  Hinging on ideas from physical-layer network coding, some promising proposals
of coded random access systems seek to improve system performance (while
preserving low complexity) by means of packet repetitions and decoding of
linear combinations of colliding packets, whenever the decoding of individual
packets fails. The resulting linear combinations are then temporarily stored in
the hope of gathering enough linearly independent combinations so as to
eventually recover all individual packets through the resolution of a linear
system at the end of the contention frame. However, it is unclear which among
the numerous linear combinations---whose number grows exponentially with the
degree of collision---will have low probability of decoding error. Since no
analytical framework exists to determine which combinations are easiest to
decode, this makes the case for a machine learning algorithm to assist the
receiver in deciding which linear combinations to target. For this purpose, we
train neural networks that approximate the error probability for every possible
linear combination based on the estimated channel gains and demonstrate the
effectiveness of our approach by numerical simulations.
