Embedded Multiple Description Scalar Quantizers

A new class of Embedded Multiple Description Scalar Quantizers (EMDSQ) is proposed. EMDSQ meet the desired features of high redundancy level, fine grain rate adaptation and progressive transmission of each description. Experimental results show that EMDSQ yield better rate-distortion performance in comparison to Multiple Description Uniform Scalar Quantizers (MDUSQ) previously proposed in the literature. Introduction: Multiple Description Coding (MDC) was introduced to efficiently overcome the channel impairments over diversity-based systems by allowing decoders to extract meaningful information from a subset of the bit-stream. Previous research focused on finding the optimal achievable rate-distortion regions [1], followed by the design of practical compression systems [2] to meet these theoretical boundaries. For robust communication over unreliable channels, the MDC system must deliver error-resilient bit-streams with a corresponding high redundancy level. Additionally a fine-grain scalability of the bit-stream is also a desirable feature for bandwidth varying channels. The proposed EMDSQ meet these desired features consisting of a high redundancy level, fine-grain rate adaptation and progressive transmission of each description. The above-mentioned MDUSQ [3] and EMDSQ are incorporated in a wavelet-based coding system and the rate-distortion performances of both MDC systems are compared when applied on a common dataset. Finally, the generalized form of EMDSQ targeting an arbitrary number of channels allows the design of realistic coders for practical multi-channel communication systems. Embedded Multiple Description Scalar Quantizers: For the two-channel EMDSQ we denote the set of embedded side-quantizers as ,0 m S Q , ,1 m S Q ,..., , m P S Q with 1,2 m = , and the set of embedded central-quantizers as 0 C Q , 1 C Q , ..., P C Q , where 1 1 1 1, 2, 1 2 1 2 ( , ) ( ) ( ) p p p k k k k C S S Q q q Q q Q q − − − = I for any quantization level , 0 p p P ≤ ≤ . The partition cells of any quantizer , m p S Q and p C Q are embedded in the partition cells of , m P S Q , , 1 m P S Q − ,..., , 1 m p S Q + and P C Q , 1 P C Q − ,..., 1 p C Q + respectively. Vaishampayan’s method [2] to design MDSQ for two channels relies on generating 2D index allocation matrices. Theoretically, the index allocation method of [2] can be generalized to more than two channels and more than two receivers, respectively. For an arbitrary number of channels M, an M-dimensional index allocation matrix must be generated. However such a matrix can no longer be graphically represented as in [2] for 2 M = . Thus, M channel quantizers can only be formulated analytically. For M-channels, the analytical expression of the proposed EMDSQ is: ) ) ) ) , , , , , , , , , , , ( ) , , ( ) ( ) , , m p m p m p m p m p A Sup Sup Inf Inf m p S m p m p m p m p m p B Sup Sup Inf Inf Q x x A A A A Q x Q x x B B B B    ∈ − −    =     ∈ − −    U U , (1)