An efficient hardware implementation of high quality AWGN generator using Box-Muller method

Abstract

Box Muller (BM) algorithm is extensively used for generation of high quality Gaussian Random Numbers (GRNs) in hardware. Most efficient published implementation of BM method utilizes transformation of 32-bit data path to 16 bits and use of first degree piece-wise polynomial approximation to compute logarithmic and square root functions. In this work, we have performed extensive error analysis to show that coefficient memory for polynomial approximation can be reduced by more than 35 percent without compromising on quality of generated Gaussian samples. This also reduces complexity of corresponding address generator, which requires most hardware resources. We have also used more efficient and statistically accurate skipahead Linear Feedback Shift Registers to generate uniformly distributed numbers for the BM algorithm. Complete hardware implementation utilizes only 407 slices, 03 DSP blocks and 1.5 memory blocks on Xilinx Virtex-4 XC4VLX15 operating at 230 MHz while providing a tail accuracy of 6.6σ. This is better in terms of accuracy and hardware utilization than any of the previously reported architecture.

Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields

“…Section 3 describes the binary equivalent model of an LFSR defined in a GF(2 n ) and the proposal of a Gaussian PRNG based on this model. The statistical analysis of the numbers produced by the proposed PRNG is presented in Section 4 and compared to the Box-Muller [23,24] algorithm, a well-known algorithm not based on CLT. Finally, conclusions are presented in Section 5.…”

Gaussian Pseudorandom Number Generator Based on Cyclic Rotations of Linear Feedback Shift Registers

“…Although the application of CLT is not the only method to generate Gaussian random numbers [19], it will always be a reference to take in mind. In [18], a comparison is performed among the hardware implementation of three of the best-known methods: CLT, Box-Muller algorithm [20,21] and polarization decision algorithm [22]. The comparison reveals that the number of gates and other hardware resources are very similar, while the CLT, implemented in a field-programmable gate array (FPGA) using directly the numbers produced by several LFSR, showed worse results in the normality tests.…”

Twister Generator of Random Normal Numbers by Box-Muller Model

“…Normal GRNGs are widely used in mathematical studies (Halim et al, 2012;Neugebauer et al, 2019), systems of message communication (Lee et al, 2006;Martino et al, 2012;Zhou et al, 2014), designing of computer games (Sukajaya et al, 2012), complicated technical systems (Malik et al, 2011;Paraskevakos and Paliouras, 2011), models for financial analysis (Sauer, 2012), biological studies (Menyaev et al, 2013;2016), development of medical devices (Menyaev and Zharov, 2005;2006a;2006b) and as well as in many other applied fields.…”