Efficient Soft-Output Demodulators for the Golden Code

In this work we design efficient soft output demodulators (also referred to as fast soft demodulators) for the 2 × 2 Golden code, which is a promising candidate space time block code in the evolving IEEE and 3GPP cellular standards. For this code, the naive approach for maximum likelihood (ML) hard decision as well as soft-output demodulation entails a complexity of O(M⁴), where M denotes the cardinality of the QAM constellation from which the underlying modulated symbols are drawn. In contrast, our efficient demodulator exploits the structure of the code and yields the ML decision and soft outputs in the form of exact max-log log-likelihood ratios (LLRs) with an O(M^2.5) complexity. Moreover, we also design a sub-optimal soft output demodulator that has an O(M^0.5) complexity comparable to that of the linear minimum mean square error (LMMSE) based demodulator but results in substantial performance gains.