Trellis coding with partially overlapped signal sets

It is shown that by using constellations with partially overlapped signal points, i.e., constellations with less than 2ⁿ⁺¹-points, it is possible to achieve a considerable coding gain in comparison to the traditional 2ⁿ⁺¹-point constellation. The increase in coding gain is due to a reduction in transmitted signal energy as a result of deleting some high-power signals from the original 2ⁿ⁺¹-point constellation and to a reuse of some of the low-power signals instead