The Cascading Haar Wavelet algorithm for computing the Walsh-Hadamard Transform

TL;DR

This paper introduces the Cascading Haar Wavelet algorithm for efficiently computing the Walsh-Hadamard Transform, leveraging Haar wavelet transforms with comparable serial complexity to existing methods and offering a natural parallelization approach.

Contribution

The paper presents a novel Haar wavelet-based algorithm for WHT with equivalent serial complexity and a new parallelization strategy.

Findings

Shares the same serial complexity as traditional divide-and-conquer algorithms

Provides a natural parallelization method with attractive features

Proposes a Haar wavelet-based approach for WHT computation

Abstract

We propose a novel algorithm for computing the Walsh-Hadamard Transform (WHT) which consists entirely of Haar wavelet transforms. We prove that the algorithm, which we call the Cascading Haar Wavelet (CHW) algorithm, shares precisely the same serial complexity as the popular divide-and-conquer algorithm for the WHT. We also propose a natural way of parallelizing the algorithm which has a number of attractive features.