An Analytical Framework and Approximation Strategy for Efficient Implementation of Distributed Arithmetic-Based Inner-Product Architectures

Distributed arithmetic (DA)-based approximate structures are used for efficient implementation of inner-products in various error-resilient applications. In the existing literature, most of these approximate architectures are developed by truncating the least significant bits (LSBs) of the inputs and/or the multiplying coefficients. The existing works do not provide any analytical study to evaluate and design an approximate structure. To address this issue, an analytical framework is proposed in this paper. It is shown that the analytical results match very closely with the Monte Carlo simulation results. The proposed framework reveals that the truncation of the LSBs of partial inner-products is a promising alternative to design more efficient DA architectures with less error. Following these observations, a novel approach to truncate the LSBs of partial inner-products, namely, a weight-dependent truncation strategy and its two variants with a suitable error compensation function are presented in this paper. Synthesis results, accuracy analysis, and evaluation in two commonly used error-tolerant applications demonstrate the superiority of the proposed architectures over the state-of-the-art DA-based approximate structures.