On Active Distances for Trellis Coded Modulation
This thesis introduces the family of active distances for nonlinear trellis coded modulation (TCM) schemes that can be encoded via finite state machine (FSM) encoders. Especially the active burst distance turns out to be an excellent tool to describe the error correcting capability of TCM. It is shown, that the active distances can be lower bounded by linearly increasing functions with identical gradient, called the slope. It is shown that an enhanced error correcting capability due to an increased slope directly results in an improved error rate performance at low signal-to-noise-ratio. For this reason, an exhaustive search for TCM schemes with respect to the slope is performed. In addition, the results obtained for stand-alone TCM schemes are applied to serially concatenated TCM (SCTCM). It is shown that an inner TCM scheme with increased slope yields an improved error rate performance of the overall SCTCM scheme.