# An Indirect Rate-Distortion Characterization for Semantic Sources: General Model and the Case of Gaussian Observation

arXiv: https://arxiv.org/abs/2201.12477 · HTML: https://mlsanity.com/paper/2201.12477/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 40 references that are in the map.
- First posted on arXiv 29 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Video Coding for Machines: A Paradigm of Collaborative Compression and Intelligent Analytics](https://mlsanity.com/paper/2001.03569/) (2020)
- [The Information Bottleneck Problem and Its Applications in Machine Learning](https://mlsanity.com/paper/2004.14941/) (2020)
- [Semantics-Empowered Communication for Networked Intelligent Systems](https://mlsanity.com/paper/2007.11579/) (2020)
- [Semantics-Native Communication with Contextual Reasoning](https://mlsanity.com/paper/2108.05681/) (2021)
- [Semantic-Effectiveness Filtering and Control for Post-5G Wireless Connectivity](https://mlsanity.com/paper/1907.02441/) (2019)

## Built on by (most cited first, 8 of 8)

- [Less Data, More Knowledge: Building Next Generation Semantic Communication Networks](https://mlsanity.com/paper/2211.14343/) (2022)
- [Joint Source-Channel Coding: Fundamentals and Recent Progress in Practical Designs](https://mlsanity.com/paper/2409.17557/) (2024)
- [Curriculum Learning for Goal-Oriented Semantic Communications with a Common Language](https://mlsanity.com/paper/2204.10429/) (2022)
- [Task-Oriented Communication Design at Scale](https://mlsanity.com/paper/2305.08481/) (2023)
- [Fundamental Limitation of Semantic Communications: Neural Estimation for Rate-Distortion](https://mlsanity.com/paper/2401.01176/) (2024)
- [On the Rate-Distortion-Complexity Tradeoff for Semantic Communication](https://mlsanity.com/paper/2602.14481/) (2026)
- [Adaptive Source-Channel Coding for Semantic Communications](https://mlsanity.com/paper/2508.07958/) (2025)
- [Semantic Communication with Distribution Learning through Sequential Observations](https://mlsanity.com/paper/2508.10350/) (2025)

## Abstract (arXiv)

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.