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Implementation of a Bi-Variate Gaussian Random Number Generator on FPGA without Using Multipliers

Eldho P Sunny , Haripriya. P

The multivariate Gaussian distribution is used to model random processes with distinct pair-wise correlations, such as stock prices that tend to rise and fall together. Multivariate Gaussian vectors with length n are usually produced by first generating a vector of n independent Gaussian samples, then multiplying with a correlation inducing matrix requiring Operations(n2) multiplications. This paper presents a method of generating bivariate vectors directly from the uniform distribution and eliminating the need for any multipliers. The method relies only on small read only memories and adders, and so can be implemented using only logic resources (lookup-tables and registers), saving multipliers, and block-memory resources for the numerical simulation that the multivariate generator is driving. As an optimization, only positive values are considered for the implementation. FPGA-optimized Random Number Generators (RNGs) used for uniform distribution are more resource efficient than software-optimized RNGs, as they can take advantage of bit-wise operations and FPGA-specific features. This paper use a new type of FPGA RNG called a LUT-SR RNG, which takes advantage of bit-wise XOR operations and the ability to turn LUTs into shift-registers of varying lengths. This paper model a Gaussian random number generator where its inputs elements are correlation matrix of standard deviation from previous history.