Being able to precisely characterize a particular communication system allows one to compare communication systems, including deciding whether two systems are equivalent, as well as providing a method by which one can rank communication systems based on their characterization. One may also characterize a system by naming or describing it, based upon its content. The Minimum Description Length (MDL) for a system is the shortest length that can describe and differentiate one process from others in the domain of possible processes [Ris89,WF87]. The Minimal Description (MD) characterizes what makes up a system, and thus identifies what is complex and special about each system. A system which is easy to describe has a relatively short description and a small MDL, while a very complex system, approaching randomness, would have a relatively large MDL.
We are describing only the two informative processes defining the communication system. If we have two processes, and there are many other processes below them on the hierarchy, we may compute the MDL by considering only the complexity of the two informative processes, with no attention being paid to processes below. We might, however, choose to view the world as containing larger processes, e.g., you as a process and me as a process, in which case the MDL would be computed for me or for you and might or might not include this medium. Because the reader differs from the author, the reader function is not a perfect inverse of the writer function, making the MDL much larger than if the author were writing for himself, the reader then being a near-perfect inverse of the writer. The ordering of systems, from simple to complex, can be accomplished by listing the systems in order of their MDL value, e.g.
|Order||Minimum Description Length (MDL) in bits|
|2||102=100 (medium complexity)|
|3||105=100000 (very complex)|