Semantic Channel Equalizer: Modelling Language Mismatch in Multi-User Semantic Communications

We consider a multi-user semantic communications system in which agents (transmitters and receivers) interact through the exchange of semantic messages to convey meanings. In this context, languages are instrumental in structuring the construction and consolidation of knowledge, influencing conceptual representation and semantic extraction and interpretation. Yet, the crucial role of languages in semantic communications is often overlooked. When this is not the case, agent languages are assumed compatible and unambiguously interoperable, ignoring practical limitations that may arise due to language mismatching. This is the focus of this work. When agents use distinct languages, message interpretation is prone to semantic noise resulting from critical distortion introduced by semantic channels. To address this problem, this paper proposes a new semantic channel equalizer to counteract and limit the critical ambiguity in message interpretation. Our proposed solution models the mismatch of languages with measurable transformations over semantic representation spaces. We achieve this using optimal transport theory, where we model such transformations as transportation maps. Then, to recover at the receiver the meaning intended by the teacher we operate semantic equalization to compensate for the transformation introduced by the semantic channel, either before transmission and/or after the reception of semantic messages. We implement the proposed approach as an operation over a codebook of transformations specifically designed for successful communication. Numerical results show that the proposed semantic channel equalizer outperforms traditional approaches in terms of operational complexity and transmission accuracy.