Design and Analysis of a Fixed-Rate Structured Vector Quantizer Derived from Variable-Length Scalar Quantizers
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The implementation complexity of the LBG VQ is unaffordable even for quantization at low rates and moderate block-lengths. To overcome the complexity problem, in this thesis we have adopted a structured quantization approach for quantizing stationary memoryless sources. For such sources the optimal variable-rate entropy-constrained scalar quantizer (ECSQ) is know to perform very well - within 1.53 dB of the rate-distortion bound at high rates. On the other hand, the error-minimizing fixed-rate Lloyd- Max quantizer (LMQ) does not generally perform well, especially for sources with sharp-peaked broad-tailed densities. Motivated by the large gap in the performances of the optimal ESCQ and the fixed-rate LMQ, we introduce the scalar-vector quantizer (SVQ). The SVQ is a fixed-rate structured vector quantizer derived from a variable-length scalar quantizer. It is shown that for large block-lengths, the performance of the optimal SVQ approaches that of the optimal ECSQ. The complexity of the SVQ is only polynomial in block-length and it can be implemented for a large block- length even at high-rates. This enables the SVQs to perform better than even the implementable LBG VQs. Next, the scope of the SVQ is extended from memoryless scalar sources to independent component vector sources. The resulting extended scalar-vector quantizer (ESVQ) is used to quantize sources with memory. This is done in the context of block transform quantization. Finally, the trellis-based scalar-vector quantizer (TB-SVQ) is described. Unlike the SVQ, the 'codevectors' of the TB-SVQ do not lie on a rectangular grid but are sequence of a trellis code. Since this leads to more spherical Voronoi regions, for the squared-error distortion measure, the TB-SVQ can perform up to 1.53 dB better than the SVQ. Performance results for the TB-SVQ show that for memoryless sources it performs better than all other reasonable complexity quantization schemes.