Gianfranco L. Pierobon

Codes for zero spectral density at zero frequency (Corresp.)

In pulse-amplitude modulation (PAM) digital transmission systems line encoding is used for shaping the spectrum of the encoded symbol sequence to suit the frequency characteristics of the transmission channel. In particular, it is often required that the encoded symbol sequence have a zero mean and spectral density vanishing at zero frequency. We show that the finite running digital sum condition is a necessary and sufficient condition for this to occur. The result holds in particular for alphabetic codes, which are the most widely used line codes.

Spectral Analysis of Functions of Markov Chains with Applications

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.

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...

Performance evaluation of Bluetooth polling schemes: an analytical approach

In the recent years, many polling schemes for Bluetooth networks have been proposed and evaluated. To the authors knowledge, however, analysis has been carried out mainly through computer simulations and, up to now, no mathematical treatment of this topic has been presented. In this paper, we propose an analytical framework for performance evaluation of polling algorithms in Bluetooth piconets. The analysis is carried out by resorting to an effective and simple mathematical method, called Equilibrium Point Analysis. The system is modelled as a multidimensional finite Markov chain and performance metrics are evaluated at the equilibrium state. The analysis is focused on three classical polling schemes, namely Pure Round Robin, Gated Round Robin and Exhaustive Round Robin, which are compared in terms of packet delay, channel utilization, and fairness among users. Both analytical and simulation results are presented for three relevant scenarios, in order to validate the accuracy of the analysis proposed.

Codes with a multiple spectral null at zero frequency

Codes whose spectral density and its lower order derivatives vanish at zero frequency are investigated, and necessary and sufficient conditions for the spectral properties are given. In particular, for the most common balanced alphabets, a complete characterization is furnished for the class of symbol-by-symbol codes with vanishing spectrum and second derivative. The fundamental results are extended to block codes, and suitable criteria for their design are given. Specific examples of binary and ternary block codes are presented; their performance in terms of low power content at low frequencies compares advantageously with that of some conventional codes. >

Jitter analysis of a double modulated threshold pulse stuffing synchronizer

A pulse stuffing technique (used for TDM) in which both positive and negative stuffings are allowed with two stuffing thresholds periodically modulated by a sawtooth waveform is discussed. A suitable mathematical model of the technique and a frequency domain analysis of the inherent pulse stuffing jitter are provided. It is found that the approach reduces the peak-to-peak pulse stuffing jitter according to the inverse of the threshold modulation period. The analytical results are confirmed by numerical simulations. >

Performance of quantum data transmission systems in the presence of thermal noise

In the literature the performance of quantum data transmission systems is usually evaluated in the absence of thermal noise. A more realistic approach taking into account the thermal noise is intrinsically more difficult because it requires dealing with Glauber coherent states in an infinite-dimensional space. In particular, the exact evaluation of the optimal measurement operators is a very difficult task, and numerical approximation is unavoidable. The paper faces the problem by approximating the P-representation of the noisy quantum states with a large but finite numbers of terms and applying to them the square root measurement (SRM) approach. Comparisons with cases where the exact solution are known show that the SRM approach gives quite accurate results. As application, the performance of quadrature amplitude modulation (QAM) and phase shift keying (PSK) systems is considered. In spite of the fact that the SRM approach is not optimal and overestimates the error probability, also in these cases the quantum detection maintains its superiority with respect to the classical homodyne detection.

Spectral analysis of variable-length coded digital signals

Spectral analysis is performed for a digital message produced by a variable-length encoder driven by a stationary memoryless source. In particular, closed form expressions are derived for both the continuous and the discrete part of the spectral density. The continuous part turns out to be a rational function of z=\exp (j2\pi fT) ,where T is the symbol period, whereas the discrete part exhibits in general spectral lines at multiple integers of (\lambda_{0}T)^{-1} , where \lambda_{0} is the greatest common divisor of the codeword lengths. As an application of the theory explicit formulas are derived for the spectra of B n ZS and HDB n codes.

Power Spectrum of Angle Modulated Correlated Digital Signals

The paper deals with the spectral analysis of both phase and frequency modulated digital signals with correlated messages, where correlation is obtained by encoding. Also, a possible general filtering of the baseband digital signal is taken into account. The method of computation is fast, since the computational complexity increases linearly with the baseband pulse duration. The main result is concerned with frequency modulation. It is shown that for some well-known baseband encoding schemes, such as bipolar, pair selected ternary, high density bipolar, and bipolar with n zeros substitution, the spectrum exhibits lines no matter what the value of the modulation index.

Accurate performance evaluation of weakly coherent optical systems

An accurate performance evaluation approach which uses a closed-form exact analytical expression of the phase noise moments is presented. This enables one to derive a high-order Gaussian quadrature rule for the integrations needed to take into account the phase noise in the computation of error probability. A systematic comparison with results obtained through a Monte Carlo simulation shows that the approach is more accurate than previous methods. The analysis is performed on ASK and FSK heterodyne receivers with integrate-and-dump filtering, envelope detection, and optimized postdetection low-pass filtering. The feasibility of ASK and FSK heterodyne systems at bit rates comparable to the spectral line bandwidth of the laser sources is confirmed. The theory applied seems to be adequate to attack other problems, such as the evaluation of the effects of crosstalk between the FSK filters or among frequency division multiplexed channels. >