TABLE OF CONTENTS Trellis-coded modulation (TCM) [144, 14] combines modulation and coding to achieve higher coding gains. It provides significant coding gain and a better performance for a given bandwidth compared to uncoded modulation schemes. Space-time trellis codes (STTCs) combine modulation and trellis coding to transmit information over multiple transmit antennas and MIMO channels. Therefore, one can think of STTCs as TCM schemes for MIMO channels. We start this chapter with a brief description of TCM design and the corresponding encoding and decoding. The main idea behind coding is to use structured redundancy to reduce the effects of noise. One approach is to restrict the transmitted symbols to a subset of constellation points to have a larger minimum Euclidean distance. This approach, however, results in a rate reduction due to a decrease in the size of available constellation points. To compensate for the rate reduction, one may expand the constellation and use a subset of the expanded constellation at each time slot. A finite-state machine represented by a trellis is utilized to decide which subset should be used at each time slot. The goal is to maximize the coding gain for a given rate. This is the main idea behind TCM and in such a structure the transmitted symbols at different time slots are not independent.
Let us assume that we use a trellis with I states such that 2 l branches leave every state. We enumerate the states from top to bottom starting from zero. Thus, we have...
