A new source model, which consists of an intrinsic state part and an extrinsic observation part, is proposed and its information-theoretic characterization, namely its rate-distortion function, is defined and analyzed. Such a source model is motivated by the recent surge of interest in the semantic aspect of information: the intrinsic state corresponds to the semantic feature of the source, which in general is not observable but can only be inferred from the extrinsic observation. There are two distortion measures, one between the intrinsic state and its reproduction, and the other between the extrinsic observation and its reproduction. Under a given code rate, the tradeoff between these two distortion measures is characterized by the rate-distortion function, which is solved via the indirect rate-distortion theory and is termed the semantic rate-distortion function of the source. As an application of the general model and its analysis, the case of Gaussian extrinsic observation is studied, assuming a linear relationship between the intrinsic state and the extrinsic observation, under a quadratic distortion structure. The semantic rate-distortion function is shown to be the solution of a convex programming problem with respect to an error covariance matrix, and a reverse water-filling type of solution is provided when the model further satisfies a diagonalizability condition.

中文翻译：

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语义源的间接率失真表征：一般模型和高斯观测的情况


提出了一种由内在状态部分和外在观测部分组成的新的源模型，并定义和分析了其信息论表征，即率失真函数。这种源模型的动机是最近人们对信息语义方面的兴趣激增：内在状态对应于源的语义特征，其通常是不可观察的，只能从外在观察中推断出来。有两种扭曲措施，一种是内在状态与其再现之间，另一种是外部观察与其再现之间。在给定码率下，这两种失真度量之间的权衡由速率失真函数来表征，该函数通过间接速率失真理论求解，被称为源的语义速率失真函数。作为一般模型及其分析的应用，研究了高斯外部观测的情况，假设内在状态和外部观测之间存在线性关系，在二次畸变结构下。语义率失真函数被证明是关于误差协方差矩阵的凸规划问题的解，并且当模型进一步满足可对角化条件时，提供了反向注水型解。