Reed-Solomon list decoding from a system-theoretic perspective

In this paper, the Sudan-Guruswami approach to list decoding of Reed-Solomon (RS) codes is cast in a system-theoretic framework. With the data, a set of trajectories or time series is associated which is then modeled as a so-called behavior. In this way, a connection is made with the behavioral approach to system theory. It is shown how a polynomial representation of the modeling behavior gives rise to the bivariate interpolating polynomials of the Sudan-Guruswami approach. The concept of "weighted row reduced" is introduced and used to achieve minimality. Two decoding methods are derived and a parametrization of all bivariate interpolating polynomials is given

Satellite communication performance evaluation: Computational techniques based on moments

Computational techniques that efficiently compute bit error probabilities when only moments of the various interference random variables are available are presented. The approach taken is a generalization of the well known Gauss-Quadrature rules used for numerically evaluating single or multiple integrals. In what follows, basic algorithms are developed. Some of its properties and generalizations are shown and its many potential applications are described. Some typical interference scenarios for which the results are particularly applicable include: intentional jamming, adjacent and cochannel interferences; radar pulses (RFI); multipath; and intersymbol interference. While the examples presented stress evaluation of bit error probilities in uncoded digital communication systems, the moment techniques can also be applied to the evaluation of other parameters, such as computational cutoff rate under both normal and mismatched receiver cases in coded systems. Another important application is the determination of the probability distributions of the output of a discrete time dynamical system. This type of model occurs widely in control systems, queueing systems, and synchronization systems (e.g., discrete phase locked loops)