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

Onur Günlü

TL;DR

This work provides lower bounds on Wyner’s common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness.

Abstract

We establish the randomized distributed function computation (RDFC) framework, in which a sender transmits just enough information for a receiver to generate a randomized function of the input data. Describing RDFC as a form of semantic communication, which can be essentially seen as a generalized remote-source-coding problem, we show that security and privacy constraints naturally fit this model, as they generally require a randomization step. Using strong coordination metrics, we ensure (local differential) privacy for every input sequence and prove that such guarantees can be met even when no common randomness is shared between the transmitter and receiver. This work provides lower bounds on Wyner's common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness. Experiments illustrate that a sufficient amount of common randomness can reduce the semantic communication rate by up to two orders of magnitude compared to the WCI point, while RDFC without any shared randomness still outperforms lossless transmission by a large margin. A finite blocklength analysis further confirms that the privacy parameter gap between the asymptotic and non-asymptotic RDFC methods closes exponentially fast with input length. Our results position RDFC as an energy-efficient semantic communication strategy for privacy-aware distributed computation systems.

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

TL;DR

This work provides lower bounds on Wyner’s common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness.

Abstract

We establish the randomized distributed function computation (RDFC) framework, in which a sender transmits just enough information for a receiver to generate a randomized function of the input data. Describing RDFC as a form of semantic communication, which can be essentially seen as a generalized remote-source-coding problem, we show that security and privacy constraints naturally fit this model, as they generally require a randomization step. Using strong coordination metrics, we ensure (local differential) privacy for every input sequence and prove that such guarantees can be met even when no common randomness is shared between the transmitter and receiver. This work provides lower bounds on Wyner's common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness. Experiments illustrate that a sufficient amount of common randomness can reduce the semantic communication rate by up to two orders of magnitude compared to the WCI point, while RDFC without any shared randomness still outperforms lossless transmission by a large margin. A finite blocklength analysis further confirms that the privacy parameter gap between the asymptotic and non-asymptotic RDFC methods closes exponentially fast with input length. Our results position RDFC as an energy-efficient semantic communication strategy for privacy-aware distributed computation systems.
Paper Structure (11 sections, 4 theorems, 41 equations, 2 figures, 2 tables)

This paper contains 11 sections, 4 theorems, 41 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Summary of Contributions
  3. Paper Organization
  4. Notation
  5. Preliminaries
  6. Randomized Distributed Function Computation (RDFC): Semantic Communications via Strong Coordination
  7. Local Differential Privacy
  8. RDFC for Local Differential Privacy with Additive Gaussian Noise
  9. Achievable LDP Parameters Using Non-Asymptotic RDFC Methods
  10. RDFC for Symmetric Random Response
  11. Conclusions

Key Result

Theorem 1

The coordination-randomness region $\mathcal{R}_{\text{RDFC}}$ is the union over all $P_{\widetilde{X}UY} = P_UP_{\widetilde{X}|U}P_{Y|U}$ of the rate pairs $(R,R_0)$ satisfying

Figures (2)

  • Figure 1: A two–node RDFC model where both nodes may share common randomness $C$. Within the strong coordination framework, the receiver uses the transmitted index $S$ and $C$ to output a sequence $Y^{n}$. This procedure ensures that every pair $(\widetilde{x}^{n},y^{n})$ follows any target joint distribution $Q^{n}_{\widetilde{X}Y}$ given in Eq. (\ref{['eq:coordinationconstraint']}) below, enabling a cooperation strategy that benefits both nodes. The design goal focuses on minimizing the channel rate $R$ to reduce function computation latency and energy consumption.
  • Figure 2: An example random‑response scenario in which the joint distribution $Q_{\widetilde{X}Y}$ can be expressed as a mixture of BSCs. For simplicity, assume that $W$ is uniformly distributed.

Theorems & Definitions (10)

  • Definition 1
  • Theorem 1: CuffChannelSynthesis
  • Remark 1
  • Definition 2: FlavioLDPevfimievski2003limiting4690986
  • Theorem 2
  • proof : Proof Sketch:
  • Theorem 3
  • Remark 2
  • proof : Proof Sketch:
  • Theorem 4