Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

Browse

Author: search.filters.author.Laroia, Rajiv

Search Results

Now showing 1 - 9 of 9
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    On SVQ Shaping of Multidimensional Constellations - High-Rate Large-Dimensional Constellations
    (1992) Laroia, Rajiv; Farvardin, Nariman; Tretter, S.; ISR
    An optimal shaping scheme for multidimensional constellations, motivated by some ideas from a fixed-rate structured vector quantizer (SVQ), was recently proposed by Laroia. It was shown that optimal shaping could be performed subject to a constraint on the CER2 or PAR2 by expressing the (optimally shaped) constellation as the codebook of an SVQ and using the SVQ encoding/decoding algorithms to index the constellation points. Further, compatibility with trellis coded modulation was demonstrated. The complexity of the proposed scheme was reasonable but dependent on the data transmission rate. In this paper, we use recent results due to Calderbank and Ozarow to show that complexity of this scheme can be reduced and made independent of the data rate with essentially no effect on the shaping gain. Also, we modify the SVQ encoding/decoding algorithms to reduce the implementation complexity even further. It is shown that SVQ shaping can achieve a shaping gain of about 1.20 dB with a PAR2 of 3.75 at a very reasonable complexity (about 15 multiply-adds/baud and a memory requirement of 1.5 kbytes). Further, a shaping gain of 1 dB results in a PAR2 of less than 3. This is considerable less than a PAR2 of 3.75 for Forney's trellis shaping scheme that gives about 1 dB shaping gain.
  • Thumbnail Image
    Item
    A Simple and Effective Precoding Scheme for Noise Whitening on Intersymbol Interference Channels
    (1992) Laroia, Rajiv; Tretter, S.; Farvardin, Nariman; ISR
    A precoding scheme for noise whitening on intersymbol interference channels is presented. This scheme is compatible with trellis-coded modulation and unlike Tomlinson precoding allows constellation shaping. It can be used with almost any shaping scheme (including the optimal SVQ shaping) as opposed to trellis precoding which can only be used with trellis shaping. The implementation complexity of this scheme is minimal - only three times that of the noise prediction filter, and hence effective noise whitening can be achieved by using a high-order predictor.
  • Thumbnail Image
    Item
    On Optimal Shaping of Multidimensional Constellations - An Alternative Approach to Lattice-Bounded (Voronoi) Constellations
    (1992) Laroia, Rajiv; ISR
    A scheme for the optimal shaping of multidimensional constellations is proposed. This scheme uses some of the ideas from a type of structured vector quantizer originally proposed for the quantization of memoryless sources, and results in N- sphere shaping of N-dimensional cubic lattice based constellations. Its implementation complexity is very reasonable. Because N - sphere shaping is optimal in N dimensions, shaping gains higher than those of N - dimensional Voronoi constellations can be realized. Optimal shaping for a large N however has the undesirable effect of increasing the size and the peak-to-average power ratio of the constituent 2D constellation, thus limiting its usefulness in practical implementation over QAM modems. It is shown that the proposed scheme alleviates this problem by achieving optimal constellation shapes for a given limit on the constellation expansion ratio or the peak-to-average power ratio of the constituent 2D constellation. Finally, compatibility with trellis-coded modulation is demonstrated for the realization of both shaping and coding gain, giving this scheme a distinct edge over lattice- bounded constellations.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    A Structured Fixed-Rate Vector Quantizer Derived from a Variable-Length Scalar Quantizer
    (1991) Laroia, Rajiv; Farvardin, Nariman; ISR
    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, in this paper we develop a low complexity fixed-rate structured vector quantizer in which the structure of the codebook is derived from a variable-length scalar quantizer. Consider an n-level variable- length (e.g., Huffman coded) scalar quantizer S quantizing samples from a memoryless stationary source. Out of all possible n**m-vectors (m consecutive samples) at the output of S, the 2 **(mr) vectors with the smallest total (encoded) length are chosen as the codebook of an m-dimensional rate r bits/sample structured vector quantizer derived from S. A procedure for the design of this quantizer along with fast algorithms for implementation are developed and bounds on the performance of the scheme are developed. The structured 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. Numerical results demonstrating the efficacy of this scheme along with comparisons against Lloyd-Max quantizers and optimal entropy-constrained quantizers, both in the absence and presence of channel noise are rendered. These results show that performance close to that of optimal entropy- constrained scalar quantizers is possible with this fixed-rate quantizer. The structured 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. Extension of this idea to other types of sources proves very useful and will be described in a sequel paper.
  • Thumbnail Image
    Item
    A Structured Fixed-Rate Vector Quantizer Derived from Variable- Length Encoded Scalar Quantizers
    (1990) Laroia, Rajiv; Farvardin, Nariman; ISR
    The well-known error propagation problem inherent in any variable-length coding operation limits the usefulness of variable-length encoded entropy-constrained scalar quantizers when the quantizer outputs are to be transmitted over a noisy channel. 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, in this paper we develop a fixed-rate vector quantization scheme which achieves performance close to that of optimum entropy-constrained scalar quantizers; due to the fixed-rate nature of the encoder, channel error propagation is not an issue any more. An algorithm for the design of this scheme is described and procedures for codebook search and codevector encoding are developed. We show that codebooks significantly larger than those in conventional vector quantizers can be designed. Numerical results demonstrating the efficacy of this scheme along with comparisons against Lloyd-Max quantizers and optimal entropy-constrained quantizers are rendered.
  • Thumbnail Image
    Item
    Efficient Encoding of Speech LSP Parameters Using the Discrete Cos ine Transformation.
    (1989) Farvardin, Nariman; Laroia, Rajiv; ISR
    In this paper, the intraframe and interframe correlation propeffie s are used to develop two efficient encoding algorithms for speech line spectrum pair (ISP) parameters. The first algorithm (2-D DCT) , which requires relatively large coding delays, is based on twodi mensional (time and frequency) discrete cosine transform coding te chniques; the second algorithm (DCT- DPCM), which does not need any coding delay, uses one-dimensional discrete cosine transform in th e frequency domain and DPCM in the time domain. The performance of these systems for different bit rates and delays are studied and a ppropriate comparisons are made. It is shown that an average spect ral distortion of approximately 1 dB sup 2 can be achieved with 21 and 25 bits/frame using the 2-D DCT and DCT-DPCM schemes, respecti vely. This is a noticeable improvement over the previously reporte d bit rates of 32 bits/frame and above [1], [2].