Sharif Digital Repository

In this dissertation we discuss various results presented in the literature on single user channels with causal or noncausal side information and multiuser channels with side information such as multiple access channel and broadcast channel. The Series Relay Networks (SRN) with delays, with and without channel state information (CSI) are investigated from an information theoretic point of view. For SRN with unlimited look ahead where the relays can use the whole received block to encode, upper and lower bounds on the capacity are derived which are tight for the degraded case. For SRN without-delay where the relays have access to the present received symbols in addition to the past symbols,... 

Wireless communication networks such as cell phones are rapidly expanding and every day they attract more users. Information flow in these networks is basically through free space. Thus, theses networks are inherently subjected to eavesdropping. Cryptography based on the secure key is the well known traditional way of protecting information security in wireless networks. However, these cryptosystems are just computationally secure and have their vulnerabilities. Information theoretic security is a relatively new method which doesn’t rely on any preshared key or key infrastructure and uses inherent characteristics of the communication channel to provide robust and provable security.In this... 

The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find practical schemes that approach these limits.Polar codes, recently invented by Arıkan, are the first practical codes that are known to achieve the capacity for a large class of channels. Their code construction is based on a phenomenon called “channel polarization”.
Since the performance of polar code degrades when the block length is small, several kinds of Reed – Solomon concatenation is considered in order to improve the... 

The registration of images is a fundamental task in numerous applications in medical image processing. The importance of medical image registraiton due to the imaging systems development in last decades is obvious to every one. Especially the wide employment and different capabilities of these systems has caused more attention to this field of image processing. Th e application of medical image registraiton is extended from clinical diagnosis and treatment evaluation, to image guided surgery. The dimension of images as well as modalities of imaging and imaging subjectshas made a wide variety of problems in this branch of image processing. Registration, briefly speaking, is a geometrical... 

Information Theory, as an important part of communication theory, tries to find inner and outer bounds for reliable rate of information transmission in communication networks. In Network Information Theory, It is usually assumed that the channel statistics is known to everyone. However, in some practical situations, we might not know the statistics. The compound channel and the arbitrarily varying channel (AVC) are two categories of models which have considered this problem. In this thesis, in order to have a more general model regarding information transfer in the presence of channel uncertainty, we propose a model which is essentially a combination of compound channel and AVC. In our... 

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... 

Data hiding in digital media has been widely investigated over the past decade because of covering different crucial applications. Amongst digital multimedia signals, video has been received a special attention and data hiding in video signals has reached a significant improvement in recent years. This thesis aims at introducing an information theoretic based analysis method for calculating the capacity of data hiding in video signals, as one of most challenging issues in this area. This analysis is expected to establish a reasonable basis for the design and analysis of data hiding algorithms. We study and investigate the data hiding problems that could be specific to video signals and its... 

Since the inception of the fields of quantum information and computation, the task of coherently transferring quantum states, through long and short distances has been of utmost importance. While photons are the ideal carriers of quantum information over long distances, it has become evident that the best possible method for transferring quantum information over short distances, i.e. through regular arrays of qubits, is to exploit the natural dynamics of the many body system. This idea was first introduced in the work of Bose [2] who showed that the natural dynamics of a Heisenberg ferromagnetic chain can achieve high-fidelity transfer of spin states over distances as long as 80 lattice... 

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... 

Since concepts in quantum information theory has recently been applied to characterize states in many-body systems, we survey entanglement of the ground states in the S = 1/2 antiferromagnetic Heisenberg ladder systems and 2D square lattices. The Lancz¨os method for exact diagonalization of quantum spin models are used to find the ground states. Moreover, effect of defect in ladder on entanglement and ground state energy are studied  

In this report, we have formulated a new technique for characterizing quantum optical processes based on probing unknown processes only with coherent states and simply by measuring normally-ordered moments of output states. Our method has two substantial advantages in comparison with previous methods.First, for practical purposes of uantum-optical communications and information, predicting of the classicality or nonclassicality of output states from an unknown quantum process is generally important. Because of truncation of the Hilbert space in the Fock basis and/or exploiting Klauder theorem, antecedent methods failed to carry out foretelling the [non]classicality features of the process’... 

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... 

Entropy is one of the important quantities in thermodynamics. In this project has tried to make this quantity as a bridge between quantum and thermodynamics. Entropy has many definitions that the Shannon entropy is chosen in this work. By this definition of entropy, we are able to define the entropy for a electronic system in molecules. By this definition, we are seeking an answer for this question,”whether entropy has a similar application in quantum like thermodynamics or not?”. To elucidate this hypothesis, simple diatomic molecules are computed. In fact, displacement of the Shannon entropy has investigated in bond making process. The question is that whether we can use this quantity to... 

Computational instruments such as personal computers (PC) are among the most important and developed inventions needed for the society. Nowadays, the fastest classical computing machines are based on the conventional semiconductor fabrication technology. But these computers cannot satisfy all of the requirements of today’s ongoing developments. Two important weaknesses of the undergoing technology are the speed of computing which is in the frontend of the semiconductor technology, and solving some complicated problems which may take years and even decades with these computers. This is while, based on quantum theory and related algorithms, solving of these problems would take much less time.... 

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... 

Nowadays energy consumption becomes an important design factor in communication systems because of financial reasons and environmental concerns. There would be many equipments with large energy consumption in next generation (5G) networks, so energy efficiency will play an important rule in these networks. Two alternative techniques used for energy consumption management are energy harvesting and simultaneous wireless information and power transfer (SWIPT). A useful scenario in SWIPT is to use received energy for future transmissions. In this scenario, the design of encoder and decoder is a new open problem, because of the memory now appeared in the system. Thus to understand the interplay... 

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... 

Even in the simplest of activities in the brain such as resting condition, there are connections in between different regions of the brain so that the whole system functions consistently in harmony. Studies related to brain connectivity provides an opportunity to better understand how the brain works. To assess these connectivities an estimation is usually conducted based on brain signals. Among different estimation methods, quantities of information theory are in general more practical due to avoiding any assumptions toward the system model and the ability to recognize linear and non-linear connectivity. One of the main quantities related to the information theory is in fact, entropy.... 

This thesis consists of two parts. For the first, we study the identifiability of finite mixtures of finite product measures. This class of mixture models has a large number of applications in real-world data modeling. An important example is the population genetic application of them in modeling of mixed population datasets. The identifiability means that the mapping between the class parameters and the mixture distributions is one to one. In this manuscript, we define some separability metrics inspired by methods used in clustering mixture models and study the fundamental trade off between identifiability and the number of separable variables of the mixture model. For the second part of... 

Quantum thermodynamics is a new field of study in physics, which by considering the fundamentals of statistical mechanics, open quantum system, quantum information and mesoscopic system aims at the investigation of quantum systems from a thermodynamical point of view. To achieve these aims, a better understanding of the relations between quantum and thermodynamics fundamentals is essential. Energy and correlation are two key concepts in statistical mechanics and quantum thermodynamics (and information), respectively, that studying the relation between them will shed light on the fundamentals of quantum thermodynamics. As generating any correlation in quantum systems with initial heat state...