The word error rate (WER) of soft-decision-decoded binary block codes rarely has closed-form. Bounding techniques are widely used to evaluate the performance of maximum-likelihood decoding algorithm. But the existing bounds are not tight enough especially for low signal-to-noise ratios and become looser when a suboptimum decoding algorithm is used. This paper proposes a new concept named square...

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires MonteCarlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based ...

The mathematical methods required to model simple stochastic processes are reviewed briefly. These methods are used to determine the probability-density function (PDF) for noise-induced energy perturbations of isolated (solitary) optical pulses in fiber communication systems. The analytical formula is consistent with the numerical solution of the energymoment equation. System failures are cause...

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many problems of practical interest these techniques demand procedures for sampling from probability distributions with non-standard forms, hence we are often brou...

In this paper, we consider the probability density function (pdf) of a non-central χ distribution with odd number of degrees of freedom ν. This pdf is represented in the literature as an infinite sum. Consequently, we present three alternative expressions to this pdf. The first expression is in terms of a partial derivative of the hyperbolic cosine function. The second expression, on the other ...

In this paper, we consider the probability density function (pdf) of a non-central χ distribution with odd number of degrees of freedom ν. This pdf is represented in the literature as an infinite sum. Consequently, we present three alternative expressions to this pdf. The first expression is in terms of a partial derivative of the hyperbolic cosine function. The second expression, on the other ...

In this paper, a new blind equalization algorithm for multilevel modulations is proposed. It is based on maximizing the correlation between the probability density function (pdf) of the signal at the output of the equalizer and the desired pdf. The algorithm employs the Parzen window method to estimate the pdf of the squared modulus of the equalizer output. A stochastic gradient-based algorithm...

The paper deals with the particle filter in state estimation of a discrete-time nonlinear non-Gaussian system. The goal of the paper is to design a sample size adaptation technique to guarantee the quality of an empirical probability density function (pdf) which approximates a target filtering pdf. The quality is measured by inaccuracy (cross-information) between the empirical pdf and the filte...

We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of “heavy-tailed” non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can also be inferred directly from an extremum principle, set for Shannon entropy under a cons...

We have modified the iterative procedure introduced by Lin et al. (2016), to systematically combine the submm images taken from ground based (e.g., CSO, JCMT, APEX) and space (e.g., Herschel, Planck) telescopes. We applied the updated procedure to observations of three well studied Infrared Dark Clouds (IRDCs): G11.11-0.12, G14.225-0.506 and G28.34+0.06, and then performed singlecomponent, modi...