Algorithms of DVC - Distributed Multiple Description Coding - page 154

Optimized zero-padding : In the MDDVC with zero-padding, the number of zero-
padded will affect the correlation as well as the rate-distortion performance of side
and central decoder. Generally, when more zeros are padded, correlation between
two descriptions will be higher producing better estimation and better quality from
side decoder, while the central quality drops with the increasing of zeros. That
is, more zero-padding benefits the compression in two aspects, one is that the
lost description is estimated accurately, and the other is that the frames can be
compressed easily due to the increased correlation between adjacent pixels. While
on the other hand, more zero-padding makes the size of frame increase, which
maybe requires more bits to represent it, and also, when no loss happens, more
zero-padding means more redundancy added, so the central quality decreases. The
aforementioned analysis requires an optimization for the number of zeros padded.
Let D 0 .f; N / and D 1 .f; N / (or D 2 .f; N /) denote the mean squared errors
(MSE) from the central and side decoder for the input image f, respectively, given
the number of zero-padded is N. Let R.f; N / be the bit rate for two descriptions,
while R 1 .f; N / and R 2 .f; N / be the bit rates for the two balanced description 1 and
2, respectively. Our goal is to find the optimal parameterN in solving the following
optimization problem:

min
N

D 1 .f; N / (5.14)

subject to

condition1 W R.f; N / D 2R 1 .f; N / D 2R 2 .f; N / R budget (5.15)

condition2 W D 0 .f; N / D budget (5.16)

whereR budget is the available total bit rate to encode two descriptions and D budget is
the maximum distortion acceptable for central decoder reconstruction. The encoding
optimization module in Fig. 5.22 is based on the above function. With the constraint
on the total bit rate and the central distortion, N is adjusted accordingly to minimize
the side distortion.
The optimization for the problem is carried out in an iterative way. The basic
algorithm shown in Fig. 5.25 is to make use of the monotonicity of R and D as the
function of N . After initialization, a smallest N is searched to minimize D 1 subject
to condition 1 and condition 2.

5.6.5 Experimental Results

Here, there are mainly three groups of experiments taken into account to present
the efficiency of MDDVC proposed. They are performance comparison of differ-
ent coding methods, performance comparison with optimized zero-padding, and