Error Compensation Techniques for Fixed-Width Array Multiplier Design — A Technical Survey

Abstract

This paper provides a comprehensive review of various error compensation techniques for fixed-width multiplier design along with its applications. In this paper, we have studied different error compensation circuits and their complexities in the fixed-width multipliers. Further, we present the experimental results of error metrics, including normalized maximum absolute error [Formula: see text], normalized mean error [Formula: see text] and normalized mean-square error [Formula: see text] to evaluate the accuracy of fixed-width multipliers. This survey is intended to serve as a suitable guideline and reference for future work in fixed-width multiplier design and its related research.

A modified truncation and rounding-based scalable approximate multiplier with minimum error measurement

“…Truncation and Rounding based Scalable Approximate Multiplier (TOSAM) has few modes of error measurement based upon height (h) and truncated (t) named as (h,t). These multipliers are named as TOSAM(0,2), TOSAM(0,3), TOSAM (1,5), TOSAM (2,6), TOSAM (3,7), TOSAM (4,8), and TOSAM (5,9). Multiplication provides a substantial impact on metrics like power dissipation, speed, size and power consumption.…”

“…The approximation multiplier is made up of a few basic blocks in which the approximate technique is performed by using any one of the various phases [3]. When it comes to approximation techniques, truncation of partial products is one of the most effective methods for reducing the error by using correction functions [4]. There are various types of error measurement approximate multipliers depending on the operand size.…”

Approximate Multipliers Based on New Approximate Compressors

“…Approximations can be introduced in any of these blocks [6]. For example, truncation of the partial products is a well stablished approximation technique in which some of the partial products are not formed and the truncation error is reduced with the help of suitable correction functions [7]- [9].…”

Imprecise 4‐2 compressor design used in image processing applications

“…A large number of arithmetic applications are implemented using precise and deterministic algorithms. However, some applications such as signal/image processing, communication, and multimedia can tolerate errors and produce results which are good enough for human perception [8][9][10]. Since approximate or lessthan-optimal results are sufficient, these error-tolerant applications allow computing systems to trade quality for energy, area, and performance [10][11][12][13][14].…”

“…For large size multiplier, the authors in [14] proposed approximate 15‐4 compressors which are composed of approximate 5‐3 compressors. Fixed‐width multipliers with various error correction techniques are other approximation techniques to achieve high energy efficiency with the compromising accuracy [9].…”