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.