Young-Han Kim

*IEEE Transactions on Information Theory,*vol. 54, no. 4, pp. 1488–1499, April 2008.Preliminary results appeared in

*Proceedings of IEEE International Symposium on Information Theory,*pp. 1856–1860, Nice, France, June 2007.

A coding theorem is proved for a class of stationary channels with feedback in which the output is the function of the current and past symbols from the channel input and the stationary ergodic channel noise . In particular, it is shown that the feedback capacity is equal to

where denotes the
Massey directed information from the channel input to the output, and
the supremum is taken over all causally conditioned distributions
. The main
ideas of the proof are a classical application of the Shannon strategy
for coding with side information and a new elementary coding technique
for the given channel model *without feedback*, which is in a
sense dual to Gallager's lossy coding of stationary ergodic sources.
A similar approach gives a simple alternative proof of coding theorems
for finite state channels by Yang–Kavcic–Tatikonda, Chen–Berger,
and Permuter–Weissman–Goldsmith.