Walsh Spectrum Analysis on Sampling Distributions

The dataset stores a random sampling distribution with cardinality of support of 4,294,967,296 (i.e., two raised to the power of thirty-two). Specifically, the source generator is fixed as a symmetric-key cryptographic function with 64-bit input and 32-bit output. A total of 17,179,869,184 (i.e., two raised to the power of thirty-four) randomly chosen inputs are used to produce the sampling distribution as the dataset. The integer-valued sampling distribution is formatted as 4,294,967,296 (i.e., two raised to the power of thirty-two) entries, and each entry occupies one byte in storage. The dataset is used as the experimental analysis subject of an interdisciplinary project "Noisy Sparse Walsh-Hadamard Transform". The project initiates the study of finding the largest (and/or significantly large) Walsh coefficients and the index positions of an unknown distribution by sampling. References: [1] R. Scheibler, S. Haghighatshoar, M. Vetterli, "A Fast Hadamard Transform for Signals With Sublinear Sparsity in the Transform Domain", IEEE Transactions on Information Theory, vol. 61, no. 4, pp. 2115 - 2132, 2015 (https://doi.org/10.1109/TIT.2015.2404441). [2] X. Chen, D. Guo, "Robust Sublinear Complexity Walsh-Hadamard Transform with Arbitrary Sparse Support", in Proc. IEEE Int. Symp. Information Theory, pp. 2573-2577, 2015 (https://doi.org/10.1109/ISIT.2015.7282921). [3] M. Cheraghchi, P. Indyk, "Nearly Optimal Deterministic Algorithm for Sparse Walsh-Hadamard Transform", arXiv:1504.07648v1, 2015. [4] X. Li, J. K. Bradley, S. Pawar, K. Ramchandran, "SPRIGHT: A Fast and Robust Framework for Sparse Walsh-Hadamard Transform", arXiv:1508.06336, 2015. [5] Y. Lu, Y. Desmedt, "Walsh-Hadamard Transform and Cryptographic Applications in Bias Computing", IACR eprint, 2016 (https://eprint.iacr.org/2016/419). [6] Y. Lu, "Practical Tera-scale Walsh-Hadamard Transform", FTC'2016, IEEE, pp. 1230 - 1236, 2017 (http://ieeexplore.ieee.org/document/7821757/).

该数据集存储了一个具有4,294,967,296（即32次方）支撑集基数的不规则抽样分布。具体而言，源生成器固定为一种具有64位输入和32位输出的对称密钥加密函数。共计17,179,869,184（即34次方）随机选取的输入被用于生成抽样分布，作为数据集。整数抽样分布以4,294,967,296（即32次方）个条目格式化，每个条目在存储中占用一个字节。该数据集被用作跨学科项目“噪声稀疏沃舍-哈达玛变换”的实验分析对象。该项目旨在通过抽样寻找未知分布中最大的（以及/或显著大的）沃舍系数及其索引位置。参考文献：[1] R. Scheibler, S. Haghighatshoar, M. Vetterli, "一个具有变换域中稀疏性低于线性的信号的快速哈达玛变换