Linear Computation Coding: Exponential Search and Reduced-State Algorithms

TL;DR

This paper introduces a step-wise optimal search for linear computation coding that outperforms discrete matching pursuit, and a reduced-state algorithm that balances performance and computational feasibility for large matrices.

Contribution

It presents a novel step-wise optimal search method and a reduced-state algorithm that improve performance and scalability over existing methods in linear computation coding.

Findings

Performance gain over DMP is at least 10%.

Reduced-state algorithm is computationally feasible for large matrices.

Step-wise optimal search significantly improves coding efficiency.

Abstract

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper advances over the state-of-the art, that is based on a discrete matching pursuit (DMP) algorithm, by a step-wise optimal search. Offering significant performance gains over DMP, it is however computationally infeasible for large matrices and high accuracy. Therefore, a reduced-state algorithm is introduced that offers performance superior to DMP, while still being computationally feasible even for large matrices. Depending on the matrix size, the performance gain over DMP is on the order of at least 10%.