Multiple Description Coding using Multiple Description

tion Scalar Quantizer (MDSQ)

The most commonly used approach in creating multiple descriptions is based on modifying the quantization block. Vaishampayan proposed an idea to create multiple descriptions using quantization and is known as MDSQ. The optimal design of fixed rate MDSQ and good index assignment for a memoryless Gaus- sian source has been studied previously [67]. The optimal design of entropy

0 2 3 4 6 8 9 10 7 5 1 11 12 S T C 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 5 6 7 8 9 101112 0 1 2 3 4 0 1 2 3 4 (b) s t 0 1 2 3 4 5 6 7 8 S T C 0 1 2 3 4 5 6 7 8 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 (a) s t

Figure 2.4: Two examples of index assignment matrix and the corresponding central and side quantizers (a) staggered case index assignment (b) modified nested index assignment.

constrained MDSQ is discussed in [76], while the high rate analysis of fixed rate and entropy constrained MDSQs is derived in [77].

An MDSQ consists of two parts: A scalar quantizer that maps a set of random variables O ∈ {o0, o1, o2, ...} to another countable set C ∈ {0, 1, 2, ..., n − 1}

(commonly known as the central quantizer) and an index assignment matrix that splits the indexes of the central quantizer into two complementary and redundant descriptions, commonly called the side quantizers. The reconstructed quality of the source from the side quantizers is lower than the reconstructed quality from the central quantizer. The relationship of the quantizer bins in the central quantizer to those in the side quantizers are defined by an index assignment matrix, whose row and column indexes correspond to those of the side quantizers,

S and T , respectively. The amount of redundancy between the descriptions is

controlled by the number of diagonals, f , filled in the index assignment matrix. Two different index assignment matrices and their corresponding central and side quantizers are shown in Figure 2.4.

Figure 2.4(a) shows an example of having staggered index assignment resulting in side quantizers with non-overlapped quantizer bins, while Figure 2.4(b) shows an example of having a modified nested index assignment resulting in side quantizers with overlapped quantization bins. The two descriptions are created by the row and column indices of the index assignment matrix. In either case, the number of diagonals (f ) filled in the index assignment matrix defines the maximum side quantizer bin spread, i.e., gδ, where δ is the quantizer bin width of the central

quantizer and g is the maximum side quantizer bin spread factor. The value of g for the two cases, the staggered and the modified nested index assignment matrix, is obtained by Eq. (2.11) and Eq. (2.12), respectively

g = f, (2.11) g = f 2 2 − f 2 + 1. (2.12)

The reconstructed value is the same as the central quantizer reconstruction when both the descriptions are received. On the other hand, the side reconstruction quality depends on the number of diagonals filled in index assignment matrix. In Figure 2.4(a) only 9 cells of the index assignment matrix are filled. The redun- dancy between the descriptions depends on the unfilled cells. The highest possible redundancy between the descriptions is achieved by filling only the main diago- nal of the index assignment matrix, resulting in similar central and side decoding quality. The side decoding quality is lowest if all the cells of the index assignment matrix are occupied, resulting in no redundancy between the descriptions.

The very first multiple description image coding based on MDSQ is proposed by Vaishampayan [78], in which the MDSQ is applied to the DCT coefficients of the JPEG coder. After MDSQ, two descriptions are then entropy coded sepa- rately and transmitted through different channels. A wavelet and MDSQ-based multiple description image coding is proposed by Servetto in [5]. In this coder, MDSQ is applied to the wavelet coefficients and better redundancy allocation is achieved by using different index assignment matrices for different subbands. The SPIHT algorithm then encodes the independently created descriptions. Conven- tional MDC schemes focus on generating two descriptions having balanced rate distortion performance. Most of the methods on generating more than two de- scriptions are based on subsampling of the source content [5, 66, 79]. Examples include wavelet zero tree-based subsampled packetization of the two descriptions generated from a single MDSQ [5] and grouping together of different wavelet trees using the SPIHT algorithm [66]. However, the main problem of these schemes is the severe effect on the reconstructional quality of the content on joint decoding when any of the description is unavailable, as each description carries the infor- mation of certain coefficients of the image. In Chapter 3, a new approach for generating more than two descriptions is proposed, with each description con-

taining information from all coefficients and yielding descriptions with balanced and unbalanced rate distortion performance.

Different MDSQ-based methods are proposed to incorporate quality scalability with in the multiple description image coding framework [53, 73, 80, 81]. In [73], a layered tree-based multiple description coding scheme is presented. In [53], a scalable multiple description coding (SMDC) scheme based on embedded MDSQ (EMDSQ) and quad tree type coding is discussed in detail. In EMDSQ, a set of side quantizers that generates different number of descriptions is derived from an embedded central quantizer. The index assignment matrix considered in EMDSQ results in side quantizers with non-overlapped cells and only the bal- anced joint decoding is possible. The design problem of EMDSQ is discussed in detail in [54, 82, 83]. In contrast to EMDSQ, the MDSQ-SR presented in Chap- ter 4 considers different index assignment matrices resulting into non-overlapped and overlapped side quantizer bins to incorporate different amount of redundancy between the descriptions at the base layer. MDSQ-SR not only facilitates the user to incorporate different amount of redundancy among the descriptions depending on the number of diagonals filled in the index assignment matrix of the base layer but also supports the joint decoding in balanced and unbalanced fashion.