A High-Accuracy Adaptive Conditional-Probability Estimator for Fixed-Width Booth Multipliers

Abstract

In this paper, a single compensation formula of adaptive conditional-probability estimator (ACPE) applied to fixed-width Booth multiplier is proposed. Based on the conditional-probability theory, the ACPE can be easily applied to large length Booth multipliers (such as 32-bit or larger) for achieving a higher accuracy performance. To consider the trade-off between accuracy and area cost, the ACPE provides varying column information to adjust the accuracy with respect to system requirements. The 16-bit ACPE Booth multiplier with = 3 reduces 28.9% silicon area with only 0.39 dB signal-to-noise ratio (SNR) loss when compared with post-truncated (P-T) Booth multiplier. Furthermore, the ACPE Booth multipliers are applied to two-dimensional (2-D) discrete cosine transform (DCT) to evaluate the system performance. Implemented in a TSMC 0.18 m CMOS process, the DCT core with ACPE ( = 3) can save 14.3% area cost with only 0.48 dB peak-signal-to-noise-ratio (PSNR) penalty compared to P-T method.

A high accuracy fixed-width Booth multiplier using select probability estimation bias

“…In this paper, all zeros and all ones code are defined as special conditions. The expected values with corresponding nonzero code were addressed in [8]. Fig.…”

“…The probability compensated bias was presented in [7] to reduce established time and improve accuracy. The author further improves accuracy by using an conditional probability [8]. Thus, it is very important for fining a high accuracy compensated method in fixed-with multiplier design.…”

Area-Efficient Fixed-Width Squarer With Dynamic Error-Compensation Circuit

“…Squaring operations can be executed using a fixed-width multiplier and many error-compensation methods have been proposed to deal with truncation error in fixed-width multipliers [7]- [13]. Adjusting the accuracy of fixed-width multipliers requires the inclusion of column information [10]- [13].…”

“…Adjusting the accuracy of fixed-width multipliers requires the inclusion of column information [10]- [13]. A binary threshold was presented to improve accuracy in a fixed-width Booth multiplier [11].…”

“…A binary threshold was presented to improve accuracy in a fixed-width Booth multiplier [11]. Generalized probabilistic estimation bias (GPEB) has also been introduced for Booth multipliers [12], which saves established time in the compensating circuit, and a conditional probability estimator (ACPE) has been proposed to improve accuracy [13]. Squaring operations can be executed using a fixed-width multiplier; however, this tends to results in redundant circuitry when dealing with very-large-scale integration (VLSI) designs.…”