Design of Luby Transform Codes with Gray-Mapped 16-QAM Over AWGN Channels

In this paper, we investigate Gray-mapped 16-QAM modulated Luby Transform (LT) codes over additive white Gaussian noise (AWGN) channels. Degree distributions for LT codes with a BPSK modulation have been well studied in the literature but those distributions provide unsatisfactory bit-error-rate (BER) performance under high order constellations. To improve the BER performance of LT codes with Gray-mapped QAM, this paper presents a novel optimization design of degree distributions. First, we put forth the concept of variance-to-mean ratio (VMR) in a Gaussian distribution because that the variance is two times larger than the mean in the conventional Gaussian approximation (GA) no longer applies for QAM. Second, we provide a generalized GA process using the obtained VMRs to analyze the asymptotic BER performance of LT codes and furthermore lower bound on BER. Third, aiming at minimizing the average degree of degree distribution, we propose a novel model constrained by the lower bound on BER. Simulation results show that the degree distribution offered by the proposed optimization model can provide outstanding BER performance of LT codes with Gray-mapped 16-QAM over the AWGN channel.