The Information Flow and Capacity of Channels with Noisy Feedback
Abstract
In this paper, we consider some long-standing problems in communication systems with access to noisy feedback. We introduce a new notion, the residual directed information, to capture the effective information flow (i.e. mutual information between the message and the channel outputs) in the forward channel. In light of this new concept, we investigate discrete memoryless channels (DMC) with noisy feedback and prove that the noisy feedback capacity is not achievable by using any typical closed-loop encoder (non-trivially taking feedback information to produce channel inputs). We then show that the residual directed information can be used to characterize the capacity of channels with noisy feedback. Finally, we provide computable bounds on the noisy feedback capacity, which are characterized by the causal conditional directed information.
Keywords
Cite
@article{arxiv.1108.2815,
title = {The Information Flow and Capacity of Channels with Noisy Feedback},
author = {Chong Li and Nicola Elia},
journal= {arXiv preprint arXiv:1108.2815},
year = {2015}
}
Comments
Updated due to an error in Theorem 6 in the previous version. The definition of typical closed-loop encoder is also refined in the current version