Capacity of finite alphabet channels with noisy feedback

In, the authors characterized the noisy feed- back capacity in terms of the residual directed information. However, this characterization may not be computable due to the probabilistic limit and code-functions in the formula. In this paper, we first explore a necessary and sufficient condition for the strong converse property of channels with noisy feedback. Then, for channels satisfying the strong converse property, we characterize the capacity in terms of the causal conditional directed information, which is a simplified version of the characterization in [1], This new characterization may be computable by applying some technical algorithms (e.g. dynamic programming) which are used in computing the well- known directed information.