Reduced complexity quantization under classification constraints

In optimal product vector quantization (VQ) sub-vectors within a vector are encoded separately. Optimal product VQ (PVQ) aims at maximizing the rate-distortion (RD) performance. We consider scenarios where PVQ is used to approximate the labeling obtained from an existing higher dimension quantizer or classifier. We present an efficient design technique under the labeling constraints and we show that performance is significantly improved if these are taken into account. We present two examples where this technique can be used. First we consider a PVQ designed to approximate a higher dimension classifier. In this case we show that with a small penalty in distortion (e.g., 0.04 dB loss) we can reduce significantly the misclassification (e.g., 48% relative reduction, 4.6% absolute reduction) with respect to a standard PVQ design. In our second example we show how hierarchical VQ (HVQ) can be used as a preprocessing stage for a standard unstructured VQ such that the HVQ stage enables a significant reduction of the codeword candidates to be searched in the VQ stage. Here again we show how HVQ designed to optimize the labeling enables a further reduction in complexity as the HVQ partition is designed to approximate the standard VQ partition.