Event
Ph.D. Dissertation Defense: Jianwei Xie
Thursday, April 17, 2014
1:00 p.m.
Room 2460, AVW Bldg.
Maria Hoo
301 405 3681
mch@umd.edu
ANNOUNCEMENT: Ph.D. Dissertation Defense
Name: Jianwei Xie
Date: Thursday, April 17, 2014 at 1 pm
Location: Room 2460, A V Williams Building
Committee:
Professor Sennur Ulukus, Chair/Advisor
Professor Prakash Narayan
Professor Gang Qu
Professor Adrian Papamarcou
Professor Lawrence C. Washington, Dean's Representative
Title: SECURE DEGREES OF FREEDOM OF WIRELESS NETWORKS
Abstract:
This dissertation studies the security of wireless interference
networks from an information-theoretic point of view. In this
setting, several transmitter-receiver pairs wish to have secure
communication against the eavesdropper(s). The central goal of
this dissertation is to develop a framework based on
information-theoretic principles to determine the complete
solutions for the signaling design in different wireless
interference networks with large transmit powers, and derive the
corresponding fundamental limits in terms of secure degrees of
freedom (s.d.o.f.).
First, we study one-hop wireless networks by considering four
fundamental wireless network structures: Gaussian wiretap
channel, Gaussian broadcast channel with confidential messages,
Gaussian interference channel with confidential messages, and
Gaussian multiple access wiretap channel. The secrecy capacity of
the canonical Gaussian wiretap channel does not scale with the
transmit power, and hence, the s.d.o.f. of the Gaussian wiretap
channel with no helpers is zero. It has been known that a
strictly positive s.d.o.f. can be obtained in the Gaussian
wiretap channel by using a helper which sends structured
cooperative signals. We show that the exact s.d.o.f. of the
Gaussian wiretap channel with a helper is 1/2. Our achievable
scheme is based on real interference alignment and cooperative
jamming, which renders the message signal and the cooperative
jamming signal separable at the legitimate receiver, but aligns
them perfectly at the eavesdropper preventing any reliable
decoding of the message signal. Our converse is based on two key
lemmas. The first lemma quantifies the secrecy penalty by showing
that the net effect of an eavesdropper on the system is that it
eliminates one of the independent channel inputs. The second
lemma quantifies the role of a helper by developing a direct
relationship between the cooperative jamming signal of a helper
and the message rate. We extend this result to the case of M
helpers, and show that the exact s.d.o.f. in this case is
M/(M+1). We then generalize this approach to more general network
structures with multiple messages. We show that the sum s.d.o.f.
of the Gaussian broadcast channel (BC) with confidential messages
and M helpers is 1, the sum s.d.o.f. of the two-user interference
channel (IC) with confidential messages is 2/3, the sum s.d.o.f.
of the two-user interference channel with confidential messages
and M helpers is 1, and the sum s.d.o.f. of the K-user multiple
access (MAC) wiretap channel is K(K-1)/(K(K-1)+1).
Then, we study sum s.d.o.f. of the multi-receiver network. In
this dissertation, we determine the exact sum s.d.o.f. of the
K-user Gaussian IC. We consider three different secrecy
constraints: 1) K-user interference channel with one external
eavesdropper (IC-EE), 2) K-user interference channel with
confidential messages (IC-CM), and 3) K-user interference channel
with confidential messages and one external eavesdropper
(IC-CM-EE). We show that for all of these three cases, the exact
sum s.d.o.f. is K(K-1)/(2K-1). We show converses for IC-EE
and IC-CM, which imply a converse for IC-CM-EE. We show
achievability for IC-CM-EE, which implies achievability for IC-EE
and IC-CM. We develop the converses by relating the channel
inputs of interfering users to the reliable rates of the
interfered users, and by quantifying the secrecy penalty in terms
of the eavesdroppers' observations. Our achievability uses
structured signaling, structured cooperative jamming, channel
prefixing, and asymptotic real interference alignment. While the
traditional interference alignment provides some amount of
secrecy by mixing unintended signals in a smaller sub-space at
every receiver, in order to attain the optimum sum s.d.o.f., we
incorporate structured cooperative jamming into the achievable
scheme, and intricately design the structure of all of the
transmitted signals jointly.
Next, we study the entire s.d.o.f. regions of multi-user network
structures. In this dissertation, we determine the entire
s.d.o.f. regions of the K-user MAC wiretap channel and the K-user
IC with secrecy constraints. The converse for the MAC follows
from a middle step in the converse of sum s.d.o.f. 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
dissertation 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.
Then, we determine the sum s.d.o.f. of two-unicast layered
wireless networks. Without any secrecy constraints, the sum
d.o.f. of this class of networks was shown to take only one of
three possible values: 1, 3/2 and 2, for all network
configurations. We consider the setting where, in addition to
being reliably transmitted, each message is required to be kept
information-theoretically secure from the unintended receiver. We
show that the sum s.d.o.f. can only take one of five possible
values: 0, 2/3, 1, 3/2, 2, for all network configurations. To
determine the sum s.d.o.f., we divide the class of two-unicast
layered networks into several sub-classes, and propose an
achievable scheme based on the specific structure of the networks
in each sub-class. Our achievable schemes are based on real
interference alignment, cooperative jamming, interference
neutralization and cooperative jamming neutralization techniques.
Next, we consider the Gaussian wiretap channel with M helpers,
where no eavesdropper channel state information (CSI) is
available at the legitimate entities. The exact s.d.o.f. of the
Gaussian wiretap channel with M helpers with perfect CSI at the
transmitters has been shown to be M/(M+1). One of the key
ingredients of our optimal achievable scheme with CSI is to align
cooperative jamming signals with the information symbols at the
eavesdropper to limit the information leakage rate. This requires
perfect eavesdropper CSI at the transmitters. We propose a new
achievable scheme in which cooperative jamming signals span the
entire space of the eavesdropper, but are not exactly aligned
with the information symbols. We show that this scheme achieves
the same s.d.o.f. of M/(M+1) but does not require any
eavesdropper CSI; the transmitters blindly cooperative jam the
eavesdropper.
Then, we study the separability of the parallel MAC wiretap
channel. Separability, when exists, is useful as it enables us to
code separately over parallel channels, and still achieve the
optimum overall performance. It is well-known that the parallel
single-user channel, parallel MAC and parallel BC are all
separable, however, the parallel IC is not separable in general.
In this dissertation, we show that, while MAC is separable MAC
wiretap channel is not separable in general. We prove this via a
specific linear deterministic MAC wiretap channel. We then show
that even the Gaussian MAC wiretap channel is inseparable in
general. Finally, we show that, when the channel gains are drawn
from continuous distributions, and when the s.d.o.f. region is
considered, then the Gaussian MAC wiretap channel is almost
surely separable.
Finally, we study the two-user one-sided interference channel
with confidential messages. In this interference channel, in
addition to the usual selfishness of the users, the relationship
between the two pairs of users is further adversarial in the
sense of both receivers' desires to eavesdrop on the
communication of the other pair. We develop a game-theoretic
model to study the information-theoretic secure communications in
this setting. We first start with a game-theoretic model where
each pair's payoff is their own secrecy rate. The analysis of the
binary deterministic interference channel with this payoff
