Density Evolution Analysis of Structured IRSA With Multi-Packet Reception and Orthogonal Pilots

We present an analytical framework based on density evolution (DE) for irregular repetition slotted ALOHA (IRSA) operating over orthogonal time-frequency resources. A structured IRSA scheme is introduced, in which each active user transmits multiple replicas across a selected subset of slot-subcarriers within a frame. The proposed DE formulation explicitly accounts for multi-packet reception (MPR) and orthogonal pilot selection, extending classical DE analysis to capture the combined effects of structured repetition and MPR-enabled decoding. Monte Carlo simulations, carried out under both idealized and realistic physical-layer conditions, validate the analysis and confirm its accuracy in characterizing and optimizing next-generation random access protocols.