The performance of MMSE Iterative Equalization based on MAP-SBVP and COD-MAP algorithms (for generating extrinsic information) are compared for fading and non-fading communication channels employing serial concatenated convolution codes. MAP-SBVP is a convolution decoder using a conventional softMAP decoder followed by a soft-convolution encoder using the soft-boolean value propagation (SBVP). ...

In 9] Knuth shows how to derive the convolution formulas of Ha-gen, Rothe and Abel from Vandermonde's convolution or binomial theorem for integer exponents. In the present paper, we shall rst present a short and elementary proof of the multi-extension of the above con-volution formulas, due to Raney and Mohanty. In the second part we shall present a multi-version of Knuth's approach to convolut...

The International Commission on Radiation Units and Measurements Report 62 (ICRU 1999) introduced the concept of expanding the clinical target volume (CTV) to form the planning target volume by a two-step process. The first step is adding a clinically definable internal margin, which produces an internal target volume that accounts for the size, shape and position of the CTV in relation to anat...

This note extends Voiculescu’s S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the S-transform in the case of vanishing mean, the usual formula makes perfectly good sense.

In this paper we define and study the Dunkl convolution product and the Dunkl transform on spaces of distributions on R. By using the main results obtained, we study the hypoelliptic Dunkl convolution equations in the space of distributions.

The commutative neutrix convolution product of the functions xe − and xe μx + is evaluated for r, s = 0, 1, 2, . . . and all λ, μ. Further commutative neutrix convolution products are then deduced.

Up to date, the middle convolution is the most powerful tool for realizing classical groups as Galois groups over Q(t). We study the middle convolution of local systems on the punctured affine line in the setting of singular cohomology and in the setting of étale cohomology. We derive a formula to compute the topological monodromy of the middle convolution in the general case and use it to dedu...

In the present paper we present the tensor-product approximation of multidimensional convolution transform discretized via collocation-projection scheme on the uniform or composite refined grids. Examples of convolving kernels are given by the classical Newton, Slater (exponential) and Yukawa potentials, 1/‖x‖, e−λ‖x‖ and e−λ‖x‖/‖x‖ with x ∈ Rd. For piecewise constant elements on the uniform gr...

This paper continues the investigation of the use of spectral analysis on certain noncommutative nite groups|wreath product groups|in digital signal processing. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group-based convolution is de ned in both the spatial and spect...