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122 CHAPTER 3 Algebraic Coding for Fast Fading Channels An interesting feature of the rotation operation is that the rotated signal set has exactly the same performance as the nonrotated one when used over a pure AWGN channel, while the performance over Rayleigh fading channels, for increasingly high-modulation diversity order, approaches that achievable over the Gaussian channel. 3.2.2 Lattice Constellations In the design of signal constellations, two fundamental operations should always be kept in mind: bit labeling and constellation shaping. These may be very critical for the complexity of practical imple- mentations and are strictly related to each other. If we want to avoid the use of a huge look-up table to perform bit labeling, we need to have a simple algorithm mapping bits to signal points and vice versa. However, it is well known that lattice constellations bounded by a sphere have the best shaping gain. Unfortunately, labeling a spherically shaped constellation without using a look-up table is not always an easy task. Cubic-shaped constellations offer a good trade-off: they are only slightly worse in terms of shaping gain but are usually easier to label. The simplest labeling algorithm that we can use for a lattice constellation S = {x = uM : u = (u 1 · · · u n ), u i q-PAM} is obtained by performing the bit labeling on the integer components u i of the vector u. These are