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Frederique Oggier

Publications and source records attributed to Frederique Oggier.

18 recordsLinked to original sources
arXiv2024

Constructions of non-Generalized Reed-Solomon MDS codes

Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes that are MDS yet not generalized Reed-Solomon codes, called non-generalized Reed-Solomon MDS codes, started with the work by Roth and Lemple (1989), where the first examples where exhibited. It then gained traction thanks to the work by Beelen (2017), who introduced twisted Reed-Solomon codes, and showed that families of such codes are non-generalized Reed-Solomon MDS codes. Finding non-generalized Reed-Solomon MDS codes is naturally motivated by the classification of MDS codes. In this paper, we provide a generic construction of MDS codes, yielding infinitely many examples. We then explicit families of non-generalized Reed-Solomon MDS codes. Finally we position some of the proposed codes with respect to generalized twisted Reed-Solomon codes, and provide new view points on this family of codes.

cs.IT↗
arXiv2021

A Modular Framework for Centrality and Clustering in Complex Networks

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important such network analysis techniques, namely, centrality and clustering. An information-flow based model is adopted for clustering, which itself builds upon an information theoretic measure for computing centrality. Our principal contributions include a generalized model of Markov entropic centrality with the flexibility to tune the importance of node degrees, edge weights and directions, with a closed-form asymptotic analysis. It leads to a novel two-stage graph clustering algorithm. The centrality analysis helps reason about the suitability of our approach to cluster a given graph, and determine `query' nodes, around which to explore local community structures, leading to an agglomerative clustering mechanism. The entropic centrality computations are amortized by our clustering algorithm, making it computationally efficient: compared to prior approaches using Markov entropic centrality for clustering, our experiments demonstrate multiple orders of magnitude of speed-up. Our clustering algorithm naturally inherits the flexibility to accommodate edge directionality, as well as different interpretations and interplay between edge weights and node degrees. Overall, this paper thus not only makes significant theoretical and conceptual contributions, but also translates the findings into artifacts of practical relevance, yielding new, effective and scalable centrality computations and graph clustering algorithms, whose efficacy has been validated through extensive benchmarking experiments.

cs.SI↗
arXiv2015

On Group Violations of Inequalities in five Subgroups

We consider ten linear rank inequalities, which always hold for ranks of vector subspaces, and look at them as group inequalities. We prove that groups of order pq, for p,q two distinct primes, always satisfy these ten group inequalities. We give partial results for groups of order $p^2q$, and find that the symmetric group $S_4$ is the smallest group that yield violations, for two among the ten group inequalities.

cs.IT↗
arXiv2013

Iterated Space-Time Code Constructions from Cyclic Algebras

We propose a full-rate iterated space-time code construction, to design 2n-dimensional codes from n-dimensional cyclic algebra based codes. We give a condition to determine whether the resulting codes satisfy the full-diversity property, and study their maximum likelihood decoding complexity with respect to sphere decoding. Particular emphasis is given to the cases n = 2, sometimes referred to as MIDO (multiple input double output) codes, and n = 3. In the process, we derive an interesting way of obtaining division algebras, and study their center and maximal subfield.

cs.IT↗
arXiv2013

An Overview of Codes Tailor-made for Better Repairability in Networked Distributed Storage Systems

The continuously increasing amount of digital data generated by today's society asks for better storage solutions. This survey looks at a new generation of coding techniques designed specifically for the needs of distributed networked storage systems, trying to reach the best compromise among storage space efficiency, fault tolerance, and maintenance overheads. Four families of codes tailor-made for distributed settings, namely - pyramid, hierarchical, regenerating and self-repairing codes - are presented at a high level, emphasizing the main ideas behind each of these codes, and discussing their pros and cons, before concluding with a quantitative comparison among them. This survey deliberately excluded technical details for the codes, nor does it provide an exhaustive summary of the numerous works. Instead, it provides an overview of the major code families in a manner easily accessible to a broad audience, by presenting the big picture of advances in coding techniques for distributed storage solutions.

cs.DC↗
arXiv2013

Explicit Constructions of Quasi-Uniform Codes from Groups

We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian groups. Potentials applications comprise the design of almost affine codes and non-linear network codes.

math.GR↗
arXiv2012

Quotients of Orders in Cyclic Algebras and Space-Time Codes

Let $F$ be a number field with ring of integers $\Oc_F$ and $\Dc$ a division $F$-algebra with a maximal cyclic subfield $K$. We study rings occurring as quotients of a natural $\Oc_F$-order $Λ$ in $\Dc$ by two-sided ideals. We reduce the problem to studying the ideal structure of $Λ/\qf^sΛ$, where $\qf$ is a prime ideal in $\Oc_F$, $s\geq 1$. We study the case where $\qf$ remains unramified in $K$, both when $s=1$ and $s>1$. This work is motivated by its applications to space-time coded modulation.

