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) g-group decodable, space-time block codes for the nonorthogonal amplify and forward (NAF) multiple-input 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. Furthermore, 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.