New Approach to the Reduction of Sign-Extension Overhead for Efficient Implementation of Multiple Constant Multiplications

Abstract

Sign-extension of operands in the shift-add network of multiple constant multiplication (MCM) results in a significant overhead in terms of hardware complexity as well as computation time. This paper presents an efficient approach to minimize that overhead. In the proposed method, the shift-add network of an MCM block is partitioned into three types of sub-networks based on the types of fundamentals and interconnections they involve. For each type of sub-network, a scheme which takes the best advantage of the redundancy in the computation of sign-extension part is proposed to minimize the overhead. Moreover, we also propose a technique to avoid the additions pertaining to the most significant bits (MSBs) of the fundamentals. Experimental results show that the proposed method always leads to implementations of MCM blocks with the lowest critical path delay. The existing methods for the minimization of sign-extension overhead are designed particularly for single multiplication or MCM blocks of FIR filter, but the proposed method can be used to reduce the overhead of sign-extension for MCM blocks of any application. In the case of FIR filters, the proposed method outperforms other competing methods in terms of critical path delay, area-delay product (ADP), and power-delay product (PDP), as well.Index Terms-Critical path, high-speed, low complexity, multiple constant multiplication (MCM), sign extension. 1549-8328

Design of high‐speed, low‐power, and area‐efficient FIR filters

“…This leads to an important overhead in speed, power, and area. To reduce the sign extension (SE) overhead in MCM, many approaches have been proposed, notably the MCM block partitioning [27] and positive offset [28] methods which exhibit the best results in speed and area, respectively. The conventional SE approach (CSEA) used traditionally in variable multiplication ( Y × X ) offers rather a good compromise in MCM [27], especially when both area and power are a concern.…”

“…To reduce the sign extension (SE) overhead in MCM, many approaches have been proposed, notably the MCM block partitioning [27] and positive offset [28] methods which exhibit the best results in speed and area, respectively. The conventional SE approach (CSEA) used traditionally in variable multiplication ( Y × X ) offers rather a good compromise in MCM [27], especially when both area and power are a concern. Comparatively with [27, 28], CSEA is very easy to be used: the SE is performed locally between successive PPs, assuring that at each stage, the partial sum contains the sum of the sign bits of previous PPs.…”

“…The conventional SE approach (CSEA) used traditionally in variable multiplication ( Y × X ) offers rather a good compromise in MCM [27], especially when both area and power are a concern. Comparatively with [27, 28], CSEA is very easy to be used: the SE is performed locally between successive PPs, assuring that at each stage, the partial sum contains the sum of the sign bits of previous PPs. In addition, CSEA is fully predictable, making possible the determination of the exact analytic bound of RADIX‐2 r at bit level.…”

An optimized two-level discrete wavelet implementation using residue number system

“…In LS, as the critical path delay (CPD) increases, the energy per operation increases and the operating frequency decreases [10]. In [11,12], the authors found constant bit widths [20], whereas the GE require more computational resources due to a larger search space [22].…”