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Precoding Scheme for Transmitting Data Using Optimally-Shaped Constellations Over Intersymbol-Interference Channels


A precoding scheme for noise whitening on ISI channels is presented where the scheme permits any type of shaping and is compatible with trellis coding. Its implementation complexity is significantly less than that of trellis precoding. The resulting reduction in shaping gain is small and becomes negligible as the rate per 2D of the constellation increases. This technique uses a structured vector quantization (SVQ) technique for optimal shaping of the constellation. Optimal (N-sphere) SVQ shaping results in higher shaping gains than those of Voronoi constellations based on known N-dimensional lattices. For a given CER.sub.2 (or PAR.sub.2) SVQ shaping results in optimal shaping. This is useful for implementation over QAM modems as significant shaping gains can be achieved even for a small constellation expansion. The SVQ-shaped constellations have a very reasonable implementation complexity. They allow for the possibility of opportunistic secondary channels, and there constituent 2D constellations are invariant to .pi./2 phase rotations (assuming cubic lattice based constellations). Compatibility of SVQ shaping with trellis coding was also demonstrated, resulting in the SVQ-shaped trellis-coded modulation scheme which can realize both shaping and coding gains. For transmission over ISI channels, SVQ shaping can be used together with the precoding scheme to realize shaping gains up to 1.15 dB.


Steven Tretter
Rajiv Laroia
Nariman Farvardin

Date Issued 


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