Finite alphabet source recovery in polynomial systems

Abstract

Consider a parameterised system whose output vector is a polynomial function of the elements of both the source vector and the parameter vector. Assume there are only a finite number of possible source vectors. Source recovery endeavours to determine the source vector given only the output vector and, in particular, without knowledge of the parameter vector. This paper, after proving both the decidability and implementability of source recovery, focuses on the task of deriving necessary and sufficient conditions for source recovery to be feasible. Although it is difficult to derive a condition which is readily verifiable for most systems, this paper derives a relatively simple condition for ..