Institute for Systems Research

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Author: search.filters.author.Farvardin, NarimanSubject: search.filters.subject.digital communications

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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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    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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    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.
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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.