Institute for Systems Research

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Author: search.filters.author.Laroia, RajivSubject: search.filters.subject.digital communications

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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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    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.