Rate-Distortion Theory for Strategic Semantic Communication

Abstract: This paper analyzes the fundamental limit of the strategic semantic communication problem in which a transmitter obtains a limited number of indirect observation of an intrinsic semantic information source and can then influence the receiver's decoding by sending a limited number of messages to an imperfect channel. The transmitter and the receiver can have different distortion measures and can make rational decision about their encoding and decoding strategies, respectively. The decoder can also have some side information (e.g., background knowledge and/or information obtained from previous communications) about the semantic source to assist its interpretation of the semantic information. We focus particularly on the case that the transmitter can commit to an encoding strategy and study the impact of the strategic decision making on the rate distortion of semantic communication. Three equilibrium solutions including the strong Stackelberg equilibrium, weak Stackelberg equilibrium, as well as Nash equilibrium have been studied and compared. The optimal encoding and decoding strategy profiles under various equilibrium solutions have been derived. We prove that committing to an encoding strategy cannot always bring benefit to the encoder. We therefore propose a feasible condition under which committing to an encoding strategy can always reduce the distortion performance of semantic communication.