Asymptotically Optimal Scalable Coding for Minimum Weighted Mean Square Error

In this paper, we derive an asymptotically optimal multi-layer coding scheme for entropy-coded scalar quantizers (SQ) that minimizes the weighted mean-squared error (WMSE). The optimal entropy-coded SQ is non-uniform in the case of WMSE. The conventional multi-layer coder quantizes the base-layer reconstruction error at the enhancement-layer, and is sub-optimal for the WMSE criterion. We consider the compander representation of the quantizer, and propose to implement scalability in the compressed domain. We show that such a multi-layer coding system achieves the operational rate-distortion bound given by the non-scalable entropy-coded SQ, at the limit of high resolution. Simulation results for a synthetic memoryless Laplace source with -law companding are presented for various values of layer rates. Substantial gains are also achieved on the \real-world" sources of audio signals, when the optimal multi-layer approach is applied to a two-layer scalable MPEG-4 Advanced Audio Coder.