Multiple description coding via scaling-rotation transform

We propose a two-stage transform design technique for multiple description transform coding. The first stage is the structure design in which we enforce a scaling-rotation factorization of the transform and we further constrain the transform for specific channel conditions using the knowledge of the input correlation matrix and the desired output correlation matrix. In the second stage, magnitude design, we find the optimal transform from all admissible transforms given by the structure design using the numerical algorithm proposed by Goyal et al. (see Proc. of IEEE Data Compression Conference, 1998). Such a design enables a structured transform framework which reduces both the design and implementation complexities compared to an exhaustive search through the whole space of nonorthogonal transforms. We give two examples to illustrate the design idea, the scaling-Hadamard transform for equal rate channels and the scaling-DST transform for sequential protection channels