Min-Sum algorithm for lattices constructed by Construction D

TL;DR

This paper extends the min-sum decoding algorithm to lattices built via Construction D, providing complexity bounds and demonstrating feasible decoding for high-dimensional lattices.

Contribution

It generalizes the min-sum algorithm to Construction D lattices and derives complexity bounds, enabling efficient decoding of large-dimensional lattices.

Findings

Decoding complexity per iteration is bounded by coding gain and label group sizes.

Iterative decoding of