U. Glaeser

FIGURE 29.6 Histogram of Nonzero DCT coefficients in sample MPEG stream.
Power vs. Quality and Precision Trade-offs
In many DSP applications, lower quality in visual or audio output can be tolerated for reduced power
dissipation. Recently, a number of researchers have resorted to approximate processing as a method for
reducing average system power. Ludwig et al. [31] have demonstrated an approximate filtering technique,
which dynamically reduces the filter order based on the input data characteristics. More specifically, the
number of taps of a frequency-selective FIR filter is dynamically varied based on the estimated stopband
energy of the input signal. The resulting stopband energy of the output signal is always kept under a
predefined threshold. This technique results in power savings of a factor of 6 for speech inputs. Nikol et al.
[32] have demonstrated an adaptive scheme for dynamically reducing the input amplitude of a Boothencoded
multiplier to the lowest acceptable precision level in an adaptive digital equalizer. Their scheme
simply involves an arithmetic shift (multiplication/division by a power of 2) of the multiplier input
depending on the value of the error at the equalizer output. They report power savings of 20%.
When the DA operation is performed MSB first (“Variable Supply Voltage Schemes” subsection), it
exhibits stochastically monotonic successive approximation properties. In other words, each successive
intermediate value is closer to the final value in a stochastic sense. An analytical derivation is presented
in [33]. As an example, let us assume that we have a DA structure computing the dot product of two
vectors. Each vector element is 8-bits 2’s complement integer. If we clock the DA structure of Fig. 29.5
for eight full cycles, the full precision value of the dot product will form into the RESULT register. If
instead we clock the DA structure for four cycles and perform a 4-bit arithmetic left shift of the output
in the RESULT register (multiplication by 2 4 ), we obtain an approximation of the actual dot product. If
we clock the structure once more (total of five cycles) and then perform a 3-bit arithmetic left shift of the
output (multiplication by 2 3 ), we obtain a better approximation. In this way, a DA structure can implement
a fine-grain trade-off between power and precision.
Xanthopoulos [23] is extensively using this property for power reduction in a DCT application. In
image and video compression applications not all spectral coefficients have the same visual significance.
Typically, a large number of high spatial frequencies are quantized to zero in a lossy image/video compression
environment (i.e., JPEG and MPEG) with no significant change in visual quality. The DCT
processor in [23] exploits such different precision requirements on a coefficient basis by reducing the
number of iterations of the DA units that compute the visually insignificant spectral coefficients in a userprogrammable
fashion. Figure 29.7 plots average power chip dissipation vs. compressed image quality in
terms of the image peak SNR (PSNR), a widely used quality measure in image processing. The data points
in the graph have been obtained by chip power measurements at different RAC maximum iteration settings.
The data implies that the chip can produce on average 10 additional decibels of image quality per milliwatt
of power dissipation. Figure 29.8 displays the actual compressed images for three (power, PSNR) data
points of Fig. 29.7 for visual appreciation.
© 2002 by CRC Press LLC
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Number of Nonzero DCT Coefficients