Construction of LDGM lattices
This work addresses the need for efficient lattice constructions in coding theory, but it appears incremental as it builds on existing LDGM and Construction D methods.
The paper tackles the problem of constructing lattices with good performance and low complexity by applying Construction D to low density generator matrix (LDGM) codes, resulting in lattices with acceptable performance confirmed by simulation results.
Low density generator matrix (LDGM) codes have an acceptable performance under iterative decoding algorithms. This idea is used to construct a class of lattices with relatively good performance and low encoding and decoding complexity. To construct such lattices, Construction D is applied to a set of generator vectors of a class of LDGM codes. Bounds on the minimum distance and the coding gain of the corresponding lattices and a corollary for the cross sections and projections of these lattices are provided. The progressive edge growth (PEG) algorithm is used to construct a class of binary codes to generate the corresponding lattice. Simulation results confirm the acceptable performance of these class of lattices.