The union bound for space-time turbo coded modulation over fast fading channels

A design method for recursive space-time trellis codes and parallel concatenated space-time turbo coded modulation was recently proposed as a new framework for building optimized, low-complexity, large equivalent constraint-length space-time trellis codes. In this paper the distance spectrum interpretation of the space-time turbo coded modulation is introduced to evaluate the union bound on the frame error rate over fast fading channels. The distance spectrum gives a good insight on the importance of multiplicities in the space-time coding design. Derived bounds are in some cases very tight and provide a designer with the practical tool for further optimization of the constituent space-time trellis codes within the space-time turbo coded modulation framework. Some interesting examples of the convergence of the sub-optimal iterative decoding were also presented.