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