A Rate Distortion Approach to Goal-Oriented Communication

A variant of a robust description source coding framework motivated by goal-oriented semantic information transmission is studied here. Considering two individual distortion constraints and input and output data that takes values in finite sets, we prove new bounds and structural properties for these bounds to be tight with respect to the information theoretic characterization of the problem. Then, we derive a general result that provides in parametric form the various cases of optimal solutions of this problem. Capitalizing on these results, we examine the structure of the solution for one case study of general binary alphabets under Hamming distortions and solve in closed form a special case. We also solve another general binary alphabet case where Hamming and erasure distortion are used, as a means to highlight the importance of selecting the type of the distortion constraint in the problem.