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 /spl mu/-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.
展开▼
机译:我们为熵编码的标量量化器(SQ)导出了一种渐近最优的多层编码方案,该方案使加权均方误差(WMSE)最小。在WMSE的情况下,最佳熵编码的SQ不均匀。常规的多层编码器在增强层量化基本层的重构误差,并且对于WMSE标准是次优的。我们考虑量化器的压缩扩展器表示形式,并提出在压缩域中实现可伸缩性。我们表明,这种多层编码系统在高分辨率的限制下,实现了不可缩放的熵编码SQ所给定的操作速率失真范围。针对层速率的各种值,给出了具有/ spl mu / law压扩的合成无记忆Laplace源的仿真结果。当将最佳多层方法应用于两层可伸缩MPEG-4 Advanced Audio Coder时,在“真实世界”的音频信号源上也将获得可观的收益。
展开▼