A structured irregular repetition slotted ALOHA scheme with low error floors

We propose graph-defined IRSA (G-IRSA), a new approach to design irregular repetition slotted ALOHA (IRSA) uncoordinated multiple access schemes for a controlled-size population of users that become active sporadically. The proposed scheme considers a joint design of the distribution according to which users select their repetition factors and the distribution determining how many packet replicas are transmitted per slot, as well as the connectivity of the underlying graph, i.e., to which slots users transmit. This is in sharp contrast to standard IRSA, where only the users degree distribution is optimized, while active users place their packet replicas uniformly at random and thus there is no control on how many replicas are transmitted per slot and in which slots users transmit. The key idea is to establish a link between the IRSA for the considered scenario and low-density parity-check (LDPC) codes for transmission over the binary erasure channel (BEC). Using this parallelism, the design of a G-IRSA scheme can be cast as the design of a high-rate LDPC code over the BEC. We show that the proposed scheme achieves significantly lower error floors than the original IRSA and very good decoding thresholds.