[Paper Review] Secure Broadcasting With Side-Information

K. G. Nagananda, Chandra R. Murthy+1 more|arXiv (Cornell University)|Sep 13, 2011

Wireless Communication Security Techniques15 references3 citations

TL;DR

This paper derives an inner bound on the capacity region for a two-user discrete memoryless broadcast channel with noncausal side-information at the transmitter and confidential messages. By extending Marton's coding scheme with a stochastic encoder, the authors achieve secure and reliable communication, showing that the rate region is strictly smaller than classical broadcast channels due to combined penalties from side-information and confidentiality constraints.

ABSTRACT

In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process of transmission. We derive an inner bound on the capacity region of this channel, by employing an extension of Marton's coding technique used for the classical two-user broadcast channel, in conjunction with a stochastic encoder to satisfy confidentiality constraints. Based on previously known results, we discuss a procedure to present a schematic of the achievable rate region. The rate-penalties for dealing with side-information and confidentiality constraints make the achievable region for this channel strictly smaller than the rate regions of those channels where one or both of these constraints are relaxed.

Motivation & Objective

• To characterize the information-theoretic performance limits of secure and reliable communication over a two-user discrete memoryless broadcast channel with noncausal side-information at the transmitter.
• To address the challenge of keeping each message confidential from the unintended receiver while leveraging noncausal side-information for improved reliability.
• To derive an achievable rate region that accounts for both side-information and confidentiality constraints, which are known to reduce system capacity.
• To present a schematic procedure for visualizing the achievable rate region based on known results from Gel'fand-Pinsker and wiretap channels with side-information.
• To demonstrate that the combined effect of side-information and confidentiality constraints results in a strictly smaller rate region than in classical or partially constrained broadcast channels.

Proposed method

• Extends Marton's coding technique for the classical two-user broadcast channel to incorporate noncausal side-information at the transmitter.
• Employs a stochastic encoder at the transmitter to satisfy confidentiality constraints by randomizing transmission based on side-information.
• Uses a structured coding scheme with binning: messages are split into common and private parts, with auxiliary random variables $U$, $V_1$, $V_2$, and $W$ to model dependencies.
• Applies typicality decoding at both receivers, with error probability analysis based on joint typicality and the asymptotic equipartition property (AEP).
• Employs Markov's inequality and variance bounds to analyze the probability of error in message decoding, ensuring reliability under the proposed scheme.
• Derives bounds on equivocation and uses Fano’s inequality to quantify residual uncertainty about transmitted messages at unintended receivers, ensuring confidentiality.

Experimental results

Research questions

• RQ1 What is the achievable rate region for a two-user discrete memoryless broadcast channel when the transmitter has noncausal side-information and must keep messages confidential from the unintended receiver?
• RQ2 How does the combination of side-information and confidentiality constraints affect the size of the capacity region compared to classical or partially constrained broadcast channels?
• RQ3 Can Marton’s coding scheme be extended to incorporate both side-information and secrecy constraints simultaneously while maintaining reliability and security?
• RQ4 What is the impact of stochastic encoding on achieving secrecy in the presence of noncausal side-information?
• RQ5 How can the achievable rate region be schematically represented, and what are the key dependencies on auxiliary random variables and mutual information terms?

Key findings

• The proposed scheme achieves a strictly smaller rate region than the classical two-user broadcast channel due to the combined penalties of handling side-information and enforcing confidentiality.
• The inner bound on the capacity region is characterized by three inequalities involving mutual information terms: $I(W;V_1|U)$, $I(W;V_2|U)$, and $I(V_1;V_2|U) + I(V_1,V_2;W|U)$, with rate pairs satisfying these for arbitrarily small $ ho > 0$.
• The error probability at the intended receiver $D_1$ is bounded by $ ext{Pr}(E_S) o 0$ as $N \to \infty$, provided the rates satisfy $R_1^* > I(W;V_1|U) - \epsilon_8$, $R_2^* > I(W;V_2|U) - \epsilon_9$, and $R_1^* + R_2^* > I(V_1;V_2|U) + I(V_1,V_2;W|U) - \epsilon_{10}$.
• The equivocation at $D_2$ is bounded such that $\frac{1}{N}H(\mathbf{V}_1|M_1, \mathbf{U}, \mathbf{V}_2, \mathbf{Y}_2) \leq \epsilon_2$, ensuring that the unintended receiver cannot decode the private message $m_1$.
• The analysis confirms that the rate penalty from side-information and secrecy is non-trivial, and the resulting region is strictly smaller than that of the classical BC or BC with only one constraint.
• The method generalizes known results from Gel'fand-Pinsker and wiretap channels with side-information, providing a unified framework for secure, side-informed broadcasting.