Min-Sum algorithm for lattices constructed by Construction D
This work addresses decoding complexity for lattice-based coding, but it is incremental as it extends an existing method to a related construction.
The paper tackles the problem of decoding high-dimensional lattices by generalizing the min-sum algorithm from Construction D' to Construction D, achieving a low decoding complexity that enables lattices with dimensions of a few thousands to be decoded easily.
The so-called min-sum algorithm has been applied for decoding lattices constructed by Construction D'. We generalize this iterative decoding algorithm to decode lattices constructed by Construction D. An upper bound on the decoding complexity per iteration, in terms of coding gain, label group sizes of the lattice and other factors is derived. We show that iterative decoding of LDGM lattices has a reasonably low complexity such that lattices with dimensions of a few thousands can be easily decoded.