Optimal Index Assignment for Multiple Description Scalar Quantization

We provide a method for designing an optimal index assignment for scalar K-description coding. The method stems from a construction of translated scalar lattices, which provides a performance advantage by exploiting a so-called staggered gain. Interestingly, generation of the optimal index assignment is based on a lattice in K-1 dimensional space. The use of the K-1 dimensional lattice facilitates analytic insight into the performance and eliminates the need for a greedy optimization of the index assignment. It is shown that 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 new index assignment is applied to design of a K-description quantizer, which is found to outperform a reference K-description quantizer at high rates. The performance advantage due to the staggered gain increases with increasing redundancy among the descriptions.