Joint algebraic coded modulation and lattice-reduction-aided preequalisation

Lattice-reduction-aided (LRA) preequalisation for the multiple-input/multiple-output broadcast channel has most often been considered for the uncoded case so far. However, recent advantages in the closely related field of integer-forcing equalisation, where the cancellation of the multiuser interference and the channel coding are combined, create doubt to this separated point of view. In this Letter, the philosophy of matching both the channel code and the complex-valued signal constellation to the same finite-field arithmetic is proposed. The consequences on the factorisation task present in LRA preequalisation are discussed and covered by numerical performance evaluations based on non-binary low-density parity-check codes.