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IEEE International Conference on Communications workshops

Gaussian wiretap channels with correlated sources: Approaching capacity region within a constant gap

Yanling Chen, Hendrik Vogt, Aydin Sezgin

Published Jun 1, 2014• 7 citations
Publisher

Abstract

This paper studies the Gaussian wiretap channel with correlated sources available not only at the transmitter and legitimate receiver, but also the eavesdropper. In particular, we are interested in the open problem of finding the optimal auxiliary random variable, which provides a closed-form solution to the secret-message and secret-key capacity region. To do that, we first take a deterministic approach and give a precise characterization of its secrecy capacity region. Then we translate the insights gained to the Gaussian case. As a result, we provide a sub-optimal solution by employing a specified Gaussian choice of the auxiliary random variable. This suggested choice is a compromise of keeping most source information subject to the constraint imposed by the channel capability of conducting source coding. Nevertheless, it is shown to be able to approach the secrecy capacity region within half a bit as the signal-noise-ratio of the main channel is no less than 1.

DOI
10.1109/iccw.2014.6881297

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This paper studies the Gaussian wiretap channel with correlated sources available not only at the transmitter and legitimate receiver, but also the eavesdropper. In particular, we are interested in the open problem of finding the optimal auxiliary random variable, which provides a closed-form solution to the secret-message and secret-key capacity region. To do that, we first take a deterministic approach and give a precise characterization of its secrecy capacity region. Then we translate the insights gained to the Gaussian case. As a result, we provide a sub-optimal solution by employing a specified Gaussian choice of the auxiliary random variable. This suggested choice is a compromise of keeping most source information subject to the constraint imposed by the channel capability of conducting source coding. Nevertheless, it is shown to be able to approach the secrecy capacity region within half a bit as the signal-noise-ratio of the main channel is no less than 1.
This paper considers the problem of proof for the secrecy capacity region of the Gaussian wiretap channel. In this channel, the transmitter sends confidential messages to the legitimate receivers, which need to be kept asymptotically perfectly secret from the eavesdropper. We characterize the secrecy capacity region of this channel and give a converse proof by using the fundamental relationship between information theory and the estimation theory in the Gaussian channel, relating the derivative of the mutual information to the minimum mean-square-error (MMSE). Our proof is different from the superposition coding and the random binning. We obtain that using the relationship between MMSE and mutual information one can provide insightful and simple proofs for multiuser single antenna problems and the secrecy capacity problem, such as broadcast channel.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar–Korner.
We study the secret-key capacity in a joint source-channel coding setup-the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input.
We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.
We study the Gaussian multiple access channel in presence of an adversary, who is simultaneously able to eavesdrop and jam, i.e., an active wiretapper. We assume that the adversary has a power constraint, which she can utilize to have any arbitrary jamming strategy. The multiple access channel between the legitimate transmitters and the receiver thus becomes arbitrarily varying. We derive inner and outer bounds on the secrecy rate region of our model. In the case of a degraded channel, we characterize the optimal secrecy sum-rate, and within 0.5 bits per channel use the optimal individual rate constraints. As a special case, we obtain the secrecy capacity of the point-to-point Gaussian wiretap channel when the eavesdropper is able to arbitrarily jam.
We analyze the fundamental trade-off of secret key-based authentication systems in the presence of an eavesdropper for correlated Gaussian sources. A complete characterization of the trade-off among secret-key, storage, and privacy-leakage rates of both generated and chosen secret models is provided. One of the main contributions is revealing that unlike the known results for discrete sources, there is no need for the second auxiliary random variable in characterizing the capacity regions for the Gaussian cases. In addition, it is shown that the strong secrecy for secrecy-leakage of the systems can be achieved by an information-spectrum approach, and the parametric expressions (computable forms) of the capacity regions are also derived.