Information transmission in the case of coding by finite automata

In this paper we shall consider a well-known transmission model: information source —coder —channel —decoder, supposing that both the coder and the decoder are finite automata. Naturally, we shall suppose, that our automata will be of the general type, which will not preserve the length of the input words. Then there are some difficulties in estimating the transmission quality which would not occur in the case of coding by n-tuples. The first question we have to answer is thit: what changes of source properties will occur after encoding it by means of the automaton? The secon question is connected with the circumstance, that neither in encoding nor in decoding the length of the transmissed word is necessarily preserved. How, then, can we define the error frequency? (There is no strict correspondence between time indexes of the input and output words. For instance, the word "coding" can be transmitted as "co5ng" and we have a problem whether the error frequency 1/3 or 2/3 or another value is the most suitable.) The third and it seems the most serious question is, what the comparison of the emitted and received message can tell about an "average" error frequency in our transmitting model. This paper will try to answer the questions stated above. From now the following designations will be used: