  The utility of limited feedback for coding over an individual sequence of
DMCs 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.
