Dual Capacity Upper Bounds for Binary-Input Single-Tap ISI Channels

The capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases. In this paper, we consider single-tap binary-input Gaussian channels with inter-symbol interference (ISI). The dual capacity method is used to obtain upper bounds using Markov test distributions. The bound, expressed as a single-letter optimization problem, is solved numerically. For higher memory, the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem. Bounds were obtained for the important case of the dicode channel, and these are better than the previously known upper bounds and are close to achievable rates over a wide range of SNRs.