Algorithms of MD - Distributed Multiple Description Coding - page 56

our scheme is based on a three-order “finite-context” model, that is, three previous
symbols make up the context.

Step 5: Central Decoder and Side Decoder

At the receiver, if both descriptions are received, the two descriptions can be
processed by the central decoder after arithmetic decoding, and the sequence of
fine lattice points can be reconstructed with the central distortion. However, if

either of the descriptions is lost, the conventional side decoder can only produce
0 1 or 0 2 as an approximate to , leading to a larger side distortion. In contrast, we
can obtain a better side decoding result by performing lost information prediction
when necessary, based on the neighboring inter-vector correlation of wavelet
coefficients and the above-mentioned alternative transmission scheme. The design
of the optimized side decoder with prediction will be elaborated in Sect. 4.1.3 .

f g

4.1.3 Encoding and Decoding Optimization

4.1.3.1 Encoding Parameter Optimization

In MDLVQ image encoding, there are two important factors which will affect the
reconstruction image quality and the bit rate. The first one is the area of hexagonal
lattice (in step 3), that is, the quantization “volume-size” used in LVQ, while the
other is the choice of sub-lattice index (in step 4).
Since the lattice A 2 is the space which can be spanned by two vectors (1, 0) and

. 1=2; p 3=2/, the area of the hexagonal lattice is determined by the two vectors.
However, we can keep the shape of the hexagonal lattice and change its area by
multiplying the generator matrix G by a factor ı.ı 2 R; ı > 0/. The parameter ı in
the LVQ is similar to the step-size in scalar quantization (SQ). By changing ı,the
central distortion D 0 and its associated bit rate can be adjusted.
For the lattice A 2 , the choice of index N will not change the central distortion
D 0 for a given ı. However, the side distortion D 1 and D 2 will be sensitive to the
value of N . When the index N increases, D 0 has no change, but D 1 and D 2 will
increase significantly. On the other hand, the bit rates associated with D 1 and D 2
will decrease with the increase of N . The index N is analogous to the number
of diagonal of index assignment in MDSQ [ 5 ]. In MDSQ, the increasing of the
number of diagonals will have severe impact on D 1 and D 2 and their associated
rates, while D 0 does not change. It is desired to find the optimal parameters ı and
N for striking the best trade-off among central distortion, side distortion, and their
associated bit rates. With the analysis of analogies between MDLVQ and MDSQ, we
can perform the optimization of parameters ı and N in MDLVQ encoding like the
optimization way for MDSQ encoding in [ 5 ]. Therefore, we can formulate the MD
design problem as yielding optimal performance in the presence of the constraints