Sharif Digital Repository

Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB... 

The Renyi's information dimension (RID) of an n-dimensional random vector (RV) is the average dimension of the vector when accounting for non-zero probability measures over lower-dimensional subsets. From an information-theoretical perspective, the RID can be interpreted as a measure of compressibility of a probability distribution. While the RID for continuous and discrete measures is well understood, the case of a discrete-continuous measures presents a number of interesting subtleties. In this paper, we investigate the RID for a class of multi-dimensional discrete-continuous random measures with singularities on affine lower dimensional subsets. This class of RVs, which we term affinely... 

Capacity has been found for degraded, reversely degraded, full feedback, semi-deterministic, orthogonal relay channels, also for a class of deterministic relay channels and a class of modulo sum relay channels. We indicate what the relay decodes and forwards with one auxiliary random variable having bounded cardinality and attempt to define a more general class of relay channels in order to unify most of known capacity theorems into one capacity theorem by considering additional assumptions imposed to the definition of those channels. In other words, the relay channel inputs are dependent as in multiple access channel with arbitrarily correlated sources and here we do for the relay channel... 

In a production process, when the quality of a product depends on more than one characteristic, multivariate quality control techniques are used. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In this paper, a new methodology has been developed to monitor multi-attribute processes, in which the defect counts are important and different types of defect are dependent random variables. In order to do this, based on the symmetric square root transformation concept, first, multi-attribute data is transformed, such that the correlation between variables either vanishes or... 

As of late, copulas have drawn great attention in stochastic simulation, financial engineering, and risk management. Their power lies under their ability of modeling dependent random variables. Using a known theorem in probability which proves that the fractional part of the sum of a uniform and an arbitrary independent continuous random variable follows a uniform distribution, we construct a wide class of bivariate copulas in which bivariate random vector generation can be performed easily. Some important members of this new class and their properties together with two invariant correlation measures and some insights in their application are presented. © Taylor & Francis Group, LLC  

Wireless Sensor Network (WSN) should be capable of fulfilling its mission, in a timely manner. Therefore, we propose a quantitative real-time model for multihop WSN. "Real-time degree" describes the percentage of real-time data that the network can deliver on time from any source to its destination. Most of network properties are considered as random variables and a queuing-theory based model is derived. In this model, the effect of network load on the packets ' delay and the "real-timeliness" of the network are considered. Simulation results are used to validate the proposed model. The simulation results agree very well with the model. © 2007 IEEE  

A PWM controlled class-D amplifier generates harmonics at switching frequency and its multiples. In this paper, the Random PWM (RPWM) technique is applied in order to spread the noise spectrum over a wide range, thus, considerably reducing amplitudes of these harmonics and the consequent EMI problems. A Line Impedance Stabilization Network (LISN) is used to study the RF noise emanating from the converter. Simulation and experimental results confirm the validity method and demonstrate the effectiveness of applying the RPWM technique in reducing the RF noise level  

A pulsewidth modulation (PWM)-controlled active filter generates harmonics at the switching frequency and its multiples in the RF range, and the concentrated power spectrum may produce electromagnetic interference (EMI) problems. In this paper, the random PWM (RPWM) technique is applied in order to spread the noise spectrum over a wide range, thus, considerably reducing the amplitudes of these harmonics and the consequent EMI problems. To study the operation of active filters, the case of an ac/dc converter along with a power-factor corrector is considered as a nonlinear load and a series active filter, respectively. A line impedance stabilization network is used to study the RF noise... 

In this paper, the designing of a parallel channel queuing system is considered in which it is desirable to serve the customers immediately upon their arrival. To design such a service facility, the first and the second moments of the number of customers are obtained in an infinite channel server under the assumption that the arrival process has a general probability structure and the service times of customers are independent and identically distributed random variables. With the knowledge about the above two moments, one can obtain the approximate number of channels such that the queue length becomes zero. © Sharif University of Technology, January 2006  

The classical single-period problem (SPP) is to find a product's order quantity that maximizes the expected profit in a single period under probabilistic demand. In this paper we consider a SPP model in which a percent of the quantity ordered to the supplier contains defective units and is a random variable with a known distribution function. We assume that the initial inventory at the beginning of the period is a random variable. This assumption, among other applications, may apply to the case where the decision about the order quantity must be made at a time long before the start of the period and the available inventory may decrease stochastically due to several factors, such as... 

