On the cost sequence transmission

Message transmission through the noiseless channel is considered. Message source is an arbitrary discrete stochastic process, and coding is any measurable mapping of the set of input sequences into output ones. Transmission cost is defined as the average number of output letters required to decode one letter of a message. This definition differs from the traditional one. For finite-automaton coding, the new cost is proved to be equal to the traditional one if coding is decodable, and to be infinite otherwise. The fundamental theorem for noiseless channels appears to be generalized to the widest class of sources and codings.