arXiv subjects

Frédérique Oggier

Publications and source records attributed to Frédérique Oggier.

27 records · Page 2Linked to original sources

arXiv2013

Lattice Codes for the Wiretap Gaussian Channel: Construction and Analysis

We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN channel. We propose a coding strategy based on lattice coset encoding. We analyze Eve's probability of decoding, from which we define the secrecy gain as a design criterion for wiretap lattice codes, expressed in terms of the lattice theta series, which characterizes Eve's confusion as a function of the channel parameters. The secrecy gain is studied for even unimodular lattices, and an asymptotic analysis shows that it grows exponentially in the dimension of the lattice. Examples of wiretap lattice codes are given. Interestingly, minimizing Eve's probability of error involves the same optimization of the theta series as does the flatness factor, another newly defined code design that characterizes lattice codes that achieve strong secrecy.

cs.IT↗

arXiv2012

On Abelian Group Representability of Finite Groups

A set of quasi-uniform random variables $X_1,...,X_n$ may be generated from a finite group $G$ and $n$ of its subgroups, with the corresponding entropic vector depending on the subgroup structure of $G$. It is known that the set of entropic vectors obtained by considering arbitrary finite groups is much richer than the one provided just by abelian groups. In this paper, we start to investigate in more detail different families of non-abelian groups with respect to the entropic vectors they yield. In particular, we address the question of whether a given non-abelian group $G$ and some fixed subgroups $G_1,...,G_n$ end up giving the same entropic vector as some abelian group $A$ with subgroups $A_1,...,A_n$, in which case we say that $(A, A_1,..., A_n)$ represents $(G, G_1, ..., G_n)$. If for any choice of subgroups $G_1,...,G_n$, there exists some abelian group $A$ which represents $G$, we refer to $G$ as being abelian (group) representable for $n$. We completely characterize dihedral, quasi-dihedral and dicyclic groups with respect to their abelian representability, as well as the case when $n=2$, for which we show a group is abelian representable if and only if it is nilpotent. This problem is motivated by understanding non-linear coding strategies for network coding, and network information theory capacity regions.

math.GR↗

arXiv2012

An Empirical Study of the Repair Performance of Novel Coding Schemes for Networked Distributed Storage Systems

Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through repair mechanisms, which may entail large network resource overheads. In recent years, several novel codes tailor-made for distributed storage have been proposed to optimize storage overhead and repair, such as Regenerating Codes that minimize the per repair traffic, or Self-Repairing Codes which minimize the number of nodes contacted per repair. Existing studies of these coding techniques are however predominantly theoretical, under the simplifying assumption that only one object is stored. They ignore many practical issues that real systems must address, such as data placement, de/correlation of multiple stored objects, or the competition for limited network resources when multiple objects are repaired simultaneously. This paper empirically studies the repair performance of these novel storage centric codes with respect to classical erasure codes by simulating realistic scenarios and exploring the interplay of code parameters, failure characteristics and data placement with respect to the trade-offs of bandwidth usage and speed of repairs.

cs.DC↗

arXiv2012

A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions

Lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to transmissions between a transmitter and a legitimate receiver, is considered. A new lattice invariant called the secrecy gain is used as a code design criterion for wiretap lattice codes since it was shown to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, a formula for the secrecy gain of unimodular lattices is derived. Secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension n, 16 \leq n \leq 23 are computed, covering the 4 extremal odd unimodular lattices and all the 111 nonextremal unimodular lattices (both odd and even) providing thus a classification of the best wiretap lattice codes coming from unimodular lattices in dimension n, 8 < n \leq 23. Finally, to permit lattice encoding via Construction A, the corresponding error correction codes are determined.

math.NT↗

arXiv2011

Byzantine Fault Tolerance of Regenerating Codes

Recent years have witnessed a slew of coding techniques custom designed for networked storage systems. Network coding inspired regenerating codes are the most prolifically studied among these new age storage centric codes. A lot of effort has been invested in understanding the fundamental achievable trade-offs of storage and bandwidth usage to maintain redundancy in presence of different models of failures, showcasing the efficacy of regenerating codes with respect to traditional erasure coding techniques. For practical usability in open and adversarial environments, as is typical in peer-to-peer systems, we need however not only resilience against erasures, but also from (adversarial) errors. In this paper, we study the resilience of generalized regenerating codes (supporting multi-repairs, using collaboration among newcomers) in the presence of two classes of Byzantine nodes, relatively benign selfish (non-cooperating) nodes, as well as under more active, malicious polluting nodes. We give upper bounds on the resilience capacity of regenerating codes, and show that the advantages of collaborative repair can turn to be detrimental in the presence of Byzantine nodes. We further exhibit that system mechanisms can be combined with regenerating codes to mitigate the effect of rogue nodes.

cs.DC↗

arXiv2011

A family of fast-decodable MIDO codes from crossed-product algebras over Q

Multiple Input Double Output (MIDO) asymmetric space-time codes for 4 transmit antennas and 2 receive antennas can be employed in the downlink from base stations to portable devices. Previous MIDO code constructions with low Maximum Likelihood (ML) decoding complexity, full diversity and the non-vanishing determinant (NVD) property are mostly based on cyclic division algebras. In this paper, a new family of MIDO codes with the NVD property based on crossed-product algebras over Q is introduced. Fast decodability follows naturally from the structure of the codewords which consist of four generalized Alamouti blocks. The associated ML complexity order is the lowest known for full-rate MIDO codes (O(M^{10}) instead of O(M^{16}) with respect to the real constellation size M). Numerical simulations show that these codes have a performance from comparable up to 1dB gain compared to the best known MIDO code with the same complexity.

cs.IT↗

arXiv2010

Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 x 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes. Several explicit constructions are presented and shown to have excellent performance through computer simulations.

cs.IT↗

arXiv2010

Secrecy Gain: a Wiretap Lattice Code Design

We propose the notion of secrecy gain as a code design criterion for wiretap lattice codes to be used over an additive white Gaussian noise channel. Our analysis relies on the error probabilites of both the legitimate user and the eavesdropper. We focus on geometrical properties of lattices, described by their theta series, to characterize good wiretap codes.

cs.IT↗

arXiv2007

The Secrecy Capacity of the MIMO Wiretap Channel

We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers.

cs.IT↗