  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.
