Concatenated codes using coded modulation with a phase shift

A new coded modulation with a phase shift is proposed. The parity bits decide how to shift the signal constellation point of information bits in the transmitter. In the receiver, the phase shift detector estimates how much the constellation points are shifted and then recovers the parity bit. Based on the recovered parity bit, soft input soft output decoding is carried out. The asymptotic coding gains of the proposed scheme using the (9,8) single parity check code are 3 dB and 0.7 dB when compared with the uncoded BPSK and QPSK, respectively. It is shown with simulations that the proposed scheme using the (9,8) single parity check code has at bit error rate 10^-5 about 2 dB gain compared with uncoded transmission and 0.5 dB gain compared with the (9,8) conventional single parity check code. In addition, concatenated codes are designed using the proposed coded modulation as the inner code. The concatenated code using the (255,247) Reed-Solomon code as the outer code and the proposed coded modulation as the inner code is designed as an example. It is shown that it has about 2 dB gain at bit error rate 10^-5 when compared with the conventional (255,247) Reed-Solomon code.