Institute for Systems Research

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Author: search.filters.author.Laroia, RajivSubject: search.filters.subject.information theory

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    Design and Analysis of a Fixed-Rate Structured Vector Quantizer Derived from Variable-Length Scalar Quantizers
    (1992) Laroia, Rajiv; Farvardin, N.; ISR
    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.
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    Trellis-Based Scalar-Vector Quantizer for Memoryless Sources
    (1992) Laroia, Rajiv; Farvardin, Nariman; ISR
    This paper describes a structured vector quantization approach for stationary memoryless sources that combines the scalar-vector quantizer (SVQ) ideas (Laroia and Farvardin) with trellis coded quantization (Marcellin and Fischer). The resulting quantizer is called the trellis-based scalar-vector quantizer (TB-SVQ). The SVQ structure allows the TB-SVQ to realize a large boundary gain while the underlying trellis code enables it to achieve a significant portion of the total granular gain. For large block- lengths and powerful (possibly complex) trellis codes the TB-SVQ can, in principle, achieve the rate-distortion bound. As indicated by the results obtained here, even for reasonable block-lengths and relatively simple trellis codes, the TB-SVQ outperforms all other reasonable complexity fixed-rate quantizers.
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    Extension of the Fixed-Rate Structured Vector quantizer to Vector Sources
    (1991) Laroia, Rajiv; Farvardin, Nariman; ISR
    The fixed-rate structured vector quantizer (SVQ) derived from a variable-length scalar quantizer was originally proposed for quantizing stationary memoryless sources. In this paper, the SVQ has been extended to a specific type of vector sources in which each component is a stationary memoryless scalar subsource in dependent of the other components. algorithms for the design and implementation of the original SVQ are modified to apply to this case. The resulting SVQ, referred to as the extended SVQ (ESVQ), is then used to quantize stationary sources with memory (with know autocorrelation function). This is done by first using a linear orthonormal block transformation, such as the Karhunen- Loeve transform, to decorrelate a block of source samples. The transform output vectors, which can be approximated as the output of an independent-component vector source, are then quantized using the ESVQ. Numerical results are presented for the quantization of first-order Gauss-Markov sources using this scheme. It is shown that ESVQ-based scheme performs very close to the entropy-coded transform quantization while maintaining a fixed-rate output and outperforms the fixed-rate scheme which uses scalar Lloyd-Marx quantization of the transform coefficients. Finally, it is shown that this scheme also performs better than implementable vector quantizers, specially at high rates.