TCM schemes with partially overlapped signal constellations

In conventional TCM schemes, for a rate of n bits per channel symbol, a 2ⁿ⁺¹-point constellation is used. It is shown that using constellations with less than 2ⁿ⁺¹-points, one can 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 constellation and reusing of some of the low-power signals instead