285 research outputs found
Polar Coding for Achieving the Capacity of Marginal Channels in Nonbinary-Input Setting
Achieving information-theoretic security using explicit coding scheme in
which unlimited computational power for eavesdropper is assumed, is one of the
main topics is security consideration. It is shown that polar codes are
capacity achieving codes and have a low complexity in encoding and decoding. It
has been proven that polar codes reach to secrecy capacity in the binary-input
wiretap channels in symmetric settings for which the wiretapper's channel is
degraded with respect to the main channel. The first task of this paper is to
propose a coding scheme to achieve secrecy capacity in asymmetric
nonbinary-input channels while keeping reliability and security conditions
satisfied. Our assumption is that the wiretap channel is stochastically
degraded with respect to the main channel and message distribution is
unspecified. The main idea is to send information set over good channels for
Bob and bad channels for Eve and send random symbols for channels that are good
for both. In this scheme the frozen vector is defined over all possible choices
using polar codes ensemble concept. We proved that there exists a frozen vector
for which the coding scheme satisfies reliability and security conditions. It
is further shown that uniform distribution of the message is the necessary
condition for achieving secrecy capacity.Comment: Accepted to be published in "51th Conference on Information Sciences
and Systems", Baltimore, Marylan
Polar Coding for Secure Transmission and Key Agreement
Wyner's work on wiretap channels and the recent works on information
theoretic security are based on random codes. Achieving information theoretical
security with practical coding schemes is of definite interest. In this note,
the attempt is to overcome this elusive task by employing the polar coding
technique of Ar{\i}kan. It is shown that polar codes achieve non-trivial
perfect secrecy rates for binary-input degraded wiretap channels while enjoying
their low encoding-decoding complexity. In the special case of symmetric main
and eavesdropper channels, this coding technique achieves the secrecy capacity.
Next, fading erasure wiretap channels are considered and a secret key agreement
scheme is proposed, which requires only the statistical knowledge of the
eavesdropper channel state information (CSI). The enabling factor is the
creation of advantage over Eve, by blindly using the proposed scheme over each
fading block, which is then exploited with privacy amplification techniques to
generate secret keys.Comment: Proceedings of the 21st Annual IEEE International Symposium on
Personal, Indoor, and Mobile Radio Communications (PIMRC 2010), Sept. 2010,
Istanbul, Turke
Achieving Secrecy Capacity of the Gaussian Wiretap Channel with Polar Lattices
In this work, an explicit wiretap coding scheme based on polar lattices is
proposed to achieve the secrecy capacity of the additive white Gaussian noise
(AWGN) wiretap channel. Firstly, polar lattices are used to construct
secrecy-good lattices for the mod- Gaussian wiretap channel. Then we
propose an explicit shaping scheme to remove this mod- front end and
extend polar lattices to the genuine Gaussian wiretap channel. The shaping
technique is based on the lattice Gaussian distribution, which leads to a
binary asymmetric channel at each level for the multilevel lattice codes. By
employing the asymmetric polar coding technique, we construct an AWGN-good
lattice and a secrecy-good lattice with optimal shaping simultaneously. As a
result, the encoding complexity for the sender and the decoding complexity for
the legitimate receiver are both O(N logN log(logN)). The proposed scheme is
proven to be semantically secure.Comment: Submitted to IEEE Trans. Information Theory, revised. This is the
authors' own version of the pape
On the Construction of Polar Codes for Achieving the Capacity of Marginal Channels
Achieving security against adversaries with unlimited computational power is
of great interest in a communication scenario. Since polar codes are capacity
achieving codes with low encoding-decoding complexity and they can approach
perfect secrecy rates for binary-input degraded wiretap channels in symmetric
settings, they are investigated extensively in the literature recently. In this
paper, a polar coding scheme to achieve secrecy capacity in non-symmetric
binary input channels is proposed. The proposed scheme satisfies security and
reliability conditions. The wiretap channel is assumed to be stochastically
degraded with respect to the legitimate channel and message distribution is
uniform. The information set is sent over channels that are good for Bob and
bad for Eve. Random bits are sent over channels that are good for both Bob and
Eve. A frozen vector is chosen randomly and is sent over channels bad for both.
We prove that there exists a frozen vector for which the coding scheme
satisfies reliability and security conditions and approaches the secrecy
capacity. We further empirically show that in the proposed scheme for
non-symmetric binary-input discrete memoryless channels, the equivocation rate
achieves its upper bound in the whole capacity-equivocation region
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
A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead
Physical layer security which safeguards data confidentiality based on the
information-theoretic approaches has received significant research interest
recently. The key idea behind physical layer security is to utilize the
intrinsic randomness of the transmission channel to guarantee the security in
physical layer. The evolution towards 5G wireless communications poses new
challenges for physical layer security research. This paper provides a latest
survey of the physical layer security research on various promising 5G
technologies, including physical layer security coding, massive multiple-input
multiple-output, millimeter wave communications, heterogeneous networks,
non-orthogonal multiple access, full duplex technology, etc. Technical
challenges which remain unresolved at the time of writing are summarized and
the future trends of physical layer security in 5G and beyond are discussed.Comment: To appear in IEEE Journal on Selected Areas in Communication
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