Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the applicability of uniform pseudorandom binary generators in combination with the Central Limit Theorem to propose an easy to implement, efficient and flexible algorithm that leverages the properties of the pseudorandom binary generator used as an input, specially with respect to the correlation measure of higher order, to guarantee the quality of the generated samples. Our main result provides a relationship between the pseudorandomness of the input and the statistical moments of the output. We propose a design based on the combination of pseudonoise sequences commonly used on wireless communications with known hardware implementation, which can generate sequences with guaranteed statistical distribution properties sufficient for many real life applications and simple machinery. Initial computer simulations on this construction show promising results in the quality of the output and the computational resources in terms of required memory and complexity.

翻译：高斯随机数生成器因其在多个领域的应用而受到广泛关注。重要需求包括易于实现、尾部精度高以及平坦的频谱。本文研究均匀伪随机二进制生成器与中心极限定理相结合的适用性，提出一种易于实现、高效且灵活的算法。该算法利用输入伪随机二进制生成器的特性（特别是高阶相关性度量）来保证生成样本的质量。我们的主要结果揭示了输入伪随机性与输出统计矩之间的关系。我们提出了一种基于通信领域常用伪随机序列（具有已知硬件实现）组合的设计方案，该方案能够生成具有足够统计分布特性的序列，满足许多实际应用需求且实现机制简单。对此构造的初步计算机仿真结果表明，在输出质量以及所需内存和复杂度等计算资源方面均表现出良好性能。