92 research outputs found
Lecture Notes on Network Information Theory
These lecture notes have been converted to a book titled Network Information
Theory published recently by Cambridge University Press. This book provides a
significantly expanded exposition of the material in the lecture notes as well
as problems and bibliographic notes at the end of each chapter. The authors are
currently preparing a set of slides based on the book that will be posted in
the second half of 2012. More information about the book can be found at
http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of
the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/
Secure Multiterminal Source Coding with Side Information at the Eavesdropper
The problem of secure multiterminal source coding with side information at
the eavesdropper is investigated. This scenario consists of a main encoder
(referred to as Alice) that wishes to compress a single source but
simultaneously satisfying the desired requirements on the distortion level at a
legitimate receiver (referred to as Bob) and the equivocation rate --average
uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed
the presence of a (public) rate-limited link between Alice and Bob. In this
setting, Eve perfectly observes the information bits sent by Alice to Bob and
has also access to a correlated source which can be used as side information. A
second encoder (referred to as Charlie) helps Bob in estimating Alice's source
by sending a compressed version of its own correlated observation via a
(private) rate-limited link, which is only observed by Bob. For instance, the
problem at hands can be seen as the unification between the Berger-Tung and the
secure source coding setups. Inner and outer bounds on the so called
rates-distortion-equivocation region are derived. The inner region turns to be
tight for two cases: (i) uncoded side information at Bob and (ii) lossless
reconstruction of both sources at Bob --secure distributed lossless
compression. Application examples to secure lossy source coding of Gaussian and
binary sources in the presence of Gaussian and binary/ternary (resp.) side
informations are also considered. Optimal coding schemes are characterized for
some cases of interest where the statistical differences between the side
information at the decoders and the presence of a non-zero distortion at Bob
can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table
Hybrid Digital/Analog Schemes for Secure Transmission with Side Information
Recent results on source-channel coding for secure transmission show that
separation holds in several cases under some less-noisy conditions. However, it
has also been proved through a simple counterexample that pure analog schemes
can be optimal and hence outperform digital ones. According to these
observations and assuming matched-bandwidth, we present a novel hybrid
digital/analog scheme that aims to gather the advantages of both digital and
analog ones. In the quadratic Gaussian setup when side information is only
present at the eavesdropper, this strategy is proved to be optimal.
Furthermore, it outperforms both digital and analog schemes and cannot be
achieved via time-sharing. An application example to binary symmetric sources
with side information is also investigated.Comment: 11 pages, 6 figures, 1 table. To be presented at ITW 201
Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities
This monograph presents a unified treatment of single- and multi-user
problems in Shannon's information theory where we depart from the requirement
that the error probability decays asymptotically in the blocklength. Instead,
the error probabilities for various problems are bounded above by a
non-vanishing constant and the spotlight is shone on achievable coding rates as
functions of the growing blocklengths. This represents the study of asymptotic
estimates with non-vanishing error probabilities.
In Part I, after reviewing the fundamentals of information theory, we discuss
Strassen's seminal result for binary hypothesis testing where the type-I error
probability is non-vanishing and the rate of decay of the type-II error
probability with growing number of independent observations is characterized.
In Part II, we use this basic hypothesis testing result to develop second- and
sometimes, even third-order asymptotic expansions for point-to-point
communication. Finally in Part III, we consider network information theory
problems for which the second-order asymptotics are known. These problems
include some classes of channels with random state, the multiple-encoder
distributed lossless source coding (Slepian-Wolf) problem and special cases of
the Gaussian interference and multiple-access channels. Finally, we discuss
avenues for further research.Comment: Further comments welcom
A Unified Approach for Network Information Theory
In this paper, we take a unified approach for network information theory and
prove a coding theorem, which can recover most of the achievability results in
network information theory that are based on random coding. The final
single-letter expression has a very simple form, which was made possible by
many novel elements such as a unified framework that represents various network
problems in a simple and unified way, a unified coding strategy that consists
of a few basic ingredients but can emulate many known coding techniques if
needed, and new proof techniques beyond the use of standard covering and
packing lemmas. For example, in our framework, sources, channels, states and
side information are treated in a unified way and various constraints such as
cost and distortion constraints are unified as a single joint-typicality
constraint.
Our theorem can be useful in proving many new achievability results easily
and in some cases gives simpler rate expressions than those obtained using
conventional approaches. Furthermore, our unified coding can strictly
outperform existing schemes. For example, we obtain a generalized
decode-compress-amplify-and-forward bound as a simple corollary of our main
theorem and show it strictly outperforms previously known coding schemes. Using
our unified framework, we formally define and characterize three types of
network duality based on channel input-output reversal and network flow
reversal combined with packing-covering duality.Comment: 52 pages, 7 figures, submitted to IEEE Transactions on Information
theory, a shorter version will appear in Proc. IEEE ISIT 201
Information-theoretic Secrecy in Multi-user Channels
Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective.
First, we study the Gaussian multiple-input multiple-output (MIMO)
wiretap channel. In this channel, the transmitter sends a common
message to both the legitimate user and the eavesdropper. In addition
to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. 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.
Next, we study the secure broadcasting problem, where a
transmitter wants to have secure communication with multiple
legitimate users in the presence of an external eavesdropper. We study
several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region.
Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message.
Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the
Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement
technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region.
Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO
channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel.
Next, we focus on the multiple access wiretap (MAC-WT) channel
whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where
each user's link to the legitimate receiver is stronger than its link to the
eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable
region in an n-letter form. We evaluate a looser version of our
outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT.
Then, we investigate the effects of user cooperation on the secrecy of
broadcast channels by considering the cooperative relay broadcast
channel (CRBC). We propose an achievable scheme that combines
Marton's coding scheme for broadcast channels and Cover and El
Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive
secrecy rates, which is not possible for scalar Gaussian broadcast
channels without cooperation.
We further investigate the effects of user cooperation on secrecy
by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC.
We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF.
Next, we study the two-user one-eavesdropper discrete memoryless
compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel,
and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users.
Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and
the transmitter sends a confidential message to each group of
legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group.
Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading,
both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain.
Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where
both the legitimate user and the eavesdropper have vector Gaussian
side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation.
Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We
investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme
Secure Lossless Compression with Side Information
Secure data compression in the presence of side information at both a
legitimate receiver and an eavesdropper is explored. A noise-free, limited rate
link between the source and the receiver, whose output can be perfectly
observed by the eavesdropper, is assumed. As opposed to the wiretap channel
model, in which secure communication can be established by exploiting the noise
in the channel, here the existence of side information at the receiver is used.
Both coded and uncoded side information are considered. In the coded side
information scenario, inner and outer bounds on the compression-equivocation
rate region are given. In the uncoded side information scenario, the
availability of the legitimate receiver's and the eavesdropper's side
information at the encoder is considered, and the compression-equivocation rate
region is characterized for these cases. It is shown that the side information
at the encoder can increase the equivocation rate at the eavesdropper. Hence,
the side information at the encoder is shown to be useful in terms of security;
this is in contrast with the pure lossless data compression case where side
information at the encoder would not help.Comment: To appear in the Proceedings of the 2008 IEEE Information Theory
Workshop, Porto, Portugal, May 5-9, 200
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