论文标题
MMI解码器对于典型的随机代码和消除代码渐近最佳
The MMI Decoder is Asymptotically Optimal for the Typical Random Code and for the Expurgated Code
论文作者
论文摘要
我们提供了两个有关最大互信息（MMI）解码器的最佳性的结果。首先，我们证明在最佳最大似然（ML）解码器和MMI解码器下的典型随机代码的误差指数相等。作为此结果的推论，我们还表明，ML和MMI解码器下消除的代码的误差指数相等。这些结果加强了由于Csiszár和Körner引起的众所周知的结果，因此，这些解码器获得了相等的随机编码误差指数，因为典型的随机代码的误差指数和消除的代码的误差指数严格高于至少在低编码速率下的随机编码误差指数。尽管在随机编码误差指数方面，MMI解码器的通用最优性可以通过对通道噪声的期望和对集合的期望进行通勤，而在典型和消除的指数方面可以证明这一点，但不再需要进行这种换向。因此，MMI解码器的普遍最优性的证明必须完全不同，事实证明这是高度不平凡的。
We provide two results concerning the optimality of the maximum mutual information (MMI) decoder. First, we prove that the error exponents of the typical random codes under the optimal maximum likelihood (ML) decoder and the MMI decoder are equal. As a corollary to this result, we also show that the error exponents of the expurgated codes under the ML and the MMI decoders are equal. These results strengthen the well known result due to Csiszár and Körner, according to which, these decoders achieve equal random coding error exponents, since the error exponents of the typical random code and the expurgated code are strictly higher than the random coding error exponents, at least at low coding rates. While the universal optimality of the MMI decoder, in the random-coding error exponent sense, is easily proven by commuting the expectation over the channel noise and the expectation over the ensemble, when it comes to typical and expurgated exponents, this commutation can no longer be carried out. Therefore, the proof of the universal optimality of the MMI decoder must be completely different and it turns out to be highly non-trivial.
