Value of Communication in Goal-Oriented Semantic Communications: A Pareto Analysis

Emerging cyber-physical systems increasingly operate under stringent communication constraints that preclude the reliable transmission of their extensive machine-type data streams. Since raw measurements often contain correlated or redundant components, effective operation depends not on transmitting all available data but on selecting the information that contributes to achieving the objectives of the system. Beyond accuracy, goal-oriented semantic communication assesses the \emph{value of information} and aims to generate and transmit only what is relevant and at the right time. Motivated by this perspective, this work studies the \emph{value of communication} through the canonical setting of remote estimation of Markov sources, where a value-of-information measure quantifies the relevance of information. We investigate how optimal estimation performance varies with the available communication budget and determine the marginal performance gain attributable to additional communication. Our approach is based on a \emph{Pareto analysis} that characterizes the complete set of policies that achieve optimal trade-offs between estimation performance and communication cost. The value of communication is defined as the absolute slope of the resulting Pareto frontier. Although computing this frontier is non-trivial, we demonstrate that in our setting it admits a notably tractable structure: it is strictly decreasing, convex, and piecewise linear, and its slope is governed by a finite collection of constants. Moreover, each Pareto-optimal operating point is realizable as a convex combination of two stationary deterministic policies, enabling practical implementation. Leveraging these structural insights, we introduce SPLIT, an efficient and provably optimal algorithm for constructing the complete Pareto frontier.