This paper analyzes the effect of adding a pre-decoder processing function to a receiver that contains a fixed mismatched decoder at the output of a discrete memoryless channel. We study properties of the symbolwise pre-processing function and show that it is a simple yet very powerful tool which enables to obtain reliable transmission at a positive rate for almost every metric. We present lower and upper bounds on the capacity of a channel with mismatched decoding and symbolwise(scalar-to-scalar) pre-processing, and show that the optimal pre-processing function for random coding is deterministic. We also characterize achievable error exponents. Finally, we prove that a separation principle holds for vectorwise(vector-to-vector) pre-processing functions and further, that deterministic functions maximize the reliably transmitted rate in this case.

翻译：本文分析了在离散无记忆信道输出端包含固定不匹配解码器的接收机中添加预解码处理函数的效果。我们研究了符号级预处理函数的性质，并证明它是一种简单而强大的工具，能够在几乎所有度量下实现正速率的可靠传输。我们给出了带有不匹配解码和符号级（标量到标量）预处理的信道容量的上下界，并证明了随机编码的最优预处理函数是确定性的。我们还刻画了可达的错误指数。最后，我们证明了对于矢量级（矢量到矢量）预处理函数存在分离定理，并且在此情况下确定性函数能够最大化可靠传输速率。