Gianfranco Pierobon

Bio: Gianfranco Pierobon is an academic researcher from University of Padua. The author has contributed to research in topics: Quantum state & Gaussian. The author has an hindex of 14, co-authored 40 publications receiving 544 citations.

Spectral Analysis of Functions of Markov Chains with Applications

Abstract: This paper deals with the spectral analysis of digital processes obtained through memoryless functions of stationary Markov chains. Under the assumption that the Markov chain is ergodic, not necessarily acyclic, closed form formulas are derived for both the discrete part (spectral lines) and the continuous part of the spectral density. The results are applied at the output of a finite state sequential machine driven by a stationary Markov chain, which represents a general model of several situations of engineering interest. Finally, the theory is used to evaluate the spectrum of encoded and modulated digital signals.

On the limiting performance of broadcast algorithms over unidimensional ad-hoc radio networks

Abstract: Broadcast mechanisms are widely used in self-organizing wireless networks, for management, control and data exchange pur- poses. In general, broadcast algorithms are required to provide a rapid, reliable and energy-efficient way to diffuse information over a network of randomly distributed nodes. In this paper, we address such issues in the context of uni- dimensional networks, with nodes distributed according to a 1- dimension inhomogeneous Poisson process. We statistically derive the propagation dynamic of the optimum broadcast algorithm defined over the Minimum Connected Dominating Set (MCDS) of nodes. Hence, we derive the limiting broadcast performance over uni-dimensional networks, in terms of some useful measures, thus providing common reference values for comparing the effectiveness of different broadcast algorithms.

Optimality of square-root measurements in quantum state discrimination

Abstract: Distinguishing assigned quantum states with assigned probabilities via quantum measurements is a crucial problem for the transmission of classical information through quantum channels. Measurement operators maximizing the probability of correct discrimination have been characterized by Helstrom, Holevo, and Yuen since the 1970s. On the other hand, closed-form solutions are available only for particular situations enjoying high degrees of symmetry. As a suboptimal solution to the problem, measurement operators, directly determined from states and probabilities and known as square-root measurements (SRMs), were introduced by Hausladen and Wootters. These operators were also recognized to be optimal for pure states equipped with geometrical uniform symmetry (GUS). In this paper we discuss the optimality of the SRM and find necessary and sufficient conditions in order that SRM maximize the correct decision probabilities for the set of states formed by several constellations of GUS states. The results are applied to some specific examples concerning double constellations of quantum phase-shift keying and pulse-position modulation states, with possible applications to practical systems of quantum communications.

Invited paper Analysis of codes and spectra calculations

Abstract: The paper deals with the statistical analysis of the several kinds of signals encountered in digital transmission systems in which the data are coded by a line coder before being transmitted. In the preliminary sections, models of signals and systems are formulated. In particular, a general model is presented in which a line coder is split into three parts : a serial-to-parallel conversion, a finite-state sequential machine, and a parallel-to-serial conversion, where the fundamental coding function is described by a finite-state machine operating on blocks of source-symbols to produce blocks of code-symbols. On the basis of this model, the complete statistics of the coded sequence are evaluated in terms of the source probabilities. In the final part, consideration is given to spectral analysis, where both the continuous and the discrete part (spectral lines) of the spectral densities are calculated in closed form. The results obtained have a general validity and can be used for any line coding sc...

Revisiting the Dolinar receiver through multiple-copy state discrimination theory

Abstract: We consider the problem of discriminating between two quantum coherent states by interpreting a single state as being a collection of several successive copies of weaker coherent states. By means of recent results on multiple-copy state discrimination, it is possible to give a reinterpretation of the Dolinar receiver and carry out a quite-straightforward analysis of its behavior. We also propose and investigate a suboptimal detection scheme derived from the Dolinar's architecture, which is shown to slightly outperform some other near-optimal schemes available in the literature.

Continuous phase modulation

Abstract: M inimum Shift Keying (MSK) [ 11 or Fast Frequency Shift Keying (FFSK) is a digital modulation technique with constant amplitude which has been studied extensively during recent years. The properties of MSK are now understood [2-51. In this article, we report on methods to improve on MSK while maintaining a constant amplitude. By improvement we mean a narrower power spectrum, lower spectral sidelobes, better error probability, or all of the above. The cost of signal processing and the speed and complexity with which it can be performed has steadily been improved over recent years. Further improvements are to be expected. Therefore, it is reasonable to study what can be accomplished with methods that might be too complex for cost effective realization today, but perhaps may be easily achievable tomorrow. In this paper, we consider a number of methods for constructing constant amplitude signals which significantly outperform MSK [5-1031. We also discuss at what level of complexity these improvements are obtained and realized.

Spectral Correlation of Modulated Signals: Part I--Analog Modulation

Abstract: The importance of the concept of cyclostationarity in design and analysis of signal detectors, synchronizers, and extractors in communication systems is briefly discussed, and the central role of spectral correlation, in the characterization of random processes that are cyclostationary in the wide sense, is explained. A spectral correlation function that is a generalization of the power spectral density function is described, and a corresponding generalization of the Wiener-Khinchine relation and several other fundamental spectral correlation relations also are described. Explicit formulas for the spectral correlation function for various types of analog-modulated signals are derived. This includes pulse and carrier amplitude modulation, quadrature amplitude carrier modulation, and phase and frequency carrier modulation. To illustrate the differing spectral correlation characteristics of different modulation types, the magnitudes of the spectral correlation functions are graphed or described in graphical terms as the heights of surfaces above a bifrequency plane.

Equalizers for multiple input/multiple output channels and PAM systems with cyclostationary input sequences

Abstract: The author studies minimum mean square error (MMSE) linear and decision feedback (DF) equalisers for multiple input/multiple output (MIMO) communication systems with intersymbol interference (ISI) and wide-sense stationary (WSS) inputs. To derive these equalizers, one works in the D-transform domain and uses prediction theory results. Partial-response MMSE equalizers are also found. As an application, the author considers a pulse amplitude modulation (PAM) communication system with ISI and cyclostationary inputs. The MMSE linear and DF equalizers are determined by studying an equivalent MIMO system. The resulting filters are expressed in compact matrix notation and are time-invariant, whereas the corresponding single input/single output filters are periodically time-invariant. The author also considers MMSE equalizers for a wide-sense stationary process by introducing a 'random phase'. To aid in the performance evaluation of various equalizers, the author derives their mean square errors. >

Analysis of polling systems

Abstract: A polling system is one that contains a number of queues served in cyclic order. It is employed in computer-terminal communication systems and implemented in such standard data link protocols as BSC, SDLC, and HDLC, and its analysis is now finding a new application in local-area computer networks.This monograph analyzes polling systems to evaluate such basic performance measures as the average queue length and waiting time. Following a taxonomy of models with reference to previous work, it considers one-message buffer systems and infinite buffer systems with exhaustive, gated, and limited service disciplines. Examples to which the analysis of polling systems is applied are drawn from the field of computer communication networks. Contents: Introduction. One-Message Buffer Systems. Exhaustive Service, Discrete-Time Systems. Exhaustive Service, Continuous-Time Systems. Gated Service Systems. Limited Service Systems. Systems with Zero Reply Intervals. Sample Applications. Future Research Topics. Summary of Important Results.Hideaki Takagi is with IBM Japan Science Institute in Tokyo. "Analysis of Polling Systems" is included in the Computer Systems Series, Research Reports and Notes, edited by Herb Schwetman.