Combination of BCM and TCM with 90°, 180°, and 270° phase rotational invariance

Two systematic schemes to combine block-coded modulation (BCM) and trellis-coded modulation (TCM) are proposed. In the first scheme, the signal points which are used in TCM should be partitioned by the proper BCM systems constructed by a multilevel construction method. The asymptotic coding gain will be 6.02-3.01/n dB, where n is the length of the BCM systems. Since the average transmission power can be reduced by using a denser signal lattice, the main idea of the second scheme is to construct the TCM system based on the signal points of a denser lattice formed by a proper BCM system. Hence, we can get a higher coding gain which is a combination of both the distance gain of TCM and the density gain of BCM. Theoretically, the net coding gain of this proposed scheme can reach 5.27 dB in the case of an 8-D constellation and 7.15 dB in the case of a 16-D constellation. For practical implementation, the phase ambiguity problems for both schemes are considered and solved by a differential encoder/decoder.