Fast Finite Field Hartley Transforms Based on Hadamard Decomposition

TL;DR

This paper introduces fast algorithms for the finite field Hartley transform (FFHT) using Hadamard-Walsh decompositions, enabling efficient computation for applications in communication systems.

Contribution

It presents novel fast transform algorithms for FFHT based on Hadamard decomposition, achieving optimal multiplicative complexity.

Findings

Decompositions meet the lower bound on multiplicative complexity.

Algorithms outperform traditional methods in computational efficiency.

Applicable to multiple access and spread spectrum systems.

Abstract

A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were proposed. The FFHT exhibits interesting symmetries, which are exploited to derive tailored fast transform algorithms. The proposed fast algorithms are based on successive decompositions of the FFHT by means of Hadamard-Walsh transforms (HWT). The introduced decompositions meet the lower bound on the multiplicative complexity for all the cases investigated. The complexity of the new algorithms is compared with that of traditional algorithms.