Dimensionality Reduced Decoding for the Golden Code with the Worst-case Complexity of O(m(1.5)) for Low Range of SNR

In this paper we introduce an efficient decoding method which is based on the dimensionality reduction of the search tree in the sphere decoder for the golden code in a low SNR regime. A codeword of the golden code has four independent m-QAM data symbols, hence, the required complexity of the exhaustive-search decoder is m(4). An efficient implementation of the maximum-likelihood decoder for the golden code with a worst-case complexity is known to be proportional to m(2.5). Additionally, in low range of SNR, sphere decoding has significantly high expected decoding complexity. Our motivation is for an efficient decoder with a worst-case complexity of no more than m(2) for a low SNR regime. In this purpose, we show that our proposed method has m(1.5) complexity in the worst-case with a loss of only 1 dB with respect to optimal decoding.