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Abstract
The fixed-width multiplier is attractive to many
multimedia and digital signal processing systems which are desirable
to maintain a fixed format and allow a little accuracy loss
to output data. This paper presents the design of high-accuracy
fixed-width modified Booth multipliers. To reduce the truncation
error, we first slightly modify the partial product matrix of Booth
multiplication and then derive an effective error compensation
function that makes the error distribution be more symmetric to
and centralized in the error equal to zero, leading the fixed-width
modified Booth multiplier to very small mean and mean-square errors.
In addition, a simple compensation circuit mainly composed
of the simplified sorting network is also proposed. Compared to
the previous circuits, the proposed error compensation circuit
can achieve a tiny mean error and a significant reduction in
mean-square error (e.g., at least 12.3% reduction for the 16-bit
fixed-width multiplier) while maintaining the approximate hardware
overhead. Furthermore, experimental results on two real-life
applications also demonstrate that the proposed fixed-width
multipliers can improve the average peak signal-to-noise ratio of
output images by at least 2.0 dB and 1.1 dB, respectively.
High-Accuracy Fixed-Width Modified Booth Multipliers for Lossy Applications.pdf
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