Semantic Channel Capacity of Rayleigh Fading Channels Based on Synonymous Mapping

Classical information theory (CIT) characterizes the transmission limit for communication systems under syntactic accuracy, whereas semantic information theory (SIT) studies communication from the perspective of semantic fidelity induced by synonymous mapping. In this paper, we investigate the semantic channel capacity of Rayleigh fading channels under synonymous mapping of the channel gain and additive noise. We first derive the semantic capacity formula when synonymous mapping is applied to the channel fading coefficient and establish corresponding upper and lower bounds using Jensen's inequality. To determine an optimized synonymous partition, the partition design is formulated as a constrained optimization problem and solved numerically using a neural network-based approach with the Adam optimizer. Furthermore, we extend the framework by applying synonymous mapping to both the channel fading coefficient and the additive noise and derive the corresponding semantic capacity formula together with its theoretical bounds. The numerical results illustrate the theoretical semantic channel capacity under synonymous mapping and validate the compatibility of the proposed framework with both CIT and SIT. At a 20-dB SNR with K=8 channel gain intervals and J=4 noise intervals, the semantic capacity reached 9.86 sebits/s/Hz.