Dual Capacity Upper Bounds for Noisy Runlength Constrained Channels

Binary-input memoryless channels with a runlength constrained input are considered. Upper bounds to the capacity of such noisy runlength constrained channels are derived using the dual capacity method with Markov test distributions satisfying the Karush-Kuhn-Tucker (KKT) conditions for the capacity-achieving output distribution. Simplified algebraic characterizations of the bounds are presented for the binary erasure channel (BEC) and the binary symmetric channel (BSC). These upper bounds are very close to achievable rates, and improve upon previously known feedback-based bounds for a large range of channel parameters. For the binary-input Additive White Gaussian Noise (AWGN) channel, the upper bound is simplified to a small-scale numerical optimization problem. These results provide some of the simplest upper bounds for an open capacity problem that has theoretical and practical relevance.