Secure Semantic Communication over Wiretap Channels: Rate-Distortion-Equivocation Tradeoff

TL;DR

This paper considers the lossy joint source-channel coding (JSCC) of a memoryless semantic source transmitted over a memoryless wiretap channel, and derives single-letter converse and achievability bounds on the rate-distortion-equivocation region.

Abstract

This paper investigates an information-theoretic model of secure semantic-aware communication. For this purpose, we consider the lossy joint source-channel coding (JSCC) of a memoryless semantic source transmitted over a memoryless wiretap channel. The source consists of two correlated parts that represent semantic and observed aspects of the information. Our model assumes separate fidelity and secrecy constraints on each source component and, in addition, encompasses two cases for the source output, in order to evaluate the performance gains if the encoder has an extended access to the source. Specifically, in Case 1, the encoder has direct access only to the samples from a single (observed) source component, while in Case 2 it has additional direct access to the samples of the underlaying semantic information. We derive single-letter converse and achievability bounds on the rate-distortion-equivocation region. The converse bound explicitly contains rate-distortion functions, making it easy to evaluate, especially for some common distributions. The proposed achievability coding scheme involves novel stochastic superposition coding with two private parts to enable analysis of the equivocation for each source component, separately. Our results generalise some of the previously established source and source-channel coding problems. The general results are further specialised to Gaussian and Bernoulli sources transmitted over Gaussian and binary wiretap channels, respectively. The numerical evaluations illustrate the derived bounds for these distributions.

Figures (7)

• Figure 1: Wiretap channel model for semantic communication with two encoder configurations: Case 1 (observation-only input) and Case 2 (joint semantic-observation input). System objectives include dual distortion constraints at the legitimate receiver ($D_s, D_u$) and triple equivocation constraints at the eavesdropper ($\Delta_s, \Delta_u, \Delta_{su}$).
• Figure 2: Codebook design. Indices $m_1'$ and $m_2'$ are picked at random from a uniform distribution.
• Figure 3: Superposition coding layouts
• Figure 4: Relation between source and channel coding. The indices $i$ and $l$ are encrypted as $\hat{i} = (i + K_1 \mod 2^{k {R_{\color{blue}i}} })$ and $\hat{l} = (l + K_2 \mod 2^{k {R_{\color{blue}l}} })$, respectively
• Figure 5: Converse bounds the Gaussian and binary system models. Blue surface: Case 1 encoder. Red surface: Case 2 encoder.

Theorems & Definitions (27)

• Definition 1: Case 1: observation-only encoding
• Definition 2: Case 2: joint semantic-observation encoding
• Definition 3: Decoder
• Definition 4: Code
• Definition 5: Achievable Tuple of Region Parameters
• Definition 6: Achievable Region
• Lemma 1: Classic RDF elgamal2011book
• Lemma 2: Semantic RDF elgamal1982 for Case 2
• Lemma 3: Semantic RDF liu2022indirect for Case 1
• Theorem 1: Converse