Institute for Systems Research

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Author: search.filters.author.Farvardin, NarimanSubject: search.filters.subject.data compression

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    Quantization of Memoryless and Gauss-Markov Sources Over Binary Markov Channels
    (1994) Phamdo, N.; Alajaji, Fady; Farvardin, Nariman; ISR
    Joint source-channel coding for stationary memoryless and Gauss- Markov sources and binary Markov channels is considered. The channel is an additive-noise channel where the noise process is an M-th order Markov chain. Two joint source-channel coding schemes are considered. The first is a channel-optimized vector quantizer - optimized for both source and channel. The second scheme consists of a scalar quantizer and a maximum a posteriori detector. In this scheme, it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise. These two schemes are then compared against two schemes which use channel interleaving. Numerical results show that the proposed schemes outperform the interleaving schemes. For very noisy channels with high noise correlation, gains of 4 to 5 dB in signal-to-noise ratio are possible.
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    Speech Coding over Noisy Channels
    (1994) Farvardin, Nariman; ISR
    This chapter contains a discussion of quantization over noisy channels. The effects of channel noise on the performance of vector quantizers are discussed and algorithms for the design of noisy-channel vector quantizers are presented. It is argued that in certain practical situations where delay and complexity place hard limits on system parameters, a combined source-channel coding approach might be preferable to the more traditional tandem source-channel coding. Examples of full-searched, multi- stage and finite-state vector quantization designed for a noisy channel are provided for coding of speech line spectrum pair parameters.
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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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    Low Bit-Rate Image Coding Using a Three-Component Image Model
    (1992) Ran, X.; Farvardin, Nariman; ISR
    In this paper the use of a perceptually-motivated image model in the context of image compression is investigated. The model consists of a so-called primary component which contains the strong edge information of the image, a smooth component which represents the background slow-intensity variations and a texture component which contains the textures. The primary component, which is known to be perceptually important, is encoded separately by encoding the intensity and geometric information of the strong edge brim contours. Two alternatives for coding the smooth and texture components are studied: Entropy-coded adaptive DCT and entropy-coded subband coding. It is shown via extensive simulations that the proposed schemes, which can be thought of as a hybrid of waveform coding and featurebased coding techniques, result in both subjective and objective performance improvements over several other image coding schemes and, in particular, over the JPEG continuous-tone image compression standard. These improvements are especially noticeable at low bit rates. Furthermore, it is shown that a perceptual tuning based on the contrast-sensitivity of the human visual system can be used in the DCT-based scheme, which in conjunction with the 3- component model, leads to additional subjective performance improvements.
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    Finite-State Vector Quantization for Noisy Channels
    (1992) Hussain, Yunus; Farvardin, Nariman; ISR
    Under noiseless channel conditions and for sources with memory, finite-state vector quantizers (FSVQs) exhibit improvements over memoryless vector quantizers. It is shown, however, that in the presence of channel noise, the performance of the FSVQ degrades significantly. This suggests that for noisy channels, the FSVQ design problem needs to be reformulated by taking into account the channel noise. Using some of the developments in joint source-channel trellis coding, we describe two different methods leading to two types of noisy channel FSVQs. We show by means of simulations on the Gauss-Markov source and speech LSP parameters and for a binary symmetric channel that both schemes are fairly robust to channel noise. For the Gauss-Markov source, the proposed noisy channel FSVQs perform at least as well as or better than the channel-optimized VQ, while for speech LSP parameters, they lead to saving of 1.5-4 bits/frame over the channel-optimized VQ depending on the level of noise in the channel.
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    A Perceptually Motivated Three-Component Image Model
    (1992) Ran, X.; Farvardin, Nariman; ISR
    In this paper, results of phychovisual studies of the human visual system are discussed and interpreted in a mathematical framework. The formation of the perception is described by appropriate minimization problems and the edge information is found to be of primary importance in visual perception. Having introduced the concept of edge strength, it is demonstrated that strong edges are of higher perceptual importance than weaker edges (textures). We have also found that smooth areas of an image influence our perception together with the edge information, and that this influence can be mathematically described via a minimization problem. Based on this study, we have proposed to decompose the image into three components: (i) primary, (ii) smooth and (iii) texture, which contain, respectively, the strong edges, the background and the textures. An algorithm is developed to generate the three-component image model and an example is provided in which the resulting three components demonstrate the specific properties as expected. finally, it is shown that the primary component provides a superior representation of the strong edge information as compared with the Laplacian-Gaussian Operator scheme which is a popular edge extraction method.
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    Optimal Detection of Discrete Markov Sources Over Discrete Memoryless Channels - Applications to Combined Sources-Channel Coding
    (1992) Phamdo, N.; Farvardin, Nariman; ISR
    We consider the problem of detecting a discrete Markov source which is transmitted across a discrete memoryless channel. The detection is based upon the maximum a posteriori (MAP) criterion which yields the minimum probability of error for a given observation. Two formulations of this problem are considered: (i) a sequence MAP detection in which the objective is to determine the most probable transmitted sequence given the observed sequence and (ii) an instantaneous MAP detection which is to determine the most probable transmitted symbol at time n given all the observations prior to and including time n. The solution to the first problem results in a "Viterbi-like" implementation of the MAP detector (with large delay) while the later problem results in a recursive (with no delay). For the special case of the binary symmetric Markov source and binary symmetric channel, simulation results are presented and an analysis of these two systems yields explicit critical channel bit error rates above which the MAP detectors become useful.

    Applications of the MAP detection problem in a combined source-channel coding system are considered. Here it is assumed that the source is highly correlated and that the source encoder (in our case, a vector quantizer (VQ) fails to remove all of the source redundancy. The remaining redundancy at the output of the source encoder is referred to as the "residual" redundancy. It is shown, through simulation, that the residual redundancy can be used by the MAP detectors to combat channel errors. For small block sizes, the proposed system beats Farvardin and Vaishampayan's channel- optimized VQ by wide margins. Finally, it is shown that the instantaneous MAP detector can be combined with the VQ decoder to form a minimum mean-squared error decoder. Simulation results are also given for this case.

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    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.
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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.
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    A United Approach to Tree-Structured and Multi-Stage Vector Quantization for Noisy Channels
    (1991) Phamdo, N.; Farvardin, Nariman; Moriya, T.; ISR
    Vector quantization (VQ) is a powerful and effective scheme which is widely used in speech and image coding applications. Two basic problems can be associated with VQ: (i) its large encoding complexity, and (ii) its sensitivity to channel errors. These two problems have been independently studied in the past. In this paper, we examine these two problems jointly. Specifically, the performances of two low-complexity VQs-the tree-structured VQ (TSVQ) and the multi-stage VQ (MSVQ) - when used over noisy channels are analyzed. An algorithms is developed for the design of channel-matched TSVQ (CM-TSVQ) and channel-matched MSVQ (CM- MSVQ) under the squared-error criterion. Extensive numerical results are given for the memoryless Gaussian source and the Gauss-Markov source with correlation coefficient 0.9. Comparisons with the ordinary TSVQ and MSVQ designed for the noiseless channel show substantial improvements when the channel is very noisy. The CM-MSVQ, which can be regarded as a block- structured combined source-channel coding scheme, is then compared with a block-structured tandem source-channel coding scheme (with the same block length as the CM-MSVQ). For the Gauss-Markov source, the CM-MSVQ outperforms the tandem scheme in all cases which we have considered. Furthermore, it is demonstrated that the CM-MSVQ is fairly robust to channel mismatch.