cs.IT↗
arXiv2012

RapidRAID: Pipelined Erasure Codes for Fast Data Archival in Distributed Storage Systems

To achieve reliability in distributed storage systems, data has usually been replicated across different nodes. However the increasing volume of data to be stored has motivated the introduction of erasure codes, a storage efficient alternative to replication, particularly suited for archival in data centers, where old datasets (rarely accessed) can be erasure encoded, while replicas are maintained only for the latest data. Many recent works consider the design of new storage-centric erasure codes for improved repairability. In contrast, this paper addresses the migration from replication to encoding: traditionally erasure coding is an atomic operation in that a single node with the whole object encodes and uploads all the encoded pieces. Although large datasets can be concurrently archived by distributing individual object encodings among different nodes, the network and computing capacity of individual nodes constrain the archival process due to such atomicity. We propose a new pipelined coding strategy that distributes the network and computing load of single-object encodings among different nodes, which also speeds up multiple object archival. We further present RapidRAID codes, an explicit family of pipelined erasure codes which provides fast archival without compromising either data reliability or storage overheads. Finally, we provide a real implementation of RapidRAID codes and benchmark its performance using both a cluster of 50 nodes and a set of Amazon EC2 instances. Experiments show that RapidRAID codes reduce a single object's coding time by up to 90%, while when multiple objects are encoded concurrently, the reduction is up to 20%.

cs.DC↗
arXiv2011

Homomorphic Self-repairing Codes for Agile Maintenance of Distributed Storage Systems

Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in terms of storage space and maintenance bandwidth requirements. Erasure codes, originally designed for communication over lossy channels, provide a storage efficient alternative to replication based redundancy, however entailing high communication overhead for maintenance, when some of the encoded fragments need to be replenished in news ones after failure of some storage devices. We propose as an alternative a new family of erasure codes called self-repairing codes (SRC) taking into account the peculiarities of distributed storage systems, specifically the maintenance process. SRC has the following salient features: (a) encoded fragments can be repaired directly from other subsets of encoded fragments by downloading less data than the size of the complete object, ensuring that (b) a fragment is repaired from a fixed number of encoded fragments, the number depending only on how many encoded blocks are missing and independent of which specific blocks are missing. This paper lays the foundations by defining the novel self-repairing codes, elaborating why the defined characteristics are desirable for distributed storage systems. Then homomorphic self-repairing codes (HSRC) are proposed as a concrete instance, whose various aspects and properties are studied and compared - quantitatively or qualitatively with respect to other codes including traditional erasure codes as well as other recent codes designed specifically for storage applications.

cs.DC↗
arXiv2011

Self-Repairing Codes for Distributed Storage - A Projective Geometric Construction

Self-Repairing Codes (SRC) are codes designed to suit the need of coding for distributed networked storage: they not only allow stored data to be recovered even in the presence of node failures, they also provide a repair mechanism where as little as two live nodes can be contacted to regenerate the data of a failed node. In this paper, we propose a new instance of self-repairing codes, based on constructions of spreads coming from projective geometry. We study some of their properties to demonstrate the suitability of these codes for distributed networked storage.

cs.DC↗
arXiv2010

Homophonic Coding Design for Communication Systems Employing the Encoding-Encryption Paradigm

This paper addresses the design of a dedicated homophonic coding for a class of communication systems which, in order to provide both reliability and security, first encode the data before encrypting it, which is referred to as the encoding-encryption paradigm. The considered systems employ error-correction coding for reliability, a stream cipher for encryption, and homophonic coding to enhance the protection of the key used in the stream cipher, on which relies the security of all the system transmissions. This paper presents a security evaluation of such systems from a computational complexity point of view, which serves as a source for establishing dedicated homophonic code design criteria. The security evaluation shows that the computational complexity of recovering the secret key, given all the information an attacker could gather during passive attacks he can mount, is lower bounded by the complexity of the related LPN (Learning Parity in Noise) problem in both the average and worst case. This gives guidelines to construct a dedicated homophonic encoder which maximizes the complexity of the underlying LPN problem for a given encoding overhead. Finally, this paper proposes a generic homophonic coding strategy that fulfills the proposed design criteria and thus both enhances security while minimizing the induced overhead.

