核心概念
This work studies the theoretical framework to apply the Central Limit Theorem to generate Gaussian pseudorandom sequences from sums of binary sequences with good correlation properties, providing a relationship between the pseudorandomness of the input binary sequences and the statistical moments of the output Gaussian sequences.
要約
The paper focuses on generating Gaussian pseudorandom noise using binary sequences, which provides a simpler hardware implementation compared to other methods like the Box-Muller algorithm.
Key highlights:
- Theorem 1 and Theorem 2 establish bounds on the product moments of the generated Gaussian sequences in terms of the correlation measures of the input binary sequences.
- The authors analyze the correlation properties of Gold codes, showing that they do not exhibit full peaks in the third and fourth correlation measures, making them a good candidate for the proposed Gaussian random number generator (GRNG).
- Computational experiments compare the performance of GRNGs using m-sequences and Gold codes, demonstrating that Gold codes offer better statistical and pseudorandom properties.
- The paper discusses the influence of the correlation peaks in the input binary sequences on the Gaussian multivariate properties of the output, and proposes further research directions to study the Tausworthe model and the search for characteristic polynomials that balance memory requirements and statistical performance.