论文标题
语义来源的间接率差异表征：一般模型和高斯观察案例
An Indirect Rate-Distortion Characterization for Semantic Sources: General Model and the Case of Gaussian Observation
论文作者
论文摘要
提出了一个新的源模型，该模型由内在状态部分和外部观察部件组成，其信息理论表征（即其速率降低函数）被定义和分析。这种源模型是由于信息在信息的语义方面的最新兴趣激励：固有状态对应于源的语义特征，通常无法观察到，但只能从外部观察中推断出来。有两种失真措施，一种在固有状态及其繁殖之间，另一个是外部观察及其繁殖之间的。在给定的代码速率下，这两个失真度量之间的权衡为特征在于率延伸函数，该函数通过间接速率延伸理论求解，并被称为源的语义率延伸函数。作为一般模型及其分析的应用，在二次失真结构下，假设内在状态与外在观察之间存在线性关系，则研究了高斯外部观察的情况。在误差协方差矩阵方面，语义率延伸函数被证明是凸编程编程问题的解决方案，当模型进一步满足对角度的条件时，提供了反向水的解决方案。
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 as 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 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.
