Structured fixed-rate vector quantizer derived from a variable-length scalar quantizer. Part I. Memoryless sources

The well-known error propagation problem inherent in any variable-length coding operation limits the usefulness of variable-length encoded scalar quantizers for transmission over noisy channels. In the absence of channel noise however, these quantizers are known to perform better than error-minimizing fixed-rate Lloyd-Max quantizers for a wide class of memoryless sources. Motivated by this observation, a low complexity fixed-rate structured vector quantizer for memoryless sources is described. This quantizer is referred to as the scalar-vector quantizer and the structure of its codebook is derived from a variable-length scalar quantizer. Design and implementation algorithms for this quantizer are developed and bounds on its performance are provided. The scalar-vector quantizer can be designed and implemented even for fine (high rate) quantization at relatively large block lengths and can achieve a rate-distortion performance superior to that of implementable LBG vector quantizers. Simulation results show that performance close to that of the optimal entropy-constrained scalar quantizer is possible with this fixed-rate quantizer. The scalar-vector quantizer is also robust against channel errors and outperforms both Lloyd-Max and entropy-constrained scalar quantizers for a wide range of channel error probabilities. These ideas are extended (in Part II) to the quantization of vector sources and, consequently, to sources with memory.