Parallel Decoding of IRSA with Noise

Due to its simplicity and scalability, the Irregular Repetition Slotted ALOHA (IRSA) system that uses the successive interference cancellation (SIC) technique is a promising solution for uncoordinated multiple access of a massive number of Internet-of-Things (IoT) devices. However, the peeling (iterative) decoder for IRSA is sequential in nature, and it might lead to cascading errors due to imperfect SIC. In this paper, we propose a parallel decoding algorithm for IRSA in an Additive White Gaussian Noise (AWGN) channel. Inspired by a recent advance in collision resolution for random access, our approach is to find a SIC-decoupling matrix so that the receiver can perform interference cancellation based on the received signals only. We propose a message-passing algorithm to find the optimal SIC-decoupling matrix when the induced user-slot bipartite graph of an IRSA system is acyclic. This includes the Contention Resolution Diversity Slotted ALOHA (CRDSA) system that sends exactly two copies for each packet. Using a random graph analysis, we derive the throughput for parallel decoding of CRDSA in a threshold-based decoding model. We also conduct various numerical experiments to illustrate the tradeoffs between sequential decoding with a limited number of iterations and parallel decoding with a predefined signal-to-noise ratio (SNR) threshold. Our numerical results show that one can significantly reduce the decoding time and achieve comparable throughput by parallel decoding when the SNR is substantially larger than the decoding threshold.