Exploiting the large dimensions of space-time systems

Space-time codes are effective means by which to combat fading by exploiting diversity in both spatial and temporal dimensions. The paper proposes a fundamentally different approach to exploit the large dimensions of space-time codes by bridging the gaps between space-time block codes (STBC) and space-time trellis codes (STTC) through multiple trellis coded modulation (MTCM). Via distance preserving isometries, STBCs are constructed bottom-up; such STBCs are dubbed nonlinear hierarchical codes (NHCs). Systematic regular MTCM (RMTCM) design procedures are proposed to exploit the layered structure of NHCs which leads to optimized designs for various rates, block sizes and constellation sizes. RMTCM offers the best tradeoff between performance and complexity. The classical performance analysis criteria used for the inner code of the RMTCM design (the STBC) are diversity and coding gain. Although asymptotically tight, these criteria only account for the worst case pairwise error probability (PEP) between the codewords. We apply methods to achieve tighter bounds. NHCs optimized for low SNR are constructed based on these tighter bounds.