Sharif Digital Repository

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... 

Usually, in information theory, the length of the message (number of bits of information) is proportional to the number of channel uses, for example, in traditional channel coding, the number of messages is $ 2 ^{NR} $ and $ NR $ bits with $ N $ channel uses were sent. In fact, as the channel uses increase, the message bits increase linearly. But in this dissertation, the length of the message, or indeed the number of source observations, is a function of the number of channel uses.In this dissertation, we first study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with... 

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... 

One of the main challenges in data transmission is synchronization error. In practice there are solutions to this issue, but this incurs a cost that can not be neglected. Synchronization error consists of deletion, insertion and substitution. Investigation of such errors in a communication channel has been of a great concern in information theory. Furthermore, in many applications such as biology and data storage on disks, we observe synchronization errors. Deletion channel is defined as a channel in which input symbols are deleted with a probability d independently of each other, such that the order of symbols remains unchanged. In spite of attempts to find a closed form for the capacity of... 

In most stochastic models with uncountable cardinality of sample space with non-trivial probability measures, the inherent information is infinite. The continuous-valued random variables and continuous-domain random processes are among such objects. Therefore, a fidelity criterion must be defined between the stochastic subject and its estimated version. Although there are some criteria for of stochastic continuous signals, based on quantizing the signal in both time and amplitude domains, we are going to define a criterion which is for stochastic processes in bounded time domain. Next, the criterion will be expressed in general sources perspective and the optimum rate of coding will be... 

Molecular communication is a new paradigm in communication science, which studies opportunities and challenges of information transmission in nanoscale. Unlike the classical communication, which uses electro-magnetic waves as signal carriers, in this new method of communication, tiny agents in molecular scale are the main information barriers. In this sense, studying molecular communication requires theoretical development and updating some well-known techniques of classical communications.Although there have been some successful attempts to implement communication systems based on molecular communication, the field is still in the theoretical development phase. In this thesis, we have tried... 

We study the optimization of the payoff of a decision-maker (a player or a team) in the presence of an adversary who wishes to minimize the payoff of the decision-maker. In this situation, the decision-maker can puzzle the adversary by playing random actions and hence, gain more payoff. We assume that the decision-maker has limited access to randomness sources and is only allowed to randomize his actions by conditioning them to the limited randomness sourse to which he has access. We consider two models: in the first model, in each stage, the decision maker observes a random source independent of past, and distributed according to a time invariant probability distribution. The adversary... 

Let X be an unknown vector of size n which is to be estimated from a known m 1 vector Y. According to the MMSE criterion, the best estimator (denoted bX(Y)) is an estimator which minimizes the mean squared error. Now, consider a List Decodingproblem in which the sender delivers a list of codes instead of a single decoder. Assume that it is allowed to use multiple parallel estimators (bX1 (Y); ^X2(Y); : : : ; bX k(Y)) instead of delivering a single estimation of samples. The goal is to find the best possible list of estimators, in a way that the mean squared error is optimized between the multiple bX i(Y); (i = 1; 2; : : : ; k). As a medical example, imagine a MRI device which produces three... 

In this thesis, following a short introduction to investment problem, this problem is investigated with both probabilistic and universal approach. Using the concept of the set of reference algorithms, we present a mathematical definition for universality. We then give examples of universal algorithms for investment and prove their universality. These algorithms are:
Universal Portfolios without Side Information, Universal Portfolios with Side Information, Universal Portfolios with Semi-Constant Rebalanced Portfolio, Universal Portfolios with Switching.
We then present a new algorithm called “Universal Portfolio with Multiple Side Information Sources”. This algorithm is applied in... 

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... 

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... 

Security in operational cryptography systems is expressed as computational, in the sense that breaking these systems is not possible in polynomial time. Nowadays, advances in computing power of processors and the development of quantum computers, has incresed concerns about the security of cryptographic systems. This is the cause of proposing the information theoretic secrecy in recent decades. In information theoretic secrecy topics, recovering data at target receiver side with zero error should be acomplished along side with defining security criterias. Information leakage is one of the most common security measures. there are another security measures such as rate-distortion, maximal... 

Molecular communication (MC), is a new way of communication among nanomachines.its applications are typically in cases which the conditions of transfer such as size, nature of the medium and nature or type of the original signal, is consistent with molecules such as medicine, health care, industrial and environmental applications.In this thesis, we first review different models of molecular transmitters. In most of them, storage capacity and molecule generation rate are not considered. we try to propose practical transmitter models considering these limitations. for high storage capacity transmitters, we propose Fixed and Linear transmission methods. assuming that channel is without... 

In recent years, molecular communications have received considerable attentions for communication between nano-machines. In this communication scheme, which uses molecules as information carriers, nano transmitter and receiver are in distance apart of nano meter to meter and information is encoded into type, concentration or releasing time of molecules. Since nano transmitter and receiver can do very simple operations, such as adding, sensing, and etc., for more complicated operations, a network of nano transceivers is required. In this thesis, a small scale imaging of an abnormality in the environment is investigated. To this end, a network of sensors is assumed to be placed in the... 

Molecular communication (MC) is an emerging communication paradigm, whereas molecules are used as information carriers to establish communication among elements in nano-meter to meter scales. In this thesis, we investigate the problem of detecting and monitoring changes (abnormality) based on molecular communication, using quickest change point detection scheme. We assume the distributions and parameters of the system are known. To this end, we consider a network of multiple sensors, each sensing its surrounding and employing On-Off-keying modulation for data transmission toward a fusion center (FC). An abnormality initiates randomly in time and location, and further propagates in the... 

Studying the statistical dependence of two or several random variables is the basis of statistical estimation and prediction. The correlation measures such as mutual information, Pearson correlation, and maximal correlation are common tools in quantifying the extent to which two random variables are dependent. While such measures are highly informative and computationally simple for jointly Gaussian random variables, it is not the case for general random variables. Infinitely divisible random variables are typical examples that are characterized in the Fourier domain (characteristic functions are known); except for a few special cases, no closed-form expressions are available for the... 

Elements of a theory of cooperation and coordination in networks will be developed. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates {R(i,j)} between the nodes, we ask what the set of all is achievable joint distributions p(x1,…,xm) of actions at the nodes of the network. After describing the concepts of empirical coordination for some special networks, we will consider secrecy concepts in coordination. Then we will discuss the concepts of strong... 

In this thesis, a simple memory limited transmitter for molecular communication is proposed, in which information is encoded in the emission rate of the molecules. Taking advantage of memory, the proposed transmitter reduces the ISI problem by properly adjusting its emission rate, which can be interpreted as water-filling on the expected interference. The error probability of the proposed scheme is derived and the result is compared with the error probability of the optimal transmitter obtained by dynamic programming methods. Further, for the special case of channel with one symbol memory, a tight lower bound on error probability is derived. Numerical results show that the performance of... 

Molecular communication (MC), which utilizes molecules as its carriers of information, is one of the oldest mechanisms among micro-organisms on earth. In recent years, using MC for communication among nanomachines has attracted enormous interest because of its simplicity and bio-compatibility. Diffusion-based MC mechanism is one of the most important communication mechanisms, which has wide applications because of no needs for energy and prior infrastructure. The important challenges in MC systems include node complexity, inter-symbol interference (ISI), and co-channel interference (CCI). Due to the small sizes of the nodes in MC, complexity is a serious issue. Because nanomachines are...