。据观察，对于一类信道，包括有限输入无记忆高斯信道，其中一个界限是紧的，并给出了一个多字母的渐近表达式的可靠性函数，虽然它的确定或计算在单字母的形式仍然是一个开放的挑战性问题。最后给出了关于另一界的数值例子。
英文摘要：
A lower bound on the minimum error probability for multihypothesis testing is established. The bound, which is expressed in terms of the cumulative distribution function of the tilted posterior hypothesis distribution given the observation with tilting parameter theta larger than or equal to 1, generalizes an earlier bound due the Poor and Verdu (1995). A sufficient condition is established under which the new bound (minus a multiplicative factor) provides the exact error probability in the limit of theta going to infinity. Examples illustrating the new bound are also provided. The application of this generalized Poor-Verdu bound to the channel reliability function is next carried out, resulting in two information-spectrum upper bounds. It is observed that, for a class of channels including the finite-input memoryless Gaussian channel, one of the bounds is tight and gives a multi-letter asymptotic expression for the reliability function, albeit its determination or calculation in single-letter form remains an open challenging problem. Numerical examples regarding the other bound are finally presented.
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