Short Analog Fountain Code with Quasi-Gray Constellation Mapping Modulation Towards uRLLC

In this paper, a capacity-approaching rateless coded modulation towards ultra-reliable low latency communications (uRLLC) is proposed, including the joint design of short block-length analog fountain code (AFC) and quasi-gray constellation mapping (QGCM) modulation at the transmitter, and a limited feedback mechanism for the receiver. First, based on the nonlinear constellation and quasi-gray mapping, we design a novel rateless coded modulation scheme called AFC-QGCM, and prove it can approach to the Shannon capacity. Further, the theoretical evaluation framework of information density between the achievable rate and signal-to-noise (SNR) of the AFC-QGCM schemes is derived under short block-length. Based on the analysis, we propose a rateless transmission scheme with a limited feedback link over the fading channel without precise channel state information (CSI) at the transmitter, which could utilize the theoretical analysis to determine the optimal coding and modulation parameters during the transmission. Both analysis and simulation results shown that the proposed scheme could approaching to the Polyanskiy-Poor-Verdu (PPV) meta converse benchmark in a wide range SNRs.