Abstract

SANDOVAL-RUIZ, Cecilia E.. Numerical methods in finite differences for the estimation of FPGA hardware resources in LFSR (n,k) fractal architectures. Ing. invest. y tecnol. [online]. 2019, vol.20, n.3, e032.  Epub Oct 15, 2019. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2019.20n3.032.

In this paper we study the numerical method in finite differences for the estimation of resources in hardware, specifically on FPGA (Field Programmable Gate Arrays) technology, applied to a fractal model of LFSR architecture components (Linear Feedback Shift Registers) parallelized, as a basic element of multiplier systems in finite fields, Reed Solomon code and Artificial Neural Networks. The method addressed consisted of the discretization of the variables in the hardware synthesis report of the case studies, by means of mathematical modeling the descriptive equations are obtained, which allows to validate the strategies of optimization of the designs using the base of a mathematical operator with Linear Feedback Concurrent Structure LFCS (n,k), defined by composite functions with self-similarity. We obtain as a result a set of equations that describe the behavior of the estimated parameter, facilitating the evaluation of the design in previous stages, as well as the application of a recursive element, which allows obtaining the consumption of resources according to this logical-mathematical operator. These methods can be extended in the analysis and estimation of energy efficiency of the designs, which provide solutions in terms of energy consumption of electronic models and system performance.

Keywords : Numerical method in finite differences; resource estimation; LFCS; fractal modeling in VHDL; FPGA.

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