TY - JOUR
T1 - On Optimal Shaping of Multidimensional Constellations
AU - Laroia, Rajiv
AU - Farvardin, Nariman
AU - Tretter, Steven A.
PY - 1994/7
Y1 - 1994/7
N2 - A scheme for the optimal shaping of multidimensional constellations is proposed. This scheme is motivated by a type of structured vector quantizer for memoryless sources, and results in N-sphere shaping of N-dimensional cubic lattice-based constellations. Because V-sphere shaping is optimal in Ndimensions, shaping gains higher than those of N-dimensional Voronoi constellations can be realized. While optimal shaping for a large N can realize most of the 1.53 dB total shaping gain, it has the undesirable effect of increasing the size and the peak-to-average power ratio of the constituent 2D constellation. This limits its usefulness for many real world channels which have nonlinearities. 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. Results of Calderbank and Ozarow on nonequiprobable signaling are used to reduce the complexity of this scheme and make it independent of the data rate with essentially no effect on the shaping gain. Comparisons with Forney's trellis shaping scheme are also provided.
AB - A scheme for the optimal shaping of multidimensional constellations is proposed. This scheme is motivated by a type of structured vector quantizer for memoryless sources, and results in N-sphere shaping of N-dimensional cubic lattice-based constellations. Because V-sphere shaping is optimal in Ndimensions, shaping gains higher than those of N-dimensional Voronoi constellations can be realized. While optimal shaping for a large N can realize most of the 1.53 dB total shaping gain, it has the undesirable effect of increasing the size and the peak-to-average power ratio of the constituent 2D constellation. This limits its usefulness for many real world channels which have nonlinearities. 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. Results of Calderbank and Ozarow on nonequiprobable signaling are used to reduce the complexity of this scheme and make it independent of the data rate with essentially no effect on the shaping gain. Comparisons with Forney's trellis shaping scheme are also provided.
KW - Multidimensional constellations
KW - SVQ shaping
KW - Voronoi constellations
KW - constellation expansion
KW - optimal shaping
KW - shell mapping
KW - trellis shaping
UR - http://www.scopus.com/inward/record.url?scp=0028461532&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0028461532&partnerID=8YFLogxK
U2 - 10.1109/18.335969
DO - 10.1109/18.335969
M3 - Article
AN - SCOPUS:0028461532
SN - 0018-9448
VL - 40
SP - 1044
EP - 1056
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
ER -