The Golden Code is Fast Decodable

The golden code is a full-rate full-diversity space-time code for two transmit antennas that has a maximal coding gain. Because each codeword conveys four information symbols from an M-ary QAM alphabet, a maximum-likelihood decoder based on a conventional sphere detector has a worst-case complexity of M⁴. In this paper we present a new algorithm for maximum-likelihood decoding of the golden code that has a worst-case complexity of only 2M³. We thus prove that the golden code is fast decodable, a fact that has evidently been overlooked in prior work. Furthermore, in contrast to the overlaid Alamouti codes, which are fast decodable on quasistatic channels but not on time-varying channels, the golden code is fast decodable on both quasistatic and rapid time-varying channels.