cs.CR↗
arXiv2010

Lattice Code Design for the Rayleigh Fading Wiretap Channel

It has been shown recently that coding for the Gaussian Wiretap Channel can be done with nested lattices. A fine lattice intended to the legitimate user must be designed as a usual lattice code for the Gaussian Channel, while a coarse lattice is added to introduce confusion at the eavesdropper, whose theta series must be minimized. We present a design criterion for both the fine and coarse lattice to obtain wiretap lattice codes for the Rayleigh fading Wiretap Channel.

cs.IT↗
arXiv2010

Codes over Matrix Rings for Space-Time Coded Modulations

It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an appropriate outer code. When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding. More precisely, we take the quotient of the algebra by a two-sided ideal which leads to a finite alphabet for the outer code, with a cyclic algebra structure over a finite field or a finite ring. We show that the determinant criterion induces various metrics on the outer code, such as the Hamming and Bachoc distances. When n=2, partitioning the 2x2 Golden code by using an ideal above the prime 2 leads to consider codes over either M2(F_2) or M2(F_2[i]), both being non-commutative alphabets. Matrix rings of higher dimension, suitable for 3x3 and 4x4 perfect codes, give rise to more complex examples.

cs.IT↗
arXiv2010

An Information-Theoretic Analysis of the Security of Communication Systems Employing the Encoding-Encryption Paradigm

This paper proposes a generic approach for providing enhanced security to communication systems which encode their data for reliability before encrypting it through a stream cipher for security. We call this counter-intuitive technique the {\em encoding-encryption} paradigm, and use as motivating example the standard for mobile telephony GSM. The enhanced security is based on a dedicated homophonic or wire-tap channel coding that introduces pure randomness, combined with the randomness of the noise occurring over the communication channel. Security evaluation regarding recovery of the secret key employed in the keystream generator is done through an information theoretical approach. We show that with the aid of a dedicated wire-tap encoder, the amount of uncertainty that the adversary must face about the secret key given all the information he could gather during different passive or active attacks he can mount, is a decreasing function of the sample available for cryptanalysis. This means that the wire-tap encoder can indeed provide an information theoretical security level over a period of time, but after a large enough sample is collected the function tends to zero, entering a regime in which a computational security analysis is needed for estimation of the resistance against the secret key recovery.

cs.CR↗
arXiv2010

Self-repairing Homomorphic Codes for Distributed Storage Systems

Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to be replenished. Such overheads arise from the fundamental need to recreate (or keep separately) first a copy of the whole object before any individual encoded fragment can be generated and replenished. There has been recently intense interest to explore alternatives, most prominent ones being regenerating codes (RGC) and hierarchical codes (HC). We propose as an alternative a new family of codes to improve the maintenance process, which we call self-repairing codes (SRC), with the following salient features: (a) encoded fragments can be repaired directly from other subsets of encoded fragments without having to reconstruct first the original data, ensuring that (b) a fragment is repaired from a fixed number of encoded fragments, the number depending only on how many encoded blocks are missing and independent of which specific blocks are missing. These properties allow for not only low communication overhead to recreate a missing fragment, but also independent reconstruction of different missing fragments in parallel, possibly in different parts of the network. We analyze the static resilience of SRCs with respect to traditional erasure codes, and observe that SRCs incur marginally larger storage overhead in order to achieve the aforementioned properties. The salient SRC properties naturally translate to low communication overheads for reconstruction of lost fragments, and allow reconstruction with lower latency by facilitating repairs in parallel. These desirable properties make self-repairing codes a good and practical candidate for networked distributed storage systems.

cs.DC↗
arXiv2009

An Authentication Code against Pollution Attacks in Network Coding

Systems exploiting network coding to increase their throughput suffer greatly from pollution attacks which consist of injecting malicious packets in the network. The pollution attacks are amplified by the network coding process, resulting in a greater damage than under traditional routing. In this paper, we address this issue by designing an unconditionally secure authentication code suitable for multicast network coding. The proposed scheme is robust against pollution attacks from outsiders, as well as coalitions of malicious insiders. Intermediate nodes can verify the integrity and origin of the packets received without having to decode, and thus detect and discard the malicious messages in-transit that fail the verification. This way, the pollution is canceled out before reaching the destinations. We analyze the performance of the scheme in terms of both multicast throughput and goodput, and show the goodput gains. We also discuss applications to file distribution.

cs.IT↗
arXiv2009

On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane

We discuss certain types of cyclic and nearly cyclic interactions among N "point"-agents in the plane, leading to formations of interesting limiting geometric configurations. Cyclic pursuit and local averaging interactions have been analyzed in the context of multi-agent gathering. In this paper, we consider some nearly cyclic interactions that break symmetry leading to factor circulants rather than circulant interaction matrices.

cs.MA↗