As a promising analytic design strategy studied in [1], the design of 2-Space-Time Trellis code by using function range set expansion shows its superiority among the existing codes. The designed codes can also be further optimized its coding gain by using asymmetric constellation. However, the codes obtained by function range set expansion in the 4 states case amounts to 476*476, though those are better than the currently existing codes, cannot be analytically decided which one is the best. And also no clues show that all of them can be optimized to the same performance by using asymmetric constellation. Therefore light exhaustive search by computer is needed. Furthermore, when we deal with the case that under Bit Error Rate (BER) (not the Frame Error Rate (FER)) the Tarokh's rule using the Chernoff bound may not be effective. So the exhaustive search by merely using the eigenvalue product criterion is not applicable which renders the Monte Carlo simulations together with the necessary decoding has to be used. We deal with the Importance Sampling (IS) method used in the STTC for fast simulation. While for rare event the Large Deviation Technique can be applied for the biased density treatment in the IS, all these works (Performance analysis) will complete and justify the designed work of 2-STTC in [1] and also can be used as an extension to the r-STTC design when r is greater than 2.
