Polarizzazione dei canali B-DMC e Polar Codes

Viene proposto un metodo, trattato dal punto di vista matematico, chiamato "polarizzazione dei canali". Lo scopo e' costruire sequenza di codici che raggiungano la capacita' di canale I(W) per ogni canale binario, discreto e privo di memoria. Il termine "polarizzazione" si riferisce al fatto che, partendo da un canale W, e' possibile creare N canali binari che siano asintoticamente divisi in due classi: perfetti o inutili. I codici che saranno inviati attraverso i canali "asintoticamente perfetti" prendono il nome di Polar Codes. Ne abbiamo analizzato codifica, decodifica e limite all'errore di blocco. Nell'ultima parte della tesi lo stesso metodo e' proposto per canali di input arbitrario

Fixed-Length Strong Coordination

We consider the problem of synthesizing joint distributions of signals and actions over noisy channels in the finite-length regime. For a fixed blocklength $n$ and an upper bound on the distance $\varepsilon$, a coding scheme is proposed such that the induced joint distribution is $\varepsilon$-close in $L^1$ distance to a target i.i.d. distribution. The set of achievable target distributions and rate for asymptotic strong coordination can be recovered from the main result of this paper by having $n$ that tends to infinity.Comment: 5 pages, 2 figure

Secure Strong Coordination

We consider a network of two nodes separated by a noisy channel, in which the source and its reconstruction have to be strongly coordinated, while simultaneously satisfying the strong secrecy condition with respect to an outside observer of the noisy channel. In the case of non-causal encoding and decoding, we propose a joint source-channel coding scheme for the secure strong coordination region. Furthermore, we provide a complete characterization of the secure strong coordination region when the decoder has to reliably reconstruct the source sequence and the legitimate channel is more capable than the channel of the eavesdropper

Inferential Privacy: From Impossibility to Database Privacy

We investigate the possibility of guaranteeing inferential privacy for mechanisms that release useful information about some data containing sensitive information, denoted by $X$. We describe a general model of utility and privacy in which utility is achieved by disclosing the value of low-entropy features of $X$, while privacy is maintained by keeping high-entropy features of $X$ secret. Adopting this model, we prove that meaningful inferential privacy guarantees can be obtained, even though this is commonly considered to be impossible by the well-known result of Dwork and Naor. Then, we specifically discuss a privacy measure called pointwise maximal leakage (PML) whose guarantees are of the inferential type. We use PML to show that differential privacy admits an inferential formulation: it describes the information leaking about a single entry in a database assuming that every other entry is known, and considering the worst-case distribution on the data. Moreover, we define inferential instance privacy (IIP) as a bound on the (non-conditional) information leaking about a single entry in the database under the worst-case distribution, and show that it is equivalent to free-lunch privacy. Overall, our approach to privacy unifies, formalizes, and explains many existing ideas, e.g., why the informed adversary assumption may lead to underestimating the information leaking about each entry in the database. Furthermore, insights obtained from our results suggest general methods for improving privacy analyses; for example, we argue that smaller privacy parameters can be obtained by excluding low-entropy prior distributions from protection

Coordination of autonomous devices over noisy channels : capacity results and coding techniques

Les réseaux de 5ème génération se caractérisent par la communication directe entre machines (M2M) et l’Internet des Objets, un réseau unifié d’objets connectés. Dans ce contexte, les appareils communicants sont des décideurs autonomes qui coopérent, coordonnent leurs actions et se reconfigurent de manière dynamique enfonction de leur environnement. L’enjeu est de développer des algorithmes efficaces pour coordonner les actions des appareils autonomes constituant le réseau.La théorie de l’information nous permet d’étudier le comportement de long-terme des appareils grâce aux distributions de probabilité conjointes. En particulier, nous sommes intéressés par la coordination forte, qui exige que la distribution induite sur les suites d’actions converge en distance L^1 vers une distribution i.i.d. cible.Nous considérons un model point-à-point composé d’une source d’information, d’un encodeur, d’un canal bruité, d’un décodeur, d’une information commune et nous cherchons à coordonner les signaux en entrée et en sortie du canal avec la source et sa reconstruction.Nos premiers résultats sont des bornes intérieures et extérieure pour la région de coordination forte, c’est-à-dire l’ensemble des distributions de probabilité conjointes réalisables et la quantité d’information commune requise.Ensuite, nous caractérisons cette région de coordination forte dans trois cas particuliers: lorsque le canal est parfait, lorsque le décodeur est sans perte et lorsque les variables aléatoires du canal sont indépendantes des variables aléatoires de la source. L’étude de ce dernier cas nous permet de remettre en cause le principe de séparation source-canal pour la coordination forte. Nous démontrons également que la coordination forte offre “gratuitement” des garanties de sécurité au niveau de la couche physique.Par ailleurs, nous étudions la coordination sous l’angle du codage polaire afin de développer des algorithmes de codage implémentables. Nous appliquons la polarisation de la source de manière à créer un schéma de codage explicite qui offre une alternative constructive aux preuves de codage aléatoires.5G networks will be characterized by machine to machine communication and the Internet of Things, a unified network of connected objects. In this context, communicating devices are autonomous decision-makers that cooperate, coordinate their actions, and reconfigure dynamically according to changes in the environment.To do this, it is essential to develop effective techniques for coordinating the actions of the nodes in the network.Information theory allows us to study the long-term behavior of the devices through the analysis of the joint probability distribution of their actions. In particular, we are interested in strong coordination, which requires the joint distribution of sequences of actions to converge to an i.i.d. target distribution in L^1 distance.We consider a two-node network comprised of an information source and a noisy channel, and we require the coordination of the signals at the input and at the output of the channel with the source and the reconstruction. We assume that the encoder and decoder share a common source of randomness and we introduce a state capturing theeffect of the environment.The first objective of this work is to characterize the strong coordination region, i.e. the set of achievable joint behaviors and the required minimal rates of common randomness. We prove inner and outer bounds for this region. Then, we characterize the exact coordination region in three particular cases: when the channel is perfect, when the decoder is lossless and when the random variables of the channel are separated from the random variables of the source.The study of the latter case allows us to show that the joint source-channel separation principle does not hold for strong coordination. Moreover, we prove that strong coordination offers “free” security guarantees at the physical layer.The second objective of this work is to develop practical codes for coordination: by exploiting the technique of source polarization, we design an explicit coding scheme for coordination, providing a constructive alternative to random coding proofs

Coordination d’appareils autonomes sur canaux bruités : régions de capacité et algorithmes de codage

5G networks will be characterized by machine to machine communication and the Internet of Things, a unified network of connected objects. In this context, communicating devices are autonomous decision-makers that cooperate, coordinate their actions, and reconfigure dynamically according to changes in the environment.To do this, it is essential to develop effective techniques for coordinating the actions of the nodes in the network.Information theory allows us to study the long-term behavior of the devices through the analysis of the joint probability distribution of their actions. In particular, we are interested in strong coordination, which requires the joint distribution of sequences of actions to converge to an i.i.d. target distribution in L^1 distance.We consider a two-node network comprised of an information source and a noisy channel, and we require the coordination of the signals at the input and at the output of the channel with the source and the reconstruction. We assume that the encoder and decoder share a common source of randomness and we introduce a state capturing theeffect of the environment.The first objective of this work is to characterize the strong coordination region, i.e. the set of achievable joint behaviors and the required minimal rates of common randomness. We prove inner and outer bounds for this region. Then, we characterize the exact coordination region in three particular cases: when the channel is perfect, when the decoder is lossless and when the random variables of the channel are separated from the random variables of the source.The study of the latter case allows us to show that the joint source-channel separation principle does not hold for strong coordination. Moreover, we prove that strong coordination offers “free” security guarantees at the physical layer.The second objective of this work is to develop practical codes for coordination: by exploiting the technique of source polarization, we design an explicit coding scheme for coordination, providing a constructive alternative to random coding proofs.Les réseaux de 5ème génération se caractérisent par la communication directe entre machines (M2M) et l’Internet des Objets, un réseau unifié d’objets connectés. Dans ce contexte, les appareils communicants sont des décideurs autonomes qui coopérent, coordonnent leurs actions et se reconfigurent de manière dynamique enfonction de leur environnement. L’enjeu est de développer des algorithmes efficaces pour coordonner les actions des appareils autonomes constituant le réseau.La théorie de l’information nous permet d’étudier le comportement de long-terme des appareils grâce aux distributions de probabilité conjointes. En particulier, nous sommes intéressés par la coordination forte, qui exige que la distribution induite sur les suites d’actions converge en distance L^1 vers une distribution i.i.d. cible.Nous considérons un model point-à-point composé d’une source d’information, d’un encodeur, d’un canal bruité, d’un décodeur, d’une information commune et nous cherchons à coordonner les signaux en entrée et en sortie du canal avec la source et sa reconstruction.Nos premiers résultats sont des bornes intérieures et extérieure pour la région de coordination forte, c’est-à-dire l’ensemble des distributions de probabilité conjointes réalisables et la quantité d’information commune requise.Ensuite, nous caractérisons cette région de coordination forte dans trois cas particuliers: lorsque le canal est parfait, lorsque le décodeur est sans perte et lorsque les variables aléatoires du canal sont indépendantes des variables aléatoires de la source. L’étude de ce dernier cas nous permet de remettre en cause le principe de séparation source-canal pour la coordination forte. Nous démontrons également que la coordination forte offre “gratuitement” des garanties de sécurité au niveau de la couche physique.Par ailleurs, nous étudions la coordination sous l’angle du codage polaire afin de développer des algorithmes de codage implémentables. Nous appliquons la polarisation de la source de manière à créer un schéma de codage explicite qui offre une alternative constructive aux preuves de codage aléatoires