The key requirements for 6G systems may be summarized as: peak data rate: ≥1 Tbps; user experience data rate at least be 10 × better than in 5G; user plane latency should be a factor 40×better than in 5G; mobility - up to 1000 km/h. To meet these requirements, we plan to carry out research in the following main directions:

1. New high-throughput error-correcting codes and new decoding algorithms. The main candidates are:

   1. Concatenated codes with inner error-reducing codes. Concatenated coding is a standard way to reduce the complexity, the key part is as follows. The inner code is required to reduce the number of errors as much as possible rather than correct all the errors. It was shown [1] that non-linear codes are better than any linear code in the error-reducing regime for the binary erasure channel. Also, the constructions of non-linear sparse graph codes were proposed. Our goal is to investigate these codes in more realistic channel models. The initial results are given in [2].

   2. Lattice codes. The goal is to design lattice codes and compare them with state-of-the-art error-correcting codes.

   3. New decoding algorithms. We are going to investigate optimization-inspired decoders. The decoding task is an integer programming problem, which is computationally difficult. Making the relaxation we can apply various optimization strategies, such as gradient descent [3] or linear programming [4]. Recent papers [5,6,7] provide the results for LDPC codes, we plan to consider different classes of codes, such as polar codes, algebraic and lattice codes, as well as construct codes for these decoders. Another line of research is reducing the decoding complexity or minimizing the number of constraints.

   4. Sparse-regression codes (SPARCs) [8]. SPARCs form a new class of codes that can be decoded with use of compressed sensing techniques (approximate message passing, AMP). These codes are proven to achieve the capacity of AWGN channel. The task is to investigate the finite length performance and error-reducing properties of such codes.

2. Non-orthogonal multiple access (NOMA) techniques. It is well-known that to realize the capacity of the multiple-access channel (MAC) the users should use the channel simultaneously (time and frequency sharing are bad strategies) in combination with a joint decoder. At the same time practical schemes are far from asymptotic limits. We plan to research the following NOMA strategies:

   1. NOMA based on LDPC codes. The task is to develop the methods to design and analyze such codes for multiple-access scenarios.

   2. NOMA based on Polar codes. Polar codes are based on channel polarization phenomenon. It was proved that MAC can also be polarized. Our first task is to perform theoretical investigation of MAC polarization and characterize virtual subchannels and partial order on these subchannels. Finally, we plan to propose finite-length constructions of polar codes for MAC. The initial results are given in [9].

   3. Compute-and-Forward (CoF) approach [10]: the idea is to restore integer combinations of transmitted messages rather than the messages themselves when the transmissions collide. To implement this scheme, lattice codes are required. The task is to develop the methods to design and analyze such codes for multiple-access scenarios.

3. Physical-layer network coding [11]. Network coding (NC) is a technique where network nodes are allowed to perform operations on transmitted messages (packets), i.e., to send linear combinations of packets rather than the packets themselves. Physical-layer NC operates on the transmitted signals, i.e., real, or complex vectors. This technique allows to reduce the number of transmissions and thus increase the transmission rate. Physical-layer NC is closely related to NOMA.

4. New waveforms. We plan to consider the Faster-than-Nyquist (FTN) approach, find proper waveforms and focus on decoding complexity reduction.