We use the \conservation of entropy" 1] to derive a simple formula for the redundancy of a large class of variable-to-variable length codes on discrete, memoryless sources. We obtain new asymptotic upper bounds on the redundancy of the \Tunstall-Huuman" code and the \Tunstall-Shannon-Fano" code. For some sources we provide the best existing upper bound for the smallest achievable asymptotic red...

A time-dependent Mt/Mt/1 queue alternates through periods of under-, over-, and critical loading. We derive period-dependent, pathwise asymptotic expansions for its queue length, within the framework of strong approximations. Our main results include time-dependent fluid approximations, supported by a functional strong law of large numbers, and diffusion approximations, supported by a functiona...

The asymptotic properties of inhomogeneous products in the max-plus algebra context have been investigated. In particular, for products involving matrices with the same unique critical circuit, we have obtained some sufficiency conditions under which the rank of the final product matrix is less than or equal to the length of the critical circuit of the matrices in the product. For a product com...

This thesis addresses the problem of information transmission over noisy channels. In 1993, Berrou, Glavieux and Thitimajshima discovered Turbo-codes. These codes made it possible to achieve a very good performance at low decoding complexity. In hindsight, it was recognized that the underlying principle of using sparse graph codes in conjunction with message-passing decoding was the same as the...

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...

For a storage model with a fractional Brownian input process, an exact asymptotic expression for the queue length distribution is obtained, using a few plausible assumptions. The probability that the queue length is greater than x is shown to be asymptotically proportional to a Weibullian function multiplied by x ? : For a fractional Brownian input process with Hurst parameter H; the exponent i...

It has been noticed that all the known binary sequences having the asymptotic merit factor ≥ 6 are the modifications to the real primitive characters. In this paper, we give a new modification of the character sequences at length N = p1p2 . . . pr, where pi’s are distinct odd primes and r is finite. Based on these new modifications, for N = p1p2 . . . pr with pi’s distinct odd primes, we can co...

The traveling salesman problem is a problem of finding the shortest tour through given points. In 1959, Beardwood, Halton, and Hammersley studied asymptotic length of the shortest tour through points on Euclidean space. In particular they described the optimal tour length with Euclidean dimension for the case that points are distributed with respect to Lebesgue absolutely continuous measure. In...

This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into a number of segments and estimates the average power within each spectral segment. This method is able to estimate the power spectrum density of a signal fr...

We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finitedimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpo...