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Private Semantic Communications with Separate Blind Encoders

Amirreza Zamani, Mikael Skoglund

TL;DR

This work addresses privacy-constrained semantic communication with two blind encoders, where encoder 1 designs a semantic $f(X)$ for a task $h(X)$ and encoder 2, possessing private data $S$, outputs a disclosed signal $U$ under a leakage budget $I(U;S)\\le\\epsilon$ to maximize $I(h(X);U)$. It formulates the privacy-utility objective $h_{\\epsilon}(P_{S,f(X)}) = \sup_{P_{U|S,f(X)}} I(f(X);U)$ subject to the leakage constraint and encoder design limits, and derives computable bounds using extended FRL and SFRL, including a common-information based tightness condition. The main contributions are explicit lower bounds $L_h^1(\\epsilon)$ and $L_h^2(\\epsilon)$ and an upper bound $h_{\\epsilon}(P_{S,f(X)}) \\le H(f(X)|S) + \\epsilon$, along with a bound on $I(U;h(X))$ that is independent of the semantic, and constructive privacy mechanisms. A MNIST-based numerical example illustrates the bounds, showing that the gap between upper and lower bounds can be small under realistic leakage and that the first lower bound often dominates, supporting practical applicability of the proposed framework.

Abstract

We study a semantic communication problem with a privacy constraint where an encoder consists of two separate parts, e.g., encoder 1 and encoder 2. The first encoder has access to information source $X=(X_1,\ldots,X_N)$ which is arbitrarily correlated with private data $S$. The private data is not accessible by encoder 1, however, the second encoder has access to it and the output of encoder 1. A user asks for a task $h(X)$ and the first encoder designs the semantic of the information source $f(X)$ to disclose. Due to the privacy constraints $f(X)$ can not be revealed directly to the user and the second encoder applies a statistical privacy mechanism to produce disclosed data $U$. Here, we assume that encoder 2 has no access to the task and the design of the disclosed data is based on the semantic and the private data. In this work, we propose a novel approach where $U$ is produced by solving a privacy-utility trade-off based on the semantic and the private data. We design $U$ utilizing different methods such as using extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma. We evaluate our design by computing the utility attained by the user. Finally, we study and compare the obtained bounds in a numerical example.

Private Semantic Communications with Separate Blind Encoders

TL;DR

This work addresses privacy-constrained semantic communication with two blind encoders, where encoder 1 designs a semantic for a task and encoder 2, possessing private data , outputs a disclosed signal under a leakage budget to maximize . It formulates the privacy-utility objective subject to the leakage constraint and encoder design limits, and derives computable bounds using extended FRL and SFRL, including a common-information based tightness condition. The main contributions are explicit lower bounds and and an upper bound , along with a bound on that is independent of the semantic, and constructive privacy mechanisms. A MNIST-based numerical example illustrates the bounds, showing that the gap between upper and lower bounds can be small under realistic leakage and that the first lower bound often dominates, supporting practical applicability of the proposed framework.

Abstract

We study a semantic communication problem with a privacy constraint where an encoder consists of two separate parts, e.g., encoder 1 and encoder 2. The first encoder has access to information source which is arbitrarily correlated with private data . The private data is not accessible by encoder 1, however, the second encoder has access to it and the output of encoder 1. A user asks for a task and the first encoder designs the semantic of the information source to disclose. Due to the privacy constraints can not be revealed directly to the user and the second encoder applies a statistical privacy mechanism to produce disclosed data . Here, we assume that encoder 2 has no access to the task and the design of the disclosed data is based on the semantic and the private data. In this work, we propose a novel approach where is produced by solving a privacy-utility trade-off based on the semantic and the private data. We design utilizing different methods such as using extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma. We evaluate our design by computing the utility attained by the user. Finally, we study and compare the obtained bounds in a numerical example.

Paper Structure

This paper contains 5 sections, 3 theorems, 18 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System model and Problem Formulation
  3. Main Results
  4. Numerical Experiment
  5. conclusion

Key Result

Theorem 1

For any $0\leq \epsilon$, joint distribution $P_{S,f(X),h(X)}$ and any semantic $f(X)$ which satisfies varoo1 and varoo2, we have where with $\alpha=\frac{\epsilon}{H(S)}$. The lower bound in th2ch11 is tight if $H(S|f(X))=0$, i.e., $S$ is a deterministic function of $f(X)$. Furthermore, if the lower bound $L_{h}^{1}(\epsilon)$ is tight then we have $H(S|f(X))=0$. Additionally, for the utility a

Figures (2)

  • Figure 1: The encoder consists of two separate parties with different goals. The goal is to design $U$ that maximizes the utility while satisfying a certain privacy constraint.
  • Figure 2: Comparing the lower and upper bounds obtained in Theorem 1. In this example, the gap between the upper bound and the first lower bound is $H(h(X)|f(X))+H(f(X)|h(X))\simeq 1.4$ nats.

Theorems & Definitions (12)

  • Example 1
  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3
  • Example 2
  • Remark 4
  • Corollary 1
  • proof
  • ...and 2 more