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This paper (Part of the content of this manuscript has been accepted forpresentation in IEEE Globecom 2008, to be held in New Orleans) deals with lowmaximum likelihood (ML) decoding complexity, full-rate and full-diversityspace-time block codes (STBCs), which also offer large coding gain, for the 2transmit antenna, 2 receive antenna ($2\times 2$) and the 4 transmit antenna, 2receive antenna ($4\times 2$) MIMO systems. Presently, the best known STBC forthe $2\times2$ system is the Golden code and that for the $4\times2$ system isthe DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a newSTBC is presented in this paper for the $2\times 2$ system. This code matchesthe Golden code in performance and ML-decoding complexity for square QAMconstellations while it has lower ML-decoding complexity with the sameperformance for non-rectangular QAM constellations. This code is also shown tobe \emph{information-lossless} and \emph{diversity-multiplexing gain} (DMG)tradeoff optimal. This design procedure is then extended to the $4\times 2$system and a code, which outperforms the DjABBA code for QAM constellationswith lower ML-decoding complexity, is presented. So far, the Golden code hasbeen reported to have an ML-decoding complexity of the order of $M^4$ forsquare QAM of size $M$. In this paper, a scheme that reduces its ML-decodingcomplexity to $M^2\sqrt{M}$ is presented.

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 X 2 and 4 X 2 MIMO Systems