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#### New Approaches for Achievability Proof in Network Information Theory: Asymptotic Regime and Beyond

, Ph.D. Dissertation Sharif University of Technology ; Aref, Mohammad Reza (Supervisor)
Abstract

Two new frameworks for achievability proof in network information theory (NIT) are introduced . The first framework which we call it OSRB (Output Statistics of Random Binning) framework, uses random binning arguments and is based on a duality between channel and source coding problems. Furthermore, the OSRB framework uses pmf approximation arguments instead of counting and typicality which are used widely in conventional achievability proofs in NIT. This allows for proving coordination and strong secrecy problems, where certain statistical conditions on the

distribution of random variables need to be satisfied. These statistical conditions include independence between messages and...

distribution of random variables need to be satisfied. These statistical conditions include independence between messages and...

#### Linear decoupled space-time codes

, Article 14th IEEE 2003 International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC2003, Beijing, 7 September 2003 through 10 September 2003 ; Volume 3 , 2003 , Pages 2862-2867 ; 0780378229 (ISBN); 9780780378223 (ISBN) ; Khalaj, B. H ; Sharif University of Technology
2003

Abstract

In this paper, we will introduce a new constraint on linear space-time block codes that will result in a novel decoupled symbol-by-symbol detection scheme. Based on the new framework, a quasi-decoupled space-time code that is applicable to any number of transmit and receive antennas will be proposed. We will also solve a more general case and show that all other known solutions to this problem such as orthogonal designs and Clifford algebra representations, represent special cases of such general solution which will provide an easier framework, to deal with such codes. It is noticeable that the new framework not only provides better understanding of earlier solutions but may also help in...

#### On hypercontractivity and a data processing inequality

, Article IEEE International Symposium on Information Theory - Proceedings ; 29 June through 4 July , 2014 , pp. 3022-3026 ; Gohari, A ; Kamath, S ; Nair, C ; Sharif University of Technology
Abstract

In this paper we provide the correct tight constant to a data-processing inequality claimed by Erkip and Cover. The correct constant turns out to be a particular hypercontractivity parameter of (X,Y), rather than their squared maximal correlation. We also provide alternate geometric characterizations for both maximal correlation as well as the hypercontractivity parameter that characterizes the data-processing inequality

#### Secure noisy network coding

, Article 2013 Iran Workshop on Communication and Information Theory ; 2013 ; 9781467350235 (ISBN) ; Aref, M. R ; Gohari, A ; Sharif University of Technology
2013

Abstract

In this paper we use the Output Statistics of Random Binning (ORSB) framework to extend the noisy network coding of Lim et al. to include an eavesdropper

#### Achievability proof via output statistics of random binning

, Article IEEE Transactions on Information Theory ; Vol. 60, issue. 11 , July , 2014 , pages 6760-6786 ; 21578095 ; 978-1-4673-2580-6 ; Aref, M. R ; Gohari, A ; Sharif University of Technology
Abstract

This paper introduces a new and ubiquitous framework for establishing achievability results in network information theory problems. The framework uses random binning arguments and is based on a duality between channel and source coding problems. Furthermore, the framework uses pmf approximation arguments instead of counting and typicality. This allows for proving coordination and strong secrecy problems, where certain statistical conditions on the distribution of random variables need to be satisfied. These statistical conditions include independence between messages and eavesdropper's observations in secrecy problems and closeness to a certain distribution (usually, i.i.d. distribution) in...

#### A new capacity upper bound for "relay-with-delay" channel

, Article 2009 IEEE International Symposium on Information Theory, ISIT 2009, Seoul, 28 June 2009 through 3 July 2009 ; 2009 , Pages 26-30 ; 21578102 (ISSN); 9781424443130 (ISBN) ; Mirmohseni, M ; Aref, M. R ; Sharif University of Technology
2009

Abstract

In this paper we prove a new capacity upper bound for a class of relay channels known as Relay-With-Delay channels. The proposed bound is general and holds for any arbitrary amount of delay. We have shown that the previously introduced bounds can be considered as special cases of our proposed upper bound. The new introduced bound is, in some cases, tighter than the previously established bounds. It is also notable that the proposed bound coincides with the previously known capacity of "Relay-With-Delay" channels. © 2009 IEEE

#### Comment II on "Dense coding in entangled states"

, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 68, Issue 1 , 2003 , Pages - ; 10502947 (ISSN) ; Rezakhani, A. T ; Sharif University of Technology
American Physical Society
2003

#### An Investigation on Entanglement and Its Applications in Quantum Communication Protocols

, M.Sc. Thesis Sharif University of Technology ; Aref, Mohammad Reza (Supervisor) ; Aminzadeh Gohari, Amin (Co-Advisor)
Abstract

In this thesis, we propose a new method for deriving the achievability results in quantum information theoretic problems. The calssical quan- tum decoupling lemma is an essential component in our method. Assume that each classical source is randomly binned at a ﬁnite rate. We ﬁnd suﬃcient conditions on these rates such that the bin indices are nearly mutually independent of each other and of a quantum source Qn. Us- ing this theorem in conjunction with the calssical quantum Slepian Wolf (CQSW) result, this method suggest a new comprehensive framework for the achievability of network quantum information theoretic prob- lems. We’ve used the new method to redrive the Holevo bound, private...

