Zero-rate feedback can achieve the empirical capacity

Authors:
Krishnan Eswaran;Anand D. Sarwate;Anant Sahai;Michael C. Gastpar
Affiliations:
Google, Inc., Mountain View, CA and Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA;Information Theory and Applications Center, University of California, San Diego, La Jolla, CA and Department of Electrical Engineering and Computer Sciences, University of California, Berkeley;Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA;Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 17
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Abstract

The utility of limited feedback for coding over an individual sequence of discrete memoryless channels is investigated. This study complements recent results showing how limited or noisy feedback can boost the reliability of communication. A strategy with fixed input distribution P is given that asymptotically achieves rates arbitrarily close to the mutual information induced by P and the state-averaged channel. When the capacity-achieving input distribution is the same over all channel states, this achieves rates at least as large as the capacity of the state-averaged channel, sometimes called the empirical capacity.