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This paper studies the fundamental limit of semantic communications over thediscrete memoryless channel. We consider the scenario to send a semantic sourceconsisting of an observation state and its corresponding semantic state, bothof which are recovered at the receiver. To derive the performance limitation,we adopt the semantic rate-distortion function (SRDF) to study the relationshipamong the minimum compression rate, observation distortion, semanticdistortion, and channel capacity. For the case with unknown semantic sourcedistribution, while only a set of the source samples is available, we propose aneural-network-based method by leveraging the generative networks to learn thesemantic source distribution. Furthermore, for a special case where thesemantic state is a deterministic function of the observation, we design acascade neural network to estimate the SRDF. For the case with perfectly knownsemantic source distribution, we propose a general Blahut-Arimoto algorithm toeffectively compute the SRDF. Finally, experimental results validate ourproposed algorithms for the scenarios with ideal Gaussian semantic source andsome practical datasets.

Fundamental Limitation of Semantic Communications: Neural Estimation for Rate-Distortion