Multidimensional signal sets through the shell construction for parallel channels
Abstract
A procedure is derived of sending r bits on M parallel channels such that the average energy per point is minimized. A decomposition of the best constellation in Z to the M + (1/2,...,1/2) is given in terms of the cross-products of lower dimensional shells of points. The constellations obtained with the shell construction have peak-to-average energy ratio and constellation expansion ratio values comparable to those of a hyperspherical constellation. The proposed scheme can be used with good shaping gains for low encoder complexity. The method is also generalized for channels with unequal gains. A significant performance advantage is found at shaping gain, in certain cases, with respect to the Voronoi Constellations in terms of peak-to-average power and constellation expansion. It is also shown that coset codes can be used with these constellations.
- Publication:
-
IEEE Transactions on Communications
- Pub Date:
- March 1992
- Bibcode:
- 1992ITCom..40..500F
- Keywords:
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- Channels (Data Transmission);
- Signal Transmission;
- Amplitude Modulation;
- Binary Codes;
- Communications and Radar