The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM). The capability of supporting a so-called opportunistic secondary channel, often used for internal control signaling, is considered. The gain in SNR efficiency of a multidimensional constellation (lattice code) consisting of the points from a lattice Lambda within a region R compared to a cubic constellation is shown to be approximately separable into the coding gain of Lambda and the shape gain of R, for large constellations. Similarly, the expansion of the associated constituent 2-D constellation is shown to be approximately separable into a constellation expansion ratio (CER) coding component CER/sub c/( Lambda ) and a shaping component CER/sub s/(R). The N sphere is the region R with the best shape gain, but N also has large constellation expansion. Bounds for the best possible shape gain versus CER/sub s/(R) or peak-to-average-power ratio (PAR) are given. Generalized cross constellations are discussed. These constellations yield a modest shape gain with very low CER/sub s/(R) or PAR, are easily implemented, are well suited for use with coded QAM modems, and can be readily adapted to support an opportunistic secondary channel. >
[1]
Allen Gersho,et al.
Asymptotically optimal block quantization
,
1979,
IEEE Trans. Inf. Theory.
[2]
Lee-Fang Wei.
Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space-Part I: 180°
,
1984,
IEEE J. Sel. Areas Commun..
[3]
Lee-Fang Wei,et al.
Trellis-coded modulation with multidimensional constellations
,
1987,
IEEE Trans. Inf. Theory.
[4]
G. David Forney,et al.
Efficient Modulation for Band-Limited Channels
,
1984,
IEEE J. Sel. Areas Commun..
[5]
Gottfried Ungerboeck,et al.
Channel coding with multilevel/phase signals
,
1982,
IEEE Trans. Inf. Theory.
[6]
N. J. A. Sloane,et al.
Tables of sphere packings and spherical codes
,
1981,
IEEE Trans. Inf. Theory.
[7]
N. J. A. Sloane,et al.
New trellis codes based on lattices and cosets
,
1987,
IEEE Trans. Inf. Theory.
[8]
Richard D. Gitlin,et al.
An inband coding method for the transmission of secondary data
,
1988,
IEEE International Conference on Communications, - Spanning the Universe..
[9]
G. David Forney,et al.
Coset codes-I: Introduction and geometrical classification
,
1988,
IEEE Trans. Inf. Theory.