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.

翻译：我们考虑一个多用户语义通信系统，其中智能体（发送方和接收方）通过交换语义消息来传递含义。在此背景下，语言在构建和巩固知识的结构化过程中起着关键作用，影响着概念表征以及语义提取与解释。然而，语言在语义通信中的关键作用常被忽视。即便未被忽视，也通常假设智能体的语言兼容且可无歧义地互操作，忽略了因语言失配可能产生的实际局限性。这正是本文的研究重点。当智能体使用不同语言时，消息解释易受语义信道引入的关键畸变所导致的语义噪声的影响。为应对此问题，本文提出一种新型语义信道均衡器，以抵消并限制消息解释中的关键歧义。所提方案利用语义表征空间上的可测变换对语言失配进行建模。我们通过最优传输理论实现该操作，将此类变换建模为传输映射。随后，为在接收端恢复发送方所意图的含义，我们进行语义均衡操作，以补偿语义信道引入的变换——该操作可在语义消息传输前和/或接收后执行。我们将所提方法实现为一种基于变换码本的操作，该码本专为实现成功通信而设计。数值结果表明，所提出的语义信道均衡器在运算复杂度与传输准确性方面均优于传统方法。