On Tanner graphs of lattices and codes

The problem of finding a low-complexity Tanner graph for a general lattice Λ is studied. The problem is divided into two subproblems: (1) Finding an orthogonal sublattice Λ of Λ which minimizes the complexity of the label code of the quotient group Λ Λ. (2) Constructing a simple Tanner graph for the label code obtained in part 1. The proposed approach for solving subproblem 2 can also be applied to any abelian group block code with arbitrary finite alphabets at different coordinates. The results of this work are useful in finding low-complexity graph representation of lattices and codes, which consequently results in efficient graph-based decoding algorithms