Robust vector quantization by a linear mapping of a block code

Abstract

In this paper we propose a novel technique for vector quantizer design where the reconstruction vectors are given by a linear mapping of a binary block code (LMBC). The LMBC framework provides a relation between the index bits and the reconstruction vectors through mapping properties. We define a framework, show its flexibility, and give optimality conditions. We consider source optimized vector quantization (VQ), where the objective is to directly obtain a VQ with inherent good channel robustness properties. Several instructive theoretical results and properties of the distortion experienced due to channel noise are demonstrated. These results are used to guide the design process. Both optimization algorithms and a block code selection procedure are devised. Experimental results for Gauss-Markov sources show that quantization performance close to an unconstrained VQ is obtained with a short block code which implies a constrained VQ. The resulting VQs have better channel noise robustness than conventional VQs designed with the generalized Lloyd algorithm (GLA) and splitting initialization, even when a post-processing index assignment algorithm is applied to the GLA-based VQ. We have, thus, demonstrated a unique method for direct design resulting in an inherent good index assignment combined with small losses in quantization performance.