On embedded scalable code stream of minimum expected distortion for variable rate channels

We consider the problem of constructing an embedded scalable code stream from a given tree structured quantizer (TSQ) to minimize the expected distortion weighted over a range of operational rates. If the rate weighting function is exponential, the problem is solvable by a simple algorithm reminiscent to merge sort. The complexity of the algorithm is O(NlogN) where N is the number of internal nodes of the corresponding quantizer tree.