  In this paper, for linear time-invariant plants, where a collection of
possible inputs and outputs are known a priori, we address the problem of
determining the communication between outputs and inputs, i.e., information
patterns, such that desired control objectives of the closed-loop system (for
instance, stabilizability) through static output feedback may be ensured.
  We address this problem in the structural system theoretic context. To this
end, given a specified structural pattern (locations of zeros/non-zeros) of the
plant matrices, we introduce the concept of essential information patterns,
i.e., communication patterns between outputs and inputs that satisfy the
following conditions: (i) ensure arbitrary spectrum assignment of the
closed-loop system, using static output feedback constrained to the information
pattern, for almost all possible plant instances with the specified structural
pattern; and (ii) any communication failure precludes the resulting information
pattern from attaining the pole placement objective in (i).
  Subsequently, we study the problem of determining essential information
patterns. First, we provide several necessary and sufficient conditions to
verify whether a specified information pattern is essential or not. Further, we
show that such conditions can be verified by resorting to algorithms with
polynomial complexity (in the dimensions of the state, input and output).
Although such verification can be performed efficiently, it is shown that the
problem of determining essential information patterns is in general NP-hard.
The main results of the paper are illustrated through examples.
