Fast-Decodable Space-Time Codes for the $N$-Relay and Multiple-Access MIMO Channel

In this article, the first general constructions of fast-decodable, more specifically (conditionally) ggroup decodable, space–time block codes for the Nonorthogonal Amplify and Forward (NAF) MultipleInput Multiple-Output (MIMO) relay channel under the half-duplex constraint are proposed. In this scenario, the source and the intermediate relays used for data amplification are allowed to employ multiple antennas for data transmission and reception. The worst-case decoding complexity of the obtained codes is reduced by up to 75%. In addition to being fast-decodable, the proposed codes achieve full-diversity and have nonvanishing determinants, which has been shown to be useful for achieving the optimal Diversity-Multiplexing Tradeoff (DMT) of the NAF channel. Further, it is shown that the same techniques as in the cooperative scenario can be utilized to achieve fast-decodability for K-user MIMO Multiple-Access Channel (MAC) space–time block codes. The resulting codes in addition exhibit the conditional nonvanishing determinant property which, for its part, has been shown to be useful for achieving the optimal MAC-DMT.