Source coding theory for cascade and branching communication systems

A necessary and sufficient condition for a source to satisfythe ergodic theorem and the ShannonMcMillan theoremthe two basicmathematicaltools of the Shannon theory-is that it be asymptoticallymean stationary (AMS). A channel is defined here to be AMS if wheneveran AMS input source is connected to the channel, the resulting input/out.put process is AMS. We develop several characterizations and propertiesof AMS channels that resemble those of AMS sources. As an applicationwe show that these ideas are useful in characterizing composite sources,and in particular that there exist sources that exhibit distinct short termand long term stationarity properties. Thus “locally stationary” or “quasi-stationary” processes such as those used to model speech waveforms mayalso be stationary. In addition, some preliminary results on coding forAMS channels are presented.