Invariant properties in an irreversible transformation

We have conducted preliminary research on possibilities of finding some invariant properties in an irreversible transformation, which is defined by a simple matrix model in information theory. At this point, there seems no general way to state an invariance theorem without imposing a set of strong assumptions for the decoding model itself. In a coarse graining approach, we obtained some exact results but, eventually, they were found out to be quite trivial from the point of view of practical engineering. However, we were able to report related non-trivial findings in an international conference.