Hierarchical Vector Quantizers: Structure versus Performance

Hierarchical Table-Lookup Vector Quantization (HVQ) is a type of structured vector quantization first described by Chang and Gray. By replacing a full search of the codebook with a recursive series of tablelookups, HVQs pay a distortion and memory requirement penalty in return for computational simplicity, and hence speed, at the encoder. Earlier work has shown that HVQs achieving the same rate fall into classes of similar SNR performance. However, a survey of the literature indicates that little is known about how to optimally allocate memory within an HVQ in order to minimize distortion. In this paper I describe the results of simulating 2744 different HVQs with the goal of gaining insight into the relationship between HVQ memory allocation and distortion performance. I define two metrics characterizing the width and height of the lookup tables comprising an HVQ and compare the SNR achieved by an HVQ to these metrics. The simulation results suggest that HVQs wherein, on average, the number of bits produced by a table equals one-half of the number of bits consumed by a table achieve the best SNR performance.