Algorithms of MD - Distributed Multiple Description Coding - page 57

Fig. 4.4 The encoding optimization process

of the side distortion and its bit rate. To facilitate the description, some notations are
defined in the following.
Let I denotes an image, and S

D f s 1 ;s 2 ;:::;s m g

its m wavelet sub-bands after
the decomposition. ı S refers to the magnified degree of the lattice area (i.e., quan-
tization “volume-size”) used for all the sub-bands. N S D f N s i j i D 1;2;:::;m g
represents the set of the index numbers used in the labeling function for different
sub-bands. D 0 .S; ı S ;N S /, D 1 .S; ı S ;N S /,andD 2 .S; ı S ;N S / denote the mean
squared errors (MSE) from the central decoder and the side decoders for the input
image I , respectively, given the lattice vector quantizers with parameter ı S and the
index set N S R 1 .S; ı S ;N S /.R 1 .S; ı S ;N S / and R 2 .S; ı S ;N S / are the bit rates for
encoding each description of I , respectively.
Our goal is to find the optimal parameters ı S and N S in solving the following

optimization problem:

ı S ;N S D 0 .S; ı S ;N S /

min (4.2)

subject to

Condition 1 W R 1 .S; ı S ;N S / D R 2 .S; ı S ;N S / D R budget (4.3)

Condition 2 W D 1 .S; ı S ;N S / D D 2 .S; ı S ;N S / D D budget (4.4)

where R budget is the available bit rate to encode each description, and D budget is
the maximum distortion acceptable for single-channel reconstruction. The encoding
optimization module in Fig. 4.1 is based on the above functions. With the constraints
on the bit rate per channel and the side distortion, ı S and N S are adjusted

accordingly to minimize the central distortion.
The optimization for the problem is carried out in an iterative way. The basic
algorithm shown in Fig. 4.4 is to make use of the monotonicity of both R and
D as the functions of ı S . Firstly, after initialization a smallest ı S is searched to
minimize subject to Condition 1. Secondly, according to Condition 2, we can update