Fundamental Limitation of Semantic Communications: Neural Estimation for Rate-Distortion
Dongxu Li, Jianhao Huang, Chuan Huang, Xiaoqi Qin, Han Zhang, Ping Zhang
Abstract
This paper studies the fundamental limit of semantic communications over the discrete memoryless channel. We consider the scenario to send a semantic source consisting of an observation state and its corresponding semantic state, both of which are recovered at the receiver. To derive the performance limitation, we adopt the semantic rate-distortion function (SRDF) to study the relationship among the minimum compression rate, observation distortion, semantic distortion, and channel capacity. For the case with unknown semantic source distribution, while only a set of the source samples is available, we propose a neural-network-based method by leveraging the generative networks to learn the semantic source distribution. Furthermore, for a special case where the semantic state is a deterministic function of the observation, we design a cascade neural network to estimate the SRDF. For the case with perfectly known semantic source distribution, we propose a general Blahut-Arimoto (BA) algorithm to effectively compute the SRDF. Finally, experimental results validate our proposed algorithms for the scenarios with ideal Gaussian semantic source and some practical datasets.