Efficient bit-rate scalability for weighted squared error optimization in audio coding
We propose two quantization techniques for improving the bit-rate scalability of compression systems that optimize a weighted squared error (WSE) distortion metric. We show that quantization of the base-layer reconstruction error using entropy-coded scalar quantizers is suboptimal for the WSE metric. By considering the compandor representation of the quantizer, we demonstrate that asymptotic (high resolution) optimal scalability in the operational rate-distortion sense is achievable by quantizing the reconstruction error in the compandor's companded domain. We then fundamentally extend this work to the low-rate case by the use of enhancement-layer quantization which is conditional on the base-layer information. In the practically important case that the source is well modeled as a Laplacian process, we show that such conditional coding is implementable by only two distinct switchable quantizers. Conditional coding leads to substantial improvement over the companded scalable quantization scheme introduced in the first part, which itself significantly outperforms standard techniques. Simulation results are presented for synthetic memoryless Laplacian sources with mu-law companding, and for real-world audio signals in conjunction with MPEG AAC. Using the objective noise-mask ratio (NMR) metric, the proposed approaches were found to result in bit-rate savings of a factor of 2 to 3 when implemented within the scalable MPEG AAC. Moreover, the four-layer scalable coder consisting of 16-kb/s layers achieves performance close to that of the 64-kb/s nonscalable coder on the standard test database of 44.1-kHz audio