Optimal Index Assignment for Multiple Description Scalar Quantization With Translated Lattice Codebooks

We design a K-description scalar quantizer, whose construction is based on a structure of translated scalar lattices and a lattice in K - 1 dimensional space. The use of translated lattices provides a performance advantage by exploiting a so-called staggering gain. The use of the K -1 dimensional lattice facilitates analytic insight into the performance and significantly speeds up the computation of the index assignment compared to state-of-the-art methods. Using a common decoding method, the proposed index assignment is proven to be optimal for the K-description case. It is shown that the optimal index assignment is not unique. This is illustrated for the two-description case, where a periodic index assignment is selected from possible optimal assignments and described in detail. The performance of the proposed quantizer accurately matches theoretic analysis over the full range of operational redundancies. Moreover, the quantizer outperforms the state-of-the-art MD scheme as the redundancy among the description increases.