The Role of Fidelity in Goal-Oriented Semantic Communication: A Rate Distortion Approach

We study a variant of a robust description source coding framework, which is a relevant model for goal-oriented semantic information transmission, via its corresponding characterization. Considering two individual single-letter separable distortion constraints and input and output data acting as the intrinsic and extrinsic message, respectively, we first derive a lower bound on the optimal rates of the problem, as well as necessary and sufficient conditions for this bound to be tight. Subsequently, we prove a general result that provides in parametric form the optimal solution of the characterization 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 a Hamming and an erasure distortion coexist, as a means to highlight the importance of selecting the type of the distortion constraint in goal-oriented semantic communication. Furthermore, we develop a goal-oriented Blahut-Arimoto (BA) algorithm, which can be used for the computation of any finite alphabet intrinsic or extrinsic message under individual distortion criteria. Finally, we revisit the problem for multidimensional independent and identically distributed (
$\mathop {\mathrm {i.i.d.}}$
) jointly Gaussian processes with individual mean-square error (MSE) distortion constraints, providing new insights that have previously been overlooked. This work reveals the cardinal role of context-dependent fidelity criteria in goal-oriented semantic communication.