Achievability Bounds for T-Fold Irregular Repetition Slotted ALOHA Scheme in the Gaussian Multiple Access Channel.

We address the problem of massive random access for an uncoordinated Gaussian multiple access channel (MAC). The performance of $T$-fold irregular repetition slotted ALOHA (IRSA) scheme for this channel is investigated. The main difference of this scheme in comparison to IRSA is as follows: any collisions of order up to $T$ can be resolved with some probability of error introduced by Gaussian noise. First, we generalize the density evolution method for T-fold IRSA and noisy channel and find optimal degree distributions for different values of $T$. Then we perform analysis and find minimal $E_b/N_0$ for a fixed length, rate and packet loss probability. The scheme is shown to work closer to finite length random coding bound proposed by Y. Polyanskiy, than existing solutions.