Non-orthogonal multiple access (NOMA) employing nested lattice codes is investigated in a downlink transmission scenario. The fundamental idea is the multiple access scheme via Compute-and-Forward framework, which produces an equivalent MIMO channel such that multiuser detection can be performed. Approaches including the successive lattice decoding of linear functions of transmitted messages by cancelling decoded equations and ML detection are investigated. Power allocation as a precoding scheme as well as an allocation strategy are proposed to deal with channel fadings and to enhance system throughput.