Optimal constellation labeling for iteratively decoded bit-interleaved space-time coded modulation

We consider the design of iteratively decoded bit-interleaved space-time coded modulation (BI-STCM) over fast Rayleigh-fading channels with N-t transmit and N-r receive antennas. We propose the design criterion to achieve the largest asymptotic coding gain inherited in the constellation labeling. In particular, for orthogonal space-time block codes, the labeling design criterion reduces to maximizing the (-NtNr)th power mean of the complete set of squared Euclidean distances associated with all "error-free feedback" events in the constellation. Based on this power mean criterion, we show that the labeling optimization problem falls into the category of quadratic assignment problems for constellations of any shape and with an arbitrary number of transmit and receive antennas. For a set of practical values of N-t and N-r, we present optimal labeling maps for 8-PSK, 16-QAM, and 64-QAM constellations.