Methodology for FPGA Implementation of a Chaos-Based AWGN Generator

Additive White Gaussian Noise (AWGN) generators are a basic tool for the test and measurement of digital systems. One drawback for hardware implementation of the classically used algorithms is that they require the hardware implementation of complex operations (such as sinusoidal and logarithmic functions). In this chapter, a method for the design and hardware implementation of an AWGN generator based on chaotic maps is described. The advantage is that deterministic chaotic systems are described by simple nonlinear equations, and therefore, they are straightforward to implement in hardware. To ensure that the generated sequence has the desired Probability Density Function (PDF), the chaotic map, which is the heart of the system, is synthesized using an approach based on the theory of positive matrices method. The hardware implementation was developed using an Altera Cyclone III FPGA with the 3C120 Development Board. Luciana De Micco National University of Mar del Plata, Argentina Hilda Angela Larrondo National University of Mar del Plata, Argentina Methodology for FPGA Implementation of a Chaos-Based AWGN Generator

[1]  Mathieu Sinn,et al.  Ordinal analysis of time series , 2005 .

[2]  G. Marsaglia,et al.  The Ziggurat Method for Generating Random Variables , 2000 .

[3]  Joseph L. Leva.  A fast normal random number generator , 1992, TOMS.

[4]  Robert Shorten,et al.  Synthesizing chaotic maps with prescribed invariant densities , 2004 .

[5]  Werner Ebeling,et al.  PARTITION-BASED ENTROPIES OF DETERMINISTIC AND STOCHASTIC MAPS , 2001 .

[6]  Wolfgang Hörmann,et al.  Continuous random variate generation by fast numerical inversion , 2003, TOMC.

[7]  O A Rosso,et al.  Distinguishing noise from chaos. , 2007, Physical review letters.

[8]  O A Rosso,et al.  Quantifiers for randomness of chaotic pseudo-random number generators , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[10]  Karsten Keller,et al.  Symbolic Analysis of High-Dimensional Time Series , 2003, Int. J. Bifurc. Chaos.

[11]  Wayne Luk,et al.  A comparison of CPUs, GPUs, FPGAs, and massively parallel processor arrays for random number generation , 2009, FPGA '09.

[12]  Wayne Luk,et al.  Gaussian random number generators , 2007, CSUR.

[13]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[14]  C. K. Pauw,et al.  On the generation of a smooth Gaussian random variable to 5 standard deviations , 1988, COMSIG 88@m_Southern African Conference on Communications and Signal Processing. Proceedings.

[15]  Joshua D. Reiss,et al.  Construction of symbolic dynamics from experimental time series , 1999 .

[16]  Chris S. Wallace.  Fast pseudorandom generators for normal and exponential variates , 1996, TOMS.

[17]  Osvaldo A. Rosso,et al.  Randomizing nonlinear maps via symbolic dynamics , 2008 .

[18]  Osvaldo A. Rosso,et al.  Generalized statistical complexity measures: Geometrical and analytical properties , 2006 .

[19]  Wayne Luk,et al.  A Gaussian noise generator for hardware-based simulations , 2004, IEEE Transactions on Computers.