In this article, a novel cooperative secondary voltage/frequency control considering time-varying delays and noises in fading channels is presented for an autonomous alternating current (AC) voltage sourced-based converter (VSC)-based microgrid (MG), including inverter-interfaced distributed generations (DGs). Fading phenomenon makes complex random fluctuations on the voltage and frequency of every DG received from its neighbor DGs. In multi-agent cooperative systems, in addition to the total additive noise and time-variant delay, a multiplicative complex random variable is considered to model the main received signal and its replicas due to multipath propagation. The proposed... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with the transmitted bit). In this paper, we 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 memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we 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 memory are Poisson distributed random variables with a mean comprising a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we find the best codebook design by minimizing the error probability of the decoder over all codebooks. For the case of having only a total-power constraint, the... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with the transmitted bit). In this paper, we 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 memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we 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 memory are Poisson distributed random variables with a mean comprising a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we find the best codebook design by minimizing the error probability of the decoder over all codebooks. For the case of having only a total-power constraint, the... 

Blockchain technology brings about an opportunity to maintain decentralization in several applications, such as cryptocurrency. With the agents of a decentralized system operating independently, it calls for a consensus protocol that helps all nodes to agree on the state of the ledger. Most of the existing blockchains rely on Proof of Work (PoW) as the underlying consensus algorithm, resulting in a significant amount of electricity power consumption. Furthermore, it demands the miner to buy specific computation devices. Besides, a protocol to gather the society-related taxes such as public education funding and charities is lacking in existing consensus algorithms. In response, this paper... 

A group-characterizable (GC) random variable is induced by a finite group, called main group, and a collection of its subgroups. The notion extends directly to secret sharing schemes (SSSs). It is known that linear and abelian SSSs can be equivalently described in terms of GC SSSs. In this paper, we present a necessary and sufficient condition for a SSS to be equivalent to a GC one. Using this result, we show that homomorphic SSSs (HSSSs) are equivalent to GC SSSs whose subgroups are normal in the main group. We also present two applications for this equivalent description of HSSSs. One concerns lower bounding the information ratio of access structures for the class of HSSSs, and the other... 

We give an upper bound on the performance of the belief propagation algorithm in decoding a code over a binary-input output-symmetric channel in terms of the decoding threshold of the code over the erasure channel. Using this upper bound, we obtain the overhead of fountain codes on the erasure channel, provided that they are capacity-achieving on a symmetric channel. The upper bound is similar to a lower bound proved by Khandekar. The lower bound will be used to bound from above the reception overhead of fountain codes on symmetric channels  

There are various cases in physics and engineering sciences (especially communications) where one requires the envelope probability density function (pdf) of the sum of several random sinusoidal signals. According to the correspondence between a random sinusoidal signal and a random vector, the sum of random vectors can be considered as an abstract mathematical model for the above sum. Now it is desired to obtain the pdf of the length of the resulting vector. Considering the common and reasonable assumption of uniform distributions for the angles of vectors, many researchers have obtained the pdf of the length of the resulting vector only for special cases. However in this paper, the pdf is... 

The notion of compressibility of a random measure is a rather general concept which find applications in many contexts from data compression, to signal quantization, and parameter estimation. While compressibility for discrete and continuous measures is generally well understood, the case of discrete-continuous measures is quite subtle. In this paper, we focus on a class of multi-dimensional random measures that have singularities on affine lower-dimensional subsets. We refer to this class of random variables as affinely singular. Affinely singular random vectors naturally arises when considering linear transformation of component-wise independent discrete-continuous random variables. To...