A high-accuracy adaptive conditional-probability estimator for fixed-width Booth multipliers

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 ω = 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 0.18μm CMOS process, the DCT core with ACPE (ω = 3) can save 14.3% area cost with only 0.48 dB peak-signal-to-noise-ratio (PSNR) penalty compared to P-T method.