Dual Capacity Upper Bounds for Binary-input ISI and Constrained BIBO Channels

The capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases. In this work, we consider two such channels - (1) binary-input Gaussian channels with Inter-Symbol Interference (ISI), and (2) a general Binary-Input Binary-Output (BIBO) channel with the runlength constraint of no repeated 1s at the input. The dual method is used to obtain tight upper bounds for both channels. For the ISI channel, the bound is expressed as an optimization problem that is solved numerically. For the BIBO channel, analytic expressions for upper bounds are obtained. In both cases, the derived new bounds are shown to improve upon previously known bounds.