#### On Körner-Marton's sum modulo two problem

, Article IWCIT 2015 - Iran Workshop on Communication and Information Theory, 6 May 2015 through 7 May 2015 ; May , 2015 ; 9781479982356 (ISBN) ; Gohari, A ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015

Abstract

In this paper we study the sum modulo two problem proposed by Körner and Marton. In this source coding problem, two transmitters who observe binary sources X and Y, send messages of limited rate to a receiver whose goal is to compute the sum modulo of X and Y. This problem has been solved for the two special cases of independent and symmetric sources. In both of these cases, the rate pair (H(X|Y), H(Y|X)) is achievable. The best known outer bound for this problem is a conventional cut-set bound, and the best known inner bound is derived by Ahlswede and Han using a combination of Slepian-Wolf and Körner-Marton's coding schemes. In this paper, we propose a new outer bound which is strictly...

#### Secrecy capacity in large cooperative networks in presence of eavesdroppers with unknown locations

, Article 2016 Iran Workshop on Communication and Information Theory, IWCIT 2016, 3 May 2016 through 4 May 2016 ; 2016 ; 9781509019229 (ISBN) ; Kazempour, N ; Mirmohseni, M ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2016

Abstract

In this paper, an extended large wireless network, with a single transmitter-receiver pair, under the secrecy constraint is considered. In contrast to works which use idealized assumptions, a more realistic network situation with unknown eavesdroppers locations is investigated: the legitimate users only know their own Channel State Information (CSI), not the eavesdroppers CSI. Also, the network is analyzed by taking in to account the effects of both fading and path loss. Under these assumptions, a power efficient cooperative scheme, named stochastic virtual beamforming, is proposed. Applying this scheme, any desired pair of secure rate and outage level denoted by (Rs, ϵ) will be achievable...

#### High-Probability guarantees in repeated games: theory and applications in information theory

, Article Proceedings of the IEEE ; Volume 105, Issue 2 , 2017 , Pages 189-204 ; 00189219 (ISSN) ; Gohari, A ; Akbarpour, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2017

Abstract

We introduce a 'high-probability' framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high-probability counterpart of the classical result of Mertens and Zamir for the zero-sum repeated games. Any payoff that can be guaranteed with high probability can be guaranteed in expectation, but the reverse is not true. Hence, unlike the average payoff case where the payoff guaranteed by each player is the negative of the payoff by the other player, the two guaranteed payoffs would differ in the high-probability framework. One motivation for this framework...

#### Entanglement Generation and Distribution in Spin Chains

, Ph.D. Dissertation Sharif University of Technology ; Rouhani, Shahin (Supervisor) ; Jafarizadeh, Mohammad Ali (Supervisor)
Abstract

Entanglement is the most important quantity in quantum information processing tasks. However the provision of the required entanglement between various quantum parts is one of the most challenging breakthroughs in realization of quantum processors. One of the scenarios for entangling various parts is use of naturally interacting qubits, called “spin chains”. The low level of required control and the ability of entangling mesoscopicaly separated parts cause such systems to be attractive for using in future low dimensional silicone compatible technology quantum processors. Accordingly in this thesis by considering a ferromagnetic spin system in which is conserved and by initializing the...

#### Introducing an Upper bound on Capacity of Quantum Key Distillation

, M.Sc. Thesis Sharif University of Technology ; Aref, Mohammad Reza (Supervisor) ; Aminzadeh Gohari, Amin (Supervisor)
Abstract

In modern cryptography the main goal in symmetric cryptography algorithms is that the security of the protocol should be only dependent on the secrecy of key. Further, secret key agreement has a major role in perfect security. However, it is impossible to share a secrete key only by the use of a public channel and there must be another shared source. This source can be for instance random variables with some joint distribution (as in source model classical key distillation problem) or it can be some entangled quantum systems (as in quantum key distillation problem). The question here is that with the optimum efficiency, what is the maximum number of key bits that can be distilled from one...

#### Inferring the Directionality of Coupling forTwo Time Series

, M.Sc. Thesis Sharif University of Technology ; Rahimi Tabar, Mohammad Reza (Supervisor)
Abstract

The synchronization phenomena are abundant is science, nature, engineering, and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons, and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. First chapter of this thesis describes the basic ideas of the synchronization in an intuitive way. The main physical concepts are presented with experimental examples.

