Certain Results in Coding Theory for Noisy ChannelsThis work was carried out at the Research Laboratory of Electronics, Massachusetts Institute of Technology, and was supported in part by the United States Army (Signal Corps), the United States Air Force (Office of Scientific Research, Air Research and Development Command), and the United States Navy (Office of Naval Research); and in part by Bell Telephone Laboratories, Inc.

In this paper we will develop certain extensions and refinements of coding theory for noisy communication channels. First, a refinement of the argument based on ¿random¿ coding will be used to obtain an upper bound on the probability of error for an optimal code in the memoryless finite discrete channel. Next, all equation is obtained for the capacity of a finite state channel when the state can be calculated at both transmitting and receiving terminals. An analysis is also made of the more complex case where the state is calculable at the transmitting point but not necessarily at the receiving point.