314 research outputs found
Achievable Regions and Precoder Designs for the Multiple Access Wiretap Channels with Confidential and Open Messages
This paper investigates the secrecy capacity region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can communicate with Bob with arbitrarily small probability of error, while the confidential information leaked to Eve tends to zero. Due to the high implementation complexity of joint decoding, we also consider the DM MAC-WT channel where Bob simply decodes messages independently while Eve still applies joint decoding. We then extend the results in the DM case to a Gaussian vector (GV) MAC-WT channel. Based on the information theoretic results, we further maximize the sum secrecy rate of the GV MAC-WT system by designing precoders for all users. Since the problems are non-convex, we provide iterative algorithms to obtain suboptimal solutions. Simulation results show that compared with existing schemes, secure communication can be greatly enhanced by the proposed algorithms, and in contrast to the works which only focus on the network secrecy performance, the system spectrum efficiency can be effectively improved since open messages can be simultaneously transmitted
Power Allocation in Multiuser Parallel Gaussian Broadcast Channels With Common and Confidential Messages
We consider a broadcast communication over parallel channels, where the transmitter sends K+1 messages: one common message to all users, and K confidential messages to each user, which need to be kept secret from all unintended users. We assume partial channel state information at the transmitter, stemming from noisy channel estimation. Our main goal is to design a power allocation algorithm in order to maximize the weighted sum rate of common and confidential messages under a total power constraint. The resulting problem for joint encoding across channels is formulated as the cascade of two problems, the inner min problem being discrete, and the outer max problem being convex. Thereby, efficient algorithms for this kind of optimization program can be used as solutions to our power allocation problem. For the special case K=2 , we provide an almost closed-form solution, where only two single variables must be optimized, e.g., through dichotomic searches. To reduce computational complexity, we propose three new algorithms, maximizing the weighted sum rate achievable by two suboptimal schemes that perform per-user and per-channel encoding. By numerical results, we assess the performance of all proposed algorithms as a function of different system parameters
The Wiretap Channel with Feedback: Encryption over the Channel
In this work, the critical role of noisy feedback in enhancing the secrecy
capacity of the wiretap channel is established. Unlike previous works, where a
noiseless public discussion channel is used for feedback, the feed-forward and
feedback signals share the same noisy channel in the present model. Quite
interestingly, this noisy feedback model is shown to be more advantageous in
the current setting. More specifically, the discrete memoryless modulo-additive
channel with a full-duplex destination node is considered first, and it is
shown that the judicious use of feedback increases the perfect secrecy capacity
to the capacity of the source-destination channel in the absence of the
wiretapper. In the achievability scheme, the feedback signal corresponds to a
private key, known only to the destination. In the half-duplex scheme, a novel
feedback technique that always achieves a positive perfect secrecy rate (even
when the source-wiretapper channel is less noisy than the source-destination
channel) is proposed. These results hinge on the modulo-additive property of
the channel, which is exploited by the destination to perform encryption over
the channel without revealing its key to the source. Finally, this scheme is
extended to the continuous real valued modulo- channel where it is
shown that the perfect secrecy capacity with feedback is also equal to the
capacity in the absence of the wiretapper.Comment: Submitted to IEEE Transactions on Information Theor
Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure
The sum secure degrees of freedom (s.d.o.f.) of two fundamental multi-user
network structures, the K-user Gaussian multiple access (MAC) wiretap channel
and the K-user interference channel (IC) with secrecy constraints, have been
determined recently as K(K-1)/(K(K-1)+1) [1,2] and K(K-1)/(2K-1) [3,4],
respectively. In this paper, we determine the entire s.d.o.f. regions of these
two channel models. The converse for the MAC follows from a middle step in the
converse of [1,2]. The converse for the IC includes constraints both due to
secrecy as well as due to interference. Although the portion of the region
close to the optimum sum s.d.o.f. point is governed by the upper bounds due to
secrecy constraints, the other portions of the region are governed by the upper
bounds due to interference constraints. Different from the existing literature,
in order to fully understand the characterization of the s.d.o.f. region of the
IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not
illustrate the generality of the problem. In order to prove the achievability,
we use the polytope structure of the converse region. In both MAC and IC cases,
we develop explicit schemes that achieve the extreme points of the polytope
region given by the converse. Specifically, the extreme points of the MAC
region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e.,
by setting (K-m) users' secure rates to zero and utilizing them as pure
(structured) cooperative jammers. The extreme points of the IC region are
achieved by a (K-m)-user IC with confidential messages, m helpers, and N
external eavesdroppers, for m>=1 and a finite N. A byproduct of our results in
this paper is that the sum s.d.o.f. is achieved only at one extreme point of
the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC
and IC channel models.Comment: Submitted to IEEE Transactions on Information Theory, April 201
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