D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative   Communication Protocols
  We consider cooperative relay communication in a fading channel environment under the Orthogonal Amplify and Forward (OAF) and Orthogonal and Non-Orthogonal Selection Decode and Forward (OSDF and NSDF) protocols. For all these protocols, we compute the Diversity-Multiplexing Gain Tradeoff (DMT). We construct DMT optimal codes for the protocols which are sphere decodable and, in certain cases, incur minimum possible delay. Our results establish that the DMT of the OAF protocol is identical to the DMT of the Non-Orthogonal Amplify and Forward (NAF) protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time duration for which the source alone transmits is allowed to vary with the rate of communication. Among the class of static amplify-and-forward and decode-and-forward protocols, the variable-NSDF protocol is shown to have the best known DMT for any number of relays apart from the two-relay case. When there are two relays, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known protocol for higher values of the multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays. Finally, we present a DMT optimal code construction for the NAF protocol. 
Petros Elia, K. Vinodh, M. Anand and P. Vijay Kumar