Goal-Oriented Single-Letter Codes for Lossy Joint Source-Channel Coding.

A new variation of the classical point-to-point joint source-channel coding (JSCC) is studied here, which is relevant for identifying goal-oriented semantic aspects of a transmitted source message over a noisy channel in the presence of multiple distortion constraints. For this new formulation, coined goal-oriented JSCC, we first introduce optimality criteria followed by necessary and sufficient conditions for global optimality. The focus of our main theoretical results is on investigating the implications of a special subclass of block codes, namely, the single-letter codes, via a theorem in which we provide necessary and sufficient conditions for the probabilistic matching of a noisy source message with a noisy channel. We corroborate our theoretical results with two examples, in which goal-oriented single-letter codes and uncoded transmission perform optimally. Our results further highlight the important role of multiple fidelity constraints in goal-oriented communications.