Fast maximum-likelihood decoding of the golden code

Because each golden code codeword conveys four information symbols from an M-ary QAM alphabet, the complexity of an exhaustive-search decoder is proportional to M
⁴
. In this paper we prove that the golden code is fast-decodable, meaning that maximum-likelihood decoding is possible with a worst-case complexity proportional to only M
^2.5
. The golden code retains its fast-decodable property regardless of whether the channel varies with time. We also present an efficient implementation of a fast maximum-likelihood decoder that exhibits a low average complexity.