Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition
Chao Tian, Shlomo Shamai
TL;DR
This work establishes a concrete operational interpretation of Partial Information Decomposition by tying the synergistic information component to the cooperative gain in a two-user broadcast channel under a fixed signaling distribution. By leveraging Sato's outer bound and Gaussian BC results, the authors show that $I^{(S)}(T;X,Y)$ lower-bounds, and in some cases equals, the gain from receivers cooperating to decode a target $T$. The framework clarifies why PID components are meaningful for tasks such as multi-modality learning and biological signal analysis, and it connects PID to established capacity concepts like the sum-rate and channel canonic bounds. The results also motivate extensions to cooperation regimes and more general channels, providing a principled lens for incorporating PID into information-theoretic and practical design choices.
Abstract
Partial information decomposition has recently found applications in biological signal processing and machine learning. Despite its impacts, the decomposition was introduced through an informal and heuristic route, and its exact operational meaning is unclear. In this work, we fill this gap by connecting partial information decomposition to the capacity of the broadcast channel, which has been well-studied in the information theory literature. We show that the synergistic information in the decomposition can be rigorously interpreted as the cooperative gain, or a lower bound of this gain, on the corresponding broadcast channel. This interpretation can help practitioners to better explain and expand the applications of the partial information decomposition technique.