Chapter 24 - Distributed Arithmetic

Abstract

Distributed arithmetic (DA) is a computation algorithm that performs multiplication using precomputed lookup tables (LUTs) instead of logic. It is well suited to implementation on homogeneous field-programmable gate arrays (FPGAs) because of its high utilization of the available LUTs. It may also have advantages for modern heterogeneous FPGAs that contain built-in multipliers because it is area efficient for implementing long digital filters. DA targets the sum-of-products (or vector dot product) operation, and many digital signal processing (DSP) tasks such as filter implementation, matrix multiplication, and frequency transformation can be reduced to one or more sum-of-products computations. A common DA application on FPGAs is acceleration of frequency transformations such as the discrete cosine transform (DCT), which is a critical component of the MPEG video compression and JPEG image compression standards. The two-dimensional DCT can be implemented as two one-dimensional DCTs and a matrix transposition. Each DCT can be implemented as a matrix–vector multiplication, which is easy to implement on an FPGA using DA because it can be decomposed into a set of vector dot products.