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LT codes are asymptotically optimal rateless erasure codes with highly efficient encoding and decoding algorithms. In the original analysis of these codes, it was assumed that for each encoding symbol, the neighbors used to generate that encoding symbol are chosen uniformly at random. Practical implementations of LT codes cannot afford this amount of(More)
We consider a path-following problem in which the goal is to ensure that the error between the system output and the geometric path be asymptotically less than a prespecified constant, while guaranteeing a forward motion along the path and boundedness of all states. A solution to this problem was given in [12] for a class of nonlinear systems and for paths(More)
We consider the averaging method for stability of rapidly switching linear systems with disturbances. We show that the notions of strong and weak averages proposed in [1], with partial strong average defined in this paper, play an important role in the context of switched systems. Using these notions of average, we show that exponential ISS of the strong(More)
(or sampling) variable of a line parameterization must be a uniform one. Since in any real implementation, only a limited number of straight lines, say M, is assumed to go through a given image point, not a theoretically infinitely large number of straight lines could, the uniformness condition in this case is to say that the intersection angle between any(More)
— We consider the averaging method for stability of rapidly switching nonlinear and linear systems with disturbances. First, we show that the input-to-state stability (ISS) analysis results for continuous-time systems in [7] apply directly to nonlinear rapidly switched systems that we consider. We show that the notions of strong and weak averages that were(More)