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

Area of Science:

• Computer Science
• Applied Mathematics
• Digital Signal Processing

Background:

• Generating pseudorandom numbers with a Gaussian distribution is crucial for simulations and statistical analysis.
• Existing methods often face limitations in hardware implementation cost and algorithmic complexity.
• Linear Feedback Shift Registers (LFSRs) are commonly used but require careful configuration for optimal performance.

Purpose of the Study:

• To propose a novel, cost-effective pseudorandom number generator (PRNG) with Gaussian distribution.
• To design a generator suitable for low-cost hardware implementation while also considering software applications.
• To overcome the limitations of previous LFSR-based Gaussian generators through a simplified optimization algorithm.

Main Methods:

• Utilizing Linear Feedback Shift Registers (LFSRs) combined with cyclic rotations.
• Developing a less complex algorithm for finding optimal LFSR configurations.
• Applying the simulated annealing algorithm for enhanced adjustment to the normal distribution.

Main Results:

• The proposed generator offers a low implementation cost for hardware.
• It surpasses previous LFSR-based Gaussian generators in terms of algorithmic simplicity and usability.
• The simulated annealing algorithm further refines the generated numbers for better normal distribution adherence.

Conclusions:

• The presented Gaussian pseudorandom number generator is efficient and practical for real-world applications.
• Its low cost and improved algorithm make it a viable alternative for various simulation and statistical needs.
• The generator provides a usable and accurate solution for producing Gaussian-distributed pseudorandom numbers.