Multiplierless approximation of transforms using lifting scheme and coordinate descent with adder constraint

This paper describes an algorithm for systematically finding a multiplierless approximation of transforms where VLSI-friendly binary coefficients of the form k/2ⁿ are employed in the approximation. Assuming the cost of binary shifters is negligible in hardware, the total number of binary adders required to approximate the transform is used as the complexity constraint. The proposed algorithm is systematic and fast. It eliminates the need for trial-and-error binary approximations of the coefficients. Specifically, two types of multiplierless approximations of the discrete cosine transform (DCT) are presented to illustrate the algorithm.