TCM codes for 4PSK-2PSK modulation with invariance under rotation

The paper contains an example of designing a 180 degrees rotationally invariant TCM code with 3-dimensional 4PSK-2PSK signal space. All encoder input bits are carried directly to the output. No differential encoder is necessary. This eliminates the error multiplication effect caused by the differential decoding operation in the receiver. Examples are presented for 2, 4, 8, 16 and 32 encoder states. The codes achieve coding gain of 1.76 dB (for 2 encoder states) of 5.44 dB (for 32 encoder states) compared with the uncoded BPSK.<>