Low Complexity Golden Code Analytical and Deep Learning-Based Sphere-Decoders for High-Density M-QAM

In this paper, we develop low complexity Golden code sphere-decoding (SD) algorithms for high-density M-ary quadrature amplitude modulation (M-QAM). We define the high-density M-QAM as having modulation orders ( $M$ ) of at least 64, i.e. $M\ge 64. $ High-density M-QAM symbols deliver high data rates under good wireless channels. Future wireless systems must deliver high data rates and simultaneously low end-to-end latency. However, higher M-QAM modulation orders increase the Golden code SD search breadth, thus increasing decoding latency. We, therefore, propose two forms of low complexity Golden code SD to achieve low decoding latency while maintaining the near-optimal SD bit-error rate (BER). The proposed low complexity SD algorithms are based on the SD with sorted detection subsets (SD-SDS). The literature shows the SD-SDS to achieve lower detection complexity relative to the Schnorr-Euchner SD (SE-SD). The first form of the proposed Golden code SD is the SD-SDS-Descend algorithm with instantaneously varying subset lengths and a search tree search order sorted based on the worst-first search strategy. The second form of the proposed Golden code SD is an SD-SDS algorithm called SD-SDS-ES-DNN with a deep learning-based early stopping search criterion. Our proposed algorithms achieve at most 57% and 70% reduction in Golden code decoding latency relative to SD-SDS, at low SNR, for 64-QAM and 256-QAM, respectively. At high SNR, the proposed algorithms achieve 40% and 37% in Golden code decoding latency reduction relative to the SD-SDS for 64-QAM and 256-QAM, respectively. The decoding latency reduction is achieved while maintaining near-optimal BER performances.