47 research outputs found
Learning End-to-End Codes for the BPSK-constrained Gaussian Wiretap Channel
Finite-length codes are learned for the Gaussian wiretap channel in an
end-to-end manner assuming that the communication parties are equipped with
deep neural networks (DNNs), and communicate through binary phase-shift keying
(BPSK) modulation scheme. The goal is to find codes via DNNs which allow a pair
of transmitter and receiver to communicate reliably and securely in the
presence of an adversary aiming at decoding the secret messages. Following the
information-theoretic secrecy principles, the security is evaluated in terms of
mutual information utilizing a deep learning tool called MINE (mutual
information neural estimation). System performance is evaluated for different
DNN architectures, designed based on the existing secure coding schemes, at the
transmitter. Numerical results demonstrate that the legitimate parties can
indeed establish a secure transmission in this setting as the learned codes
achieve points on almost the boundary of the equivocation region
An Overview of Physical Layer Security with Finite-Alphabet Signaling
Providing secure communications over the physical layer with the objective of
achieving perfect secrecy without requiring a secret key has been receiving
growing attention within the past decade. The vast majority of the existing
studies in the area of physical layer security focus exclusively on the
scenarios where the channel inputs are Gaussian distributed. However, in
practice, the signals employed for transmission are drawn from discrete signal
constellations such as phase shift keying and quadrature amplitude modulation.
Hence, understanding the impact of the finite-alphabet input constraints and
designing secure transmission schemes under this assumption is a mandatory step
towards a practical implementation of physical layer security. With this
motivation, this article reviews recent developments on physical layer security
with finite-alphabet inputs. We explore transmit signal design algorithms for
single-antenna as well as multi-antenna wiretap channels under different
assumptions on the channel state information at the transmitter. Moreover, we
present a review of the recent results on secure transmission with discrete
signaling for various scenarios including multi-carrier transmission systems,
broadcast channels with confidential messages, cognitive multiple access and
relay networks. Throughout the article, we stress the important behavioral
differences of discrete versus Gaussian inputs in the context of the physical
layer security. We also present an overview of practical code construction over
Gaussian and fading wiretap channels, and we discuss some open problems and
directions for future research.Comment: Submitted to IEEE Communications Surveys & Tutorials (1st Revision
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
This paper provides a comprehensive review of the domain of physical layer
security in multiuser wireless networks. The essential premise of
physical-layer security is to enable the exchange of confidential messages over
a wireless medium in the presence of unauthorized eavesdroppers without relying
on higher-layer encryption. This can be achieved primarily in two ways: without
the need for a secret key by intelligently designing transmit coding
strategies, or by exploiting the wireless communication medium to develop
secret keys over public channels. The survey begins with an overview of the
foundations dating back to the pioneering work of Shannon and Wyner on
information-theoretic security. We then describe the evolution of secure
transmission strategies from point-to-point channels to multiple-antenna
systems, followed by generalizations to multiuser broadcast, multiple-access,
interference, and relay networks. Secret-key generation and establishment
protocols based on physical layer mechanisms are subsequently covered.
Approaches for secrecy based on channel coding design are then examined, along
with a description of inter-disciplinary approaches based on game theory and
stochastic geometry. The associated problem of physical-layer message
authentication is also introduced briefly. The survey concludes with
observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with
arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials,
201
Construction of lattices for communications and security
In this thesis, we propose a new class of lattices based on polar codes, namely polar lattices. Polar lattices enjoy explicit construction and provable goodness for the additive white Gaussian noise (AWGN) channel, \textit{i.e.}, they are \emph{AWGN-good} lattices, in the sense that the error probability (for infinite lattice coding) vanishes for any fixed volume-to-noise ratio (VNR) greater than . Our construction is based on the multilevel approach of Forney \textit{et al.}, where on each level we construct a capacity-achieving polar code. We show the component polar codes are naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We present a more precise analysis of the VNR of the resultant lattice, which is upper-bounded in terms of the flatness factor and the capacity losses of the component codes. The proposed polar lattices are efficiently decodable by using multi-stage decoding. Design examples are presented to demonstrate the superior performance of polar lattices.
However, there is no infinite lattice coding in the practical applications. We need to apply the power constraint on the polar lattices which generates the polar lattice codes. We prove polar lattice codes can achieve the capacity \frac{1}{2}\log(1+\SNR) of the power-constrained AWGN channel with a novel shaping scheme. The main idea is that by implementing the lattice Gaussian distribution over the AWGN-good polar lattices, the maximum error-free transmission rate of the resultant coding scheme can be arbitrarily close to the capacity \frac{1}{2}\log(1+\SNR). The shaping technique is based on discrete lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. Then it is straightforward to employ multilevel asymmetric polar codes which is a combination of polar lossless source coding and polar channel coding. The construction of polar codes for an asymmetric channel can be converted to that for a related symmetric channel, and it turns out that this symmetric channel is equivalent to an minimum mean-square error (MMSE) scaled channel in lattice coding in terms of polarization, which eventually simplifies our coding design.
Finally, we investigate the application of polar lattices in physical layer security. Polar lattice codes are proved to be able to achieve the strong secrecy capacity of the Mod- AWGN wiretap channel. The Mod- assumption was due to the fact that a practical shaping scheme aiming to achieve the optimum shaping gain was missing. In this thesis, we use our shaping scheme and extend polar lattice coding to the Gaussian wiretap channel. By employing the polar coding technique for asymmetric channels, we manage to construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. Then we prove the resultant wiretap coding scheme can achieve the strong secrecy capacity for the Gaussian wiretap channel.Open Acces
Polar codes for degradable quantum channels
Channel polarization is a phenomenon in which a particular recursive encoding
induces a set of synthesized channels from many instances of a memoryless
channel, such that a fraction of the synthesized channels becomes near perfect
for data transmission and the other fraction becomes near useless for this
task. Mahdavifar and Vardy have recently exploited this phenomenon to construct
codes that achieve the symmetric private capacity for private data transmission
over a degraded wiretap channel. In the current paper, we build on their work
and demonstrate how to construct quantum wiretap polar codes that achieve the
symmetric private capacity of a degraded quantum wiretap channel with a
classical eavesdropper. Due to the Schumacher-Westmoreland correspondence
between quantum privacy and quantum coherence, we can construct quantum polar
codes by operating these quantum wiretap polar codes in superposition, much
like Devetak's technique for demonstrating the achievability of the coherent
information rate for quantum data transmission. Our scheme achieves the
symmetric coherent information rate for quantum channels that are degradable
with a classical environment. This condition on the environment may seem
restrictive, but we show that many quantum channels satisfy this criterion,
including amplitude damping channels, photon-detected jump channels, dephasing
channels, erasure channels, and cloning channels. Our quantum polar coding
scheme has the desirable properties of being channel-adapted and symmetric
capacity-achieving along with having an efficient encoder, but we have not
demonstrated that the decoding is efficient. Also, the scheme may require
entanglement assistance, but we show that the rate of entanglement consumption
vanishes in the limit of large blocklength if the channel is degradable with
classical environment.Comment: 12 pages, 1 figure; v2: IEEE format, minor changes including new
figure; v3: minor changes, accepted for publication in IEEE Transactions on
Information Theor
Randomized Convolutional Codes for the Wiretap Channel
We study application of convolutional codes to the randomized encoding scheme introduced by Wyner as a way of confusing the eavesdropper over a wiretap channel. We describe optimal and practical sub-optimal decoders for the main and the eavesdropper's channels, and estimate the security gap, which is used as the main metric. The sub-optimal decoder works based on the trellis of the code generated by a convolutional code and its dual, where one encodes the data bits and the other encodes the random bits. By developing a code design metric, we describe how these two generators should be selected for optimal performance over a Gaussian wiretap channel. We also propose application of serially concatenated convolutional codes to this setup so as to reduce the resulting security gaps. Furthermore, we provide an analytical characterization of the system performance by extending existing lower and upper bounds for coded systems to the current randomized convolutional coding scenario. We illustrate our findings via extensive simulations and numerical examples, which show that the newly proposed coding scheme can outperform the other existing methods in the literature in terms of security gap. © 1972-2012 IEEE
Confident decoding with GRAND
We establish that during the execution of any Guessing Random Additive Noise
Decoding (GRAND) algorithm, an interpretable, useful measure of decoding
confidence can be evaluated. This measure takes the form of a log-likelihood
ratio (LLR) of the hypotheses that, should a decoding be found by a given
query, the decoding is correct versus its being incorrect. That LLR can be used
as soft output for a range of applications and we demonstrate its utility by
showing that it can be used to confidently discard likely erroneous decodings
in favor of returning more readily managed erasures. As an application, we show
that feature can be used to compromise the physical layer security of short
length wiretap codes by accurately and confidently revealing a proportion of a
communication when code-rate is above capacity
An Overview of Physical Layer Security with Finite Alphabet Signaling
Providing secure communications over the physical layer with the objective of achieving secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step towards a practical implementation of physical layer security. With this motivation, this article reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and discuss some open problems and directions for future research
How to Achieve the Capacity of Asymmetric Channels
We survey coding techniques that enable reliable transmission at rates that
approach the capacity of an arbitrary discrete memoryless channel. In
particular, we take the point of view of modern coding theory and discuss how
recent advances in coding for symmetric channels help provide more efficient
solutions for the asymmetric case. We consider, in more detail, three basic
coding paradigms.
The first one is Gallager's scheme that consists of concatenating a linear
code with a non-linear mapping so that the input distribution can be
appropriately shaped. We explicitly show that both polar codes and spatially
coupled codes can be employed in this scenario. Furthermore, we derive a
scaling law between the gap to capacity, the cardinality of the input and
output alphabets, and the required size of the mapper.
The second one is an integrated scheme in which the code is used both for
source coding, in order to create codewords distributed according to the
capacity-achieving input distribution, and for channel coding, in order to
provide error protection. Such a technique has been recently introduced by
Honda and Yamamoto in the context of polar codes, and we show how to apply it
also to the design of sparse graph codes.
The third paradigm is based on an idea of B\"ocherer and Mathar, and
separates the two tasks of source coding and channel coding by a chaining
construction that binds together several codewords. We present conditions for
the source code and the channel code, and we describe how to combine any source
code with any channel code that fulfill those conditions, in order to provide
capacity-achieving schemes for asymmetric channels. In particular, we show that
polar codes, spatially coupled codes, and homophonic codes are suitable as
basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published
in IEEE Trans. Inform. Theor