Punctured vs. multidimensional TCM — A comparison w.r.t. complexity

Trellis-coded modulation (TCM) is a power- and bandwidth efficient digital transmission scheme which offers very low structural delay of the data stream. Classical TCM uses a signal constellation of twice the cardinality compared to an uncoded transmission with one bit of redundancy per PAM symbol, i.e., application of codes with rates n-1/2 when 2ⁿ denotes the cardinality of the signal constellation. In order to offer a higher granularity of rates, multi-dimensional (i.e., D-dimensional) constellations had been proposed by means of combining subsequent one- or two-dimensional modulation steps, resulting in TCM schemes with 1/D bit redundancy per (real) dimension. A recently published alternative approach allows rate adjustment for TCM by means of puncturing of the convolutional code (CC) on which a TCM scheme is based on. In this paper it is shown that punctured TCM not only offers a higher flexibility in rate adjustment but significantly less decoding complexity when compared to MD-TCM. Throughout the paper, structural delay is considered, which is a lower bound on the actual delay and describes the inevitable delay solely depending on the structural properties of the coding scheme but not on processing time, propagation delay, etc.