High dimensional trellis-coded modulation (HDTCM) is a new trellis-coded modulation scheme aimed at applications in spread spectrum communications. This dissertation presents theoretical performance analysis of HDTCM and investigation of its decoding algorithms. HDTCM integrates a block code with a state-permuted trellis structure and an expanded high-dimensional signal constellation. Bi-orthogonal signaling is chosen as the signal constellation in this dissertation. HDTCM unifies not only coding and modulation, but also PN spreading into one single process. The properties of the HDTCM scheme are investigated. First, HDTCM with bi-orthogonal signal constellation is shown to be uniform, thus an arbitrary reference can be chosen and the performance analysis is simplified. Then minimum Euclidean distance is found to be bounded by free Euclidean distance. Optimum selection of design parameters is accomplished by examining the weight distribution of Euclidean distance. The cyclic property of HDTCM is also studied and a grouping rule is given. Next, theoretical error performance of HDTCM is analyzed by deriving analytical expressions for lower bounds and upper bounds of error probabilities. Then an asymptotic upper bound at high signal-to-noise ratios is discussed. The minimum Euclidean distance is identified as a determining factor of the error performance of HDTCM. Finally, asymptotic coding gain over uncoded conventional spread spectrum systems is derived. The asymptotic coding gain ranges between 3 dB and 8 dB for reasonable spreading if the input alphabet size nis equal to two. Finally, a maximum likelihood decoder is developed and efficient decoding methods are investigated.