The problem of massive random access is of critical importance for 5G/6G and Internet of Things (IoT) applications. Indeed, the number of autonomous battery-powered devices (sensors) connected to the network grows exponentially, and current wireless networks cannot serve all of them and are highly inefficient in this regime. I have been working on this topic since 2018, my group has published more than 20 publications. I would especially note a publication [1] (impact-factor 5.083, Q1) and the best paper [2] award acquired at the Communication Theory Symposium at IEEE Global Communications Conference (GLOBECOM) - one of the leading conferences in telecommunications.

   Massive IoT problem formulation admits a compressed sensing (CS) interpretation. The key observation behind related research is the fact that the dimensionality of this problem is huge (the codebook or sensing matrix size is n by 2k, where k is the number of bits to be transmitted). As a result, the direct application of CS methods is computationally infeasible. Possible way to deal with the curse-of-dimensionality problem is to utilize coded CS approach, i.e., split the task into subtasks of smaller dimensionality, solve the CS problem for each subtask, and then assemble the results. The latter task has an evident connection to list-recoverable codes. We have carried out preliminary research on this topic [3] and proposed a random coding bound, which shows the efficiency of the overall scheme.

   The research tasks are as follows:

1. derive fundamental limits for massive IoT which are also limits for the sparse recovery problem.

2. develop practical constructions of list-recoverable codes, consider Reed-Solomon codes in combination with Guruswami-Sudan algorithm, convolutional codes, and polar codes.

3. consider the use of approximate message passing (AMP) algorithm [4]. Unlike standard CS algorithms, this approach utilizes the prior information. As a result, one can apply iterative decoding algorithms for the whole system.

   The main goal is to propose new practical schemes for the massive IoT scenario, compare the developed schemes to the existing solutions and fundamental limits and prepare new proposals for the 3GPP standardization committee.