Construction D Lattice Decoding and Its Application to BCH Code Lattices

The decoding of Construction D lattices is described. While similar to the multistage decoding of Code Formula codes, modification is required so that lattice components are subtracted in a process called reencoding. A generator matrix for Construction D lattices is given. Construction D lattices obtained from BCH codes were described by Barnes and Sloane. In this paper, we consider some practical issues of encoding and decoding these lattices. Using ordered statistics decoding, dimension 128 BCH code lattices outperform turbo lattices and low-density lattice codes of similar dimension. These results show relatively good performance of lattices based on algebraic constructions, compared to lattices typically designed for high dimensions. The performance over power-constrained channel is also evaluated, where the near-optimal performance is demonstrated.