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Linear computation coding is concerned with the compression ofmultidimensional linear functions, i.e. with reducing the computational effortof 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 discretematching pursuit (DMP) algorithm, by a step-wise optimal search. Offeringsignificant performance gains over DMP, it is however computationallyinfeasible for large matrices and high accuracy. Therefore, a reduced-statealgorithm is introduced that offers performance superior to DMP, while stillbeing computationally feasible even for large matrices. Depending on the matrixsize, the performance gain over DMP is on the order of at least 10%.

Linear Computation Coding: Exponential Search and Reduced-State Algorithms