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Multidimensional constellation shaping with a family of regions called truncated polydiscs is studied. This family achieves maximum shaping gain for a given two-dimensional peak-to-average energy ratio or a given two-dimensional constellation expansion ratio. An efficient algorithm for mapping data words to constellation points is described that requires O(N log N) arithmetic operations and O(N/sup 2/) lookup table space. Truncated polydisc shaping can easily be incorporated into standard coded modulation schemes.>
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Kschischang et al. (1994) studied this question.
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