Dual capacity upper bounds for noisy runlength constrained channels

Binary-input memoryless channels with a runlength constrained input, where an input of one is necessarily followed by a fixed number of zeros, are considered. Computable upper bounds to the capacity of such noisy runlength constrained channels are derived using the dual capacity method. Simplified versions of the bounds are presented for the binary erasure channel (BEC) and the binary symmetric channel (BSC). These bounds improve upon previously known computable bounds and show that feedback strictly improves the capacity of the runlength constrained BEC and BSC for all parameters.