An asymptotic approximation of the ISI channel capacity

An asymptotic method to calculate the information rate of an ISI channel is presented in this work. The method is based on an integral representation of the mutual information, which is then calculated by using a saddlepoint approximation along with an asymptotic expansion stemming from the Hubbard-Stratonovich transform. This asymptotic result is evaluated repeatedly to generate a large number of samples required for the Monte-Carlo approximation of the final result. The proposed method has the advantage of being manageable even when the channel memory becomes very large since the complexity grows with polynomial order in the memory length.