U. Glaeser

A priori knowledge of data stream distribution can be exploited at the algorithmic and architectural level
for computation minimization and power reduction.
Nielsen and Sparso [22] observed that 16-bit sampled speech data samples exhibit significant correlation,
in addition to a predominance of small signal values. As a result, they have proposed a sliced
datapath for a digital hearing aid filter bank to exploit the small magnitude of the input samples. The
arithmetic datapath has been partitioned in an MSB and an LSB slice. The MSB slice is only engaged
when the input bitwidth requires it. Activation of the slices is performed by using special data tags that
indicate the presence of sign extension bits in the MSB input slice. Additional circuit overhead is required
for the computation and update of the tags. Dynamic bitwidth adaptation is coarse and can only be
performed on a slice basis. This scheme results in data-dependent power reduction and processing time.
Xanthopoulos [23] has demonstrated a DA-based dicrete cosine transform (DCT) [24] architecture
that exploits correlation in the incoming image or video samples for computation minimization and
power reduction. DCT is a frequency domain data transform widely used in video and still image
compression standards such as MPEG [25] and JPEG [26]. The 8-point one-dimensional DCT transform
is defined as follows:
© 2002 by CRC Press LLC
X[ u]
7
c[ u]
( 2i + 1)uπ
= --------- x[]cos i ⎛------------------------- ⎞
2 ∑ ⎝ 16 ⎠
i=0
(29.8)
where c[u] = 1/ 2 if u = 0 and 1 otherwise.
Image pixels are locally well correlated and exhibit a certain number of common most significant bits.
These bits constitute a common-mode DC offset that only affects the computation of the DC DCT
coefficient (X[0] in Eq. (29.8)) and is irrelevant for the computation of the higher spectral (AC) coefficients
(X[1] …X[7]
in Eq. (29.8)). The DCT chip in [23] includes adaptive-bitwidth DA computation
units that reject common most significant bits for all AC coefficient computations resulting in arithmetic
operations with reduced bitwidth operands, thus reducing switching activity. The bit-serial nature of the
DA operation allows very fine grain (1-bit) adaptation to the input dynamic range as opposed to the
coarse slice-level adaptation in [22].
An interesting algorithmic adaptation to data distribution properties has been demonstrated in [27].
The chip computes the inverse discrete cosine transform (IDCT) and is targeted to MPEG-compressed
video data. The 8-point, one-dimensional IDCT is defined as follows:
x[] i
=
7
∑
u=0
c[ u]
--------- X[ u]cos
⎛( 2i + 1)uπ
------------------------- ⎞
2 ⎝ 16 ⎠
(29.9)
where c[u] = 1/ 2
if u = 0 and 1 otherwise.
Numerous fast IDCT algorithms can minimize the number of multiplications and additions implied
by Eq. (29.9) [28,29]. Yet, the statistical distribution of the input DCT coefficients possesses unique
properties that can affect IDCT algorithmic design. Typically, 64-coefficient DCT blocks of MPEGcompressed
video sequences have only 5–6 nonzero coefficients, mainly located in the low spatial frequency
positions due to the low pass characteristics of frame sequences [27]. The histogram of Fig. 29.6
shows the frequency of 64-coefficient block occurrence plotted versus the number of nonzero coefficient
content for a typical MPEG sequence. The mode of such distributions is invariably blocks with a single
nonzero spectral coefficient (typically the DC).
Given such input data statistics, we observe that direct application of Eq. (29.9) will result in a small
average number of operations since multiplication and accumulation with a zero-valued coefficient X[k]
constitutes a NOP [30]. The chip in [27] uses such a direct coefficient-by-coefficient algorithm coupled
with extensive clock-gating techniques to implement the implied NOPs. IDCT computation power of
4.5 mW for MPEG-2 sample rates has been reported.