A Coding Theorem for a Class of Stationary Channels With Feedback
Young-Han Kim
Dept. of Electr. & Comput. Eng., Univ. of California, La Jolla, CA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: April 2008
Volume: 54,
Issue: 4
On page(s): 1488-1499
ISSN: 0018-9448
INSPEC Accession Number: 10168633
Digital Object Identifier: 10.1109/TIT.2008.917685
Current Version Published: 2008-03-21
Abstract
A coding theorem is proved for a class of stationary channels with feedback in which the output Yn = f(Xn-mn, Zn-mn) is the function of the current and past m symbols from the channel input Xn and the stationary ergodic channel noise Zn. In particular, it is shown that the feedback capacity is equal to limnrarrinfin supp(xn||yn-1) 1/n I(Xn rarr Yn) where I(Xn rarr Yn) = Sigmai=1n I(Xi; Yi|Yi-1) denotes the Massey directed information from the channel input to the output, and the supremum is taken over all causally conditioned distributions p(xn||yn-1) = Pii=1n p(xi|xi-1,yi-1). 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.
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
