Uniquely Decodable Ternary Codes via Augmented Sylvester-Hadamard Matrices

In this paper, we consider the problem of designing uniquely decodable (UD) ternary code sets for low-density spreading code-division multiple-access (LDS-CDMA) systems. The proposed code set provides unique decodability for a number of users K that is greater than the length of the code but lower than the theoretical maximum, i.e., $K\lt K_{\max}^{t}$ *. Simulation results show that with channel encoded scenarios (e.g., turbo, LDPC, polar, etc.) the proposed UD code sets achieve 4 dB or greater performance improvement at a bit error rate (BER) of 10−3 compared to other competing code sets in an additive white Gaussian noise (AWGN) and flat Rayleigh fading channels.