The effects of the error events length on the performance of TCM in wireless communications

We investigate the effect of the error events length on the performance of TCM over wireless channels by using the generating function. Some numerical results have shown that the performance of TCM is dominated by the error events with the first few shortest lengths when the signal to noise ratio (SNR) is in the reasonable ranges in practice. For some cases, the performance of TCM is not dominated by the error events with the same length associated by the free Euclidean distance events over an AWGN channel. Likewise, the performance of TCM may not be dominated by the error events having the shortest length over a Rayleigh fading channel. These results provide us a new way to estimate or predict the performance for a given TCM code over wireless channels