Design of Structured Quantizers Based on Coset Codes

For memoryless sources, Entropy-Constrained Scalar Quantizers (ECSQs) can perform closely to the Gish-Pierce bound at high rates. There exist two fixed-rate variations of ECSQ -- Scalar- Vector Quantizer (SVQ) and Adaptive Entropy-Coded Quantizer (AECQ) -- that also perform closely to the Gish-Pierce bound. These quantization schemes have approximately cubic quantization cells while high-rate quantization theory suggests that quantization cells of the optimal quantizers should be approximately spherical. There are some coset codes whose Voronoi regions are very spherical. In this dissertation we present structured quantization schemes that combine these coset codes with the aforementioned quantizers (SVQ, ECSQ, and AECQ) so as to improve their performance beyond the Gish-Pierce bound.By combining trellis codes (that achieve a significant granular gain) with SVQ, ECSQ, and AECQ, we obtain Trellis-Based Scalar- Vector Quantizer (TB-SVQ), Entropy-Constrained Trellis- Coded Quantizer (ECTCQ), and Pathwise-Adaptive ECTCQ (PA-ECTCQ), respectively. With an 8-state underlying trellis code, these trellis-coded quantization schemes perform about 1.0 dB better than their naive counterparts. There are two approaches that can extend the quantizers (TB-SVQ, ECTCQ, and PA-ECTCQ) for quantizing sources with memory. The first is to combine the predictive coding operation of the Differential Pulse Code Modulation scheme with various quantizers, yielding Predictive TB-SVQ, Predictive ECTCQ, and Predictive PA-ECTCQ, respectively. There is a duality between quantizing sources with memory and transmitting data over channels with memory. Laroia, Tretter, and Farvardin have recently introduced a precoding idea that helps transmitting data efficiently over channels with memory. By exploiting this duality, the second approach combines the precoder with TB-SVQ and ECTCQ to arrive at Precoded TB-SVQ and Precoded ECTCQ, respectively. Simulation results indicate that the porformance of these quantizers are also close to the rate- distortion limit.The PA-ECTCQ performance has been shown to be robust, in the presence of source scale and, to a lesser extent, shape mismatch conditions. We also considered adjusting the underlying entropy encoder based on the quantized output (which provide some approximate information on the source statistics). The performance of the resulting Shape-Adjusting PA-ECTCQ has been shown to be robust to a rather wide range of source shape mismatch conditions. are also close to the rate-distortion limit