Disclosed is a method and apparatus for encoding a modulated signal in a communication system. The method comprises generating an initial constellation, applying a vertical axis symmetry to the initial constellation to generate a first resulting constellation, translating the first resulting constellation to a left direction of the initial constellation to produce a left flipped constellation, applying a horizontal axis symmetry to the initial constellation to generate a second resulting constellation, translating the second resulting constellation to an up direction of the initial constellation to produce an up flipped constellation, applying a central axis symmetry to the initial constellation to generate a third resulting constellation; and translating the third resulting constellation to a left-up direction of the initial constellation to produce a left-up flipped constellation.