Practical Tera-scale Walsh-Hadamard Transform

摘要

In the mid-second decade of new millennium, the development of IT has reachedunprecedented new heights. As one derivative of Moore's law, the operatingsystem evolves from the initial 16 bits, 32 bits, to the ultimate 64 bits. Mostmodern computing platforms are in transition to the 64-bit versions. Forupcoming decades, IT industry will inevitably favor software and systems, whichcan efficiently utilize the new 64-bit hardware resources. In particular, withthe advent of massive data outputs regularly, memory-efficient software andsystems would be leading the future. In this paper, we aim at studying practical Walsh-Hadamard Transform (WHT).WHT is popular in a variety of applications in image and video coding, speechprocessing, data compression, digital logic design, communications, just toname a few. The power and simplicity of WHT has stimulated research efforts andinterests in (noisy) sparse WHT within interdisciplinary areas including (butis not limited to) signal processing, cryptography. Loosely speaking, sparseWHT refers to the case that the number of nonzero Walsh coefficients is muchsmaller than the dimension; the noisy version of sparse WHT refers to the casethat the number of large Walsh coefficients is much smaller than the dimensionwhile there exists a large number of small nonzero Walsh coefficients. Clearly,general Walsh-Hadamard Transform is a first solution to the noisy sparse WHT,which can obtain all Walsh coefficients larger than a given threshold and theindex positions. In this work, we study efficient implementations of very largedimensional general WHT. Our work is believed to shed light on noisy sparseWHT, which remains to be a big open challenge. Meanwhile, the main idea behindwill help to study parallel data-intensive computing, which has a broad rangeof applications.