[Paper] Randomized Distributed Function Computation (RDFC): Ultra-Efficient Semantic Communication Applications to Privacy

Source: arXiv - 2603.09577v1

Overview

The paper introduces Randomized Distributed Function Computation (RDFC), a new framework that lets a sender transmit just enough information for a receiver to compute a randomized function of the original data. By treating this as a form of semantic communication, the authors show how RDFC can dramatically cut bandwidth while still satisfying strong privacy guarantees such as local differential privacy—even when the two parties share no secret randomness.

Key Contributions

• RDFC framework: Formalizes semantic communication as a generalized remote‑source‑coding problem where the goal is to reproduce a randomized function of the source.
• Privacy‑by‑design: Uses strong coordination metrics to guarantee (local) differential privacy for every input sequence, without requiring shared randomness.
• Wyner’s Common Information (WCI) bounds: Derives lower bounds on the communication cost when no common randomness is available, establishing a clear “no‑shared‑key” baseline.
• Numerical techniques for continuous alphabets: Provides practical algorithms to compute the opposite corner of the RDFC rate region (unlimited shared randomness) for real‑valued data.
• Empirical evaluation: Shows that a modest amount of common randomness can slash the required transmission rate by up to 100× compared to the WCI baseline, and that even the no‑shared‑randomness case beats naïve lossless transmission by a large margin.
• Finite‑blocklength analysis: Demonstrates that the privacy gap between asymptotic and practical (finite‑length) RDFC shrinks exponentially fast with the block size.

Methodology

1. Problem formulation – The authors model the communication task as a remote source coding problem: a sender observes a data sequence (X^n) and must enable the receiver to generate a random variable (Y^n) that follows a prescribed conditional distribution (P_{Y|X}).
2. Strong coordination – They adopt the strong coordination metric from information theory, which forces the joint distribution of ((X^n, Y^n)) to be statistically indistinguishable from the target distribution. This metric naturally enforces privacy because the output can be made independent of the exact input beyond what the function requires.
3. Rate region analysis – Two extreme points are studied:
   • No common randomness – The communication cost collapses to Wyner’s common information (C_W(X;Y)).
   • Unlimited common randomness – The cost reduces to the conditional entropy (H(Y|U)) where (U) is the shared randomness.
4. Numerical evaluation – For continuous‑alphabet sources (e.g., Gaussian data), the authors use convex‑optimization tools to approximate the rate region, allowing them to quantify the benefit of varying amounts of shared randomness.
5. Finite‑blocklength bounds – Leveraging recent non‑asymptotic results, they bound the privacy leakage for a given block length (n) and show exponential convergence to the asymptotic privacy level.

Results & Findings

• Common randomness matters: Adding even a modest amount (e.g., a few hundred bits per block) yields dramatic rate reductions.
• Privacy is robust: The DP parameter (\epsilon) stays constant across the two extremes, confirming that the rate savings do not come at the cost of weaker privacy.
• Scalability: As block length grows, the privacy gap closes exponentially, meaning practical systems can operate near the theoretical optimum with realistic latency.

Practical Implications

• Energy‑efficient edge analytics – Sensors can offload only the semantic part of their data (e.g., a noisy count, a classification label) while preserving privacy, dramatically extending battery life.
• Federated learning & secure aggregation – RDFC provides a principled way to transmit randomized gradients or model updates with provable DP, reducing uplink traffic without a trusted server.
• IoT privacy gateways – Deploying a small shared‑randomness seed (e.g., via a one‑time provisioning step) can cut network usage by 100×, making large‑scale deployments feasible on low‑bandwidth LPWANs.
• Regulatory compliance – Since the framework guarantees local differential privacy by construction, it can help meet GDPR/CCPA requirements for data minimization.
• Protocol design – RDFC can be layered on top of existing transport protocols (MQTT, CoAP) as a “semantic compression” module, requiring only minor changes to the application layer.

Limitations & Future Work

• Common randomness provisioning – While the paper shows huge gains with shared randomness, it does not address practical key‑distribution mechanisms for massive device fleets.
• Model specificity – The analysis assumes a known conditional distribution (P_{Y|X}); extending to learned functions (e.g., neural nets) remains an open challenge.
• Complexity of numerical optimization – Computing the rate region for high‑dimensional continuous data can be computationally intensive; scalable approximations are needed.
• Robustness to channel errors – The current model assumes error‑free links; integrating error‑control coding with RDFC is a natural next step.

Overall, RDFC opens a promising path toward ultra‑efficient, privacy‑preserving semantic communication—an area that’s poised to become a cornerstone of next‑generation distributed AI and IoT systems.

Authors

• Onur Günlü

Paper Information

• arXiv ID: 2603.09577v1
• Categories: cs.IT, cs.CR, cs.DC, cs.SC, eess.SP
• Published: March 10, 2026
• PDF: Download PDF