On the theory and application of space-time and graph-based codes

Recently two new paradigms for error control coding have been introduced: Space-Time, and Graph Based Codes. This thesis explores several aspects of these two coding schemes. Space-time codes were proposed for high capacity multi-antenna systems over fading channels, in which channel coding is performed across the spatial dimension (transmit antennas) as well as time. The design of space-time codes achieving full diversity is hindered by the fact that the diversity advantage of a code is the minimum rank among the set of, complex valued, matrices associated with the differences between base-band modulated codewords. It is difficult to relate such parameter to traditional code design over finite fields and rings. In the first part of the thesis, we present general binary design criteria for PSK modulated space-time codes. These criteria account for much of what is currently known about PSK-modulated space-time codes. Then, based on the proposed design criteria, we develop new fundamental code constructions suitable for both quasi-static and time varying fading channels. We provide the first nontrivial PSK-modulated space-time block codes for L = 2 and 3 antennas that simultaneously provide maximum bandwidth efficiency, full spatial diversity, and coding gain. In the second part of the thesis, we investigate several aspects of graph-based codes and iterative decoding. The convergence characteristics of iterative decoding are first studied. Our results clarify several trends in the iterative decoder performance. Then, a generalized form of the parallel concatenated convolutional codes (GPCCC) is presented. This new coding scheme is suitable for low latency applications. Both the parallel and the serially concatenated codes are shown to be special cases of this general form. The properties of the new scheme are examined, and compared with what is currently known about turbo codes. Two algorithms for decoding the proposed scheme are investigated, and the performance of the new codec with short block lengths is evaluated via simulation. Finally, we propose two novel iterative receiver architectures inspired from the turbo decoder. These receivers are shown to significantly improve the performance of spread spectrum communication systems.