Multistage decoding of block multidimensional M-PSK modulation codes

A class of block multidimensional M-PSK modulation codes was proposed by Portugeis (1991) and some 8-PSK codes were constructed. In comparison with codes using two-dimensional modulation, the constructed codes showed better phase symmetry properties and lower first error coefficients with multistage decoding. However, the trade-off between performance and decoding complexity was not thoroughly investigated. This paper presents a performance comparison of multistage decoding schemes for the constructed codes on an AWGN channel. Upper bounds to block error probability (P_B) for these schemes are obtained and their tightness confirmed by simulation. One of the schemes has a coding gain of 3.9 dB over uncoded 4-PSK at P_B=10^-4 and a gain of 0.3 dB over a two-dimensional 8-PSK code with similar parameters at the cost of an acceptable increase in decoding complexity