Rate–Distortion Theory for Task-Oriented Distributed Cross-Modal Source Coding

Zhe Yuan

doi:10.1109/TCOMM.2026.3666617

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Rate–Distortion Theory for Task-Oriented Distributed Cross-Modal Source Coding

2026-02-20

PRE

Zhe Yuan

吴丹 (Dan Wu)

Liang Zhou

DOI：10.1109/TCOMM.2026.3666617

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Abstract

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Multi-modal traffic is becoming dominant across vertical domains. Rather than reconstructing raw data with content-agnostic fidelity, many emerging applications are inherently task-oriented and exhibit exploitable inter-modal correlations. In this paper we study such scenarios within the Shannon framework, modeling them as a CEO-type multi-terminal source coding problem under logarithmic loss, where a semantic prior $S$ is available at both the encoders and the decoder. We refer to this formulation as task-oriented distributed cross-modal source coding (TD-CMSC) to emphasize its multimodal sensing application, while the underlying mathematical problem remains a classical log-loss CEO / multi-terminal source coding model augmented with the semantic prior $S$ . On the theoretical side, we characterize the corresponding rate–distortion region under log-loss with semantic prior $S$ in a general multi-encoder setting, and, under a total-rate constraint, we derive the associated distortion–rate function together with an explicit single-letter expression for the optimal per-modality rate allocation at the extreme points of the region. On the technical side, leveraging these results, we design a coding system for vector Gaussian sources that combines task-oriented conditional quantization with successive Wyner–Ziv coding. Numerical experiments confirm the feasibility and rate efficiency of the proposed design.

Keywords:

Task-oriented source coding

cross-modal source coding

distributed source coding

rate distortion theory