The predictable degree property and row reducedness for systems over a finite ring

Abstract

Motivated by applications in communications, we consider linear discrete-time systems over the finite ring Zpr. We solve the open problem of deriving a theory of row-reduced representations for these systems. We introduce a less restrictive form of representation than the adapted form introduced by Fagnani and Zampieri. We call this form the "composed form". We define the concept of "p-predictable degree property" and "p-row-reduced". We demonstrate that these concepts, coupled with the composed form, provide a natural setting that extends several classical results from the field case to the ring case. In particular, the classical rank test on the leading row coefficient matrix is generalize..