Combinatorial Unsourced Random Access Coding

The new approach to massive random access introduced by Yuri Polyanskii in 2017 has attracted the attention of many researchers. The corresponding publications explore a simplified probabilistic model to avoid considering cases when different users submit the same information. It is also considered probabilistic model of noise what doesn’t allow to fight with adversarial noise. In fact, taking into account the case of adversarial noise plus different users may transmit the same information complicates the corresponding problem of combinatorial coding and requires the use of more complex methods of coding theory. We give constructions of the corresponding codes with asymptotic optimal parameters.