Trellis coding of π/4-QPSK signals for AWGN and fading channels

A methodology for designing trellis coded modulation schemes that will conform to the π/4-QPSK (quadrature phase-shift keying) modulation format is presented. The basic idea is to use multiple trellis codes with a signal set which is the Cartesian product of the even and odd subsets in the π/4-QPSK signal constellation. Several good codes with a multiplicity of 2 are designed. Among them are an 8-state, rate 3/2 code with a throughput of 1.5 b/symbol and a 16-state, rate 2/2 code with a throughput of unity. The former can provide a second-order diversity effect in fading applications while the latter can provide a fifth-order diversity. In the AWGN (additive white Gaussian noise) channel, the rate 3/2 code is about .8 dB more energy efficient than the rate 2/2 code. Both codes compare favorably with conventional systems that use π/4-QPSK in conjunction with convolutional coding. Based on the results obtained, it appears that trellis-coded modulation is a possible alternative to convolution code