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 Gaussianmultiple access channel (MAC). The performance of $T$-fold irregular repetitionslotted ALOHA (IRSA) scheme for this channel is investigated. The maindifference of this scheme in comparison to IRSA is as follows: any collisionsof order up to $T$ can be resolved with some probability of error introduced byGaussian noise. First, we generalize the density evolution method for T-foldIRSA and noisy channel and find optimal degree distributions for differentvalues of $T$. Then we perform analysis and find minimal $E_b/N_0$ for a fixedlength, rate and packet loss probability. The scheme is shown to work closer tofinite length random coding bound proposed by Y. Polyanskiy, than existingsolutions.