One of the main effects of synchronization is the ability to infer the directionality of coupling for two time series. Uncovering the directionality of coupling is a...

One of the main effects of synchronization is the ability to infer the directionality of coupling for two time series. Uncovering the directionality of coupling is a...

####
Coordination Among Nodes of a Network: an Information Theoretic

Perspective

,
M.Sc. Thesis
Sharif University of Technology
;
Aminzadeh Gohari, Amin
(Supervisor)
Abstract

In this work, we consider a zero error coordination problem wherein the nodes of a network exchange messages to be able to perfectly coordinate their actions with the individual observations of each other. While previous works on coordination commonly assume an asymptotically vanishing error, we assume exact, zero error coordination. Furthermore, unlike previous works that employ the empirical or strong notions of coordination, we define and use a notion of set coordination. This notion of coordination bears similarities with the empirical notion of coordination. We observe that set coordination, in its special case of two nodes with a one-way communication link is equivalent with the “Hide...

#### When is it possible to simulate a DMC channel from another?

, Article 2013 IEEE Information Theory Workshop, ITW 2013 ; Sept , 2013 , Page(s): 1 - 5 ; 9781479913237 (ISBN) ; Yassaee, M. H ; Aref, M. R ; Gohari, A
2013

Abstract

In this paper, we study the problem of simulating a DMC channel from another DMC channel. We assume that the input to the channel we are simulating is i.i.d. and that the transmitter and receivers are provided with common randomness at limited rates. We prove bounds for simulating point-to-point, MAC and broadcast channels. As a special case, we recover the achievability part of the result of Cuff for point-to-point channel simulation via a noiseless link and shared randomness

#### Secure channel simulation

, Article 2012 IEEE Information Theory Workshop, ITW 2012 ; 2012 , Pages 406-410 ; 9781467302234 (ISBN) ; Yassaee, M. H ; Aref, M. R ; Sharif University of Technology
2012

Abstract

In this paper the Output Statistics of Random Binning (OSRB) framework is used to prove a new inner bound for the problem of secure channel simulation. Our results subsume some recent results on the secure function computation. We also provide an achievability result for the problem of simultaneously simulating a channel and creating a shared secret key. A special case of this result generalizes the lower bound of Gohari and Anantharam on the source model to include constraints on the rates of the public discussion

#### Coordination via a relay

, Article IEEE International Symposium on Information Theory - Proceedings ; 2012 , Pages 3048-3052 ; 9781467325790 (ISBN) ; Yassaee, M. H ; Gohari, A ; Aref, M. R ; Sharif University of Technology
IEEE
2012

Abstract

In this paper, we study the problem of coordinating two nodes which can only exchange information via a relay at limited rates. The nodes are allowed to do a two-round interactive two-way communication with the relay, after which they should be able to generate i.i.d. copies of two random variables with a given joint distribution within a vanishing total variation distance. We prove inner and outer bounds on the coordination capacity region for this problem. Our inner bound is proved using the technique of "output statistics of random binning" that has recently been developed by Yassaee, et al

#### Generating dependent random variables over networks

, Article 2011 IEEE Information Theory Workshop, ITW 2011 ; 2011 , Pages 698-702 ; 9781457704376 (ISBN) ; Anantharam, V ; Sharif University of Technology
Abstract

In this paper we study the problem of generation of dependent random variables, known as the coordination capacity [4], [5], in multiterminal networks. In this model m nodes of the network are observing i.i.d. repetitions of X (1), X (2),⋯, X (m) distributed according to q(x (1),⋯, x (m)). Given a joint distribution q(x (1),⋯,x (m), y (1), ⋯, y (m)), the final goal of the i th node is to construct the i.i.d. copies of Y (i) after the communication over the network where X (1), X (2),⋯, X (m), Y (1), Y (2),⋯, Y (m) are jointly distributed according to q(x (1), , x (m), y (1),⋯,y (m)). To do this, the nodes can exchange messages over the network at rates not exceeding the capacity constraints...

#### The capacity region of a class of 3-receiver broadcast channels with two eavesdroppers

, Article IEEE International Symposium on Information Theory - Proceedings, 31 July 2011 through 5 August 2011 ; August , 2011 , Pages 968-972 ; 21578104 (ISSN) ; 9781457705953 (ISBN) ; Aref, M. R ; Sharif University of Technology
2011

Abstract

In this paper, we consider the 3-receiver broadcast channel with one common and two confidential messages. One of the confidential messages is sent to the first and second receivers and kept secret from the third receiver (eavesdropper). The other confidential message is sent to the first receiver and kept secret from the second and third receivers (eavesdroppers). The common message is decoded by all receivers. We study some special cases of the model and determine their secrecy capacity regions