| This thesis has two main contributions: the construction of space-time codes that meet the high-SNR outage region for all channel dimensions and statistics, and the construction of cooperative schemes that meet the high-SNR outage region of wireless networks, for a plethora of cooperation protocols, for all network sizes, and for a large family of channel statistics. The results relate to wireless point-to-point and network communications that are delay-and-outage limited, and more specifically they relate to utilizing multiple nodes for achieving higher rates and reliability.; In a recent seminal paper, Zheng and Tse provided a high-SNR asymptotic approximation of the optimal rate-to-reliability tradeoff, coined the Diversity-Multiplexing Gain (D-MG) tradeoff, that any scheme can achieve in the presence of Rayleigh fading. This optimal error performance, asymptotically coincided with the probability of channel outage. The same authors also pointed out the lack of existing D-MG optimal MIMO schemes but proved the existence of random Gaussian codes that achieve the fundamental tradeoff. Their result sparked considerable worldwide interest in finding optimal codes.; We present the first explicitly constructed unified family of communication schemes that meet the performance limits placed by the high-SNR outage, and do so for any coherent quasi-static channel, independent of fading statistics, and number of antennas. These constructions are based on special cyclic division algebras. Furthermore, the schemes' existence allows for improvements on the existing performance bounds. Practical substantiation is provided by our generalizing the unified family of 'perfect space-time schemes' which exhibit near optimal performance for large ranges of rate and SNR.; In regards to cooperative wireless networks, D-MG optimality was thought to require infinite time duration, full channel knowledge, and infinite decoding complexity. We achieve the same optimality, for small delays, small decoding complexity and in some cases with much reduced channel knowledge. This is achieved for general network topologies and statistical characterizations. The existence of the above schemes leads to a constructive improvement of existing information-theoretic error-performance bounds. |
