Characterization and Optimization of Coding Performance in Downlink NOMA with Finite-Alphabet Inputs and Finite Blocklength

In this paper, the channel coding performance with finite-alphabet inputs and finite blocklength in a two-user downlink non-orthogonal-multiple-access (NOMA) system is characterized from an information-theoretic perspective, and optimized with proper power allocation and constellation design. While previous works in NOMA were mainly focused on either infinite blocklength performance or finite blocklength performance with Gaussian inputs, we obtain the information-theoretic achievable rates accurate up to second-order as a function of the blocklength for both NOMA users employing finite-alphabet inputs subject to the average total power constraint. Taking advantage of the theoretical results, we formulate the rate and error-rate performance optimization problems in the finite blocklength regime for finite-alphabet inputs, from which the optimal power allocation and constellation-rotation can be derived. Furthermore, polar codes and LDPC are employed to demonstrate how close their performances are from the second-order achievable bound when the blocklength is short. Our results are important in machine-type or IoT communications where lightweight modulations and short blocklength are more relevant compared with traditional Gaussian-inputs assumption.