Abstract
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. In this paper, we propose two parallel decoding algorithms for IRSA in an additive white Gaussian noise channel. Our first algorithm is limited to SIC-decoupling matrices that correspond to the SIC decoding process in IRSA. For this, we propose a message-passing algorithm to find the optimal SIC-decoupling matrix that can minimize the accumulated noise power 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 as a special case. Our second algorithm extends the first one by finding the optimal decoupling matrix for CRDSA through an optimal combination of two SIC-decoupling matrices. Using a random graph analysis, we derive the throughput for the two parallel decoding algorithms of CRDSA in a threshold-based decoding model. We then 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. Finally, we demonstrate how to extend our parallel decoding scheme to bipartite graphs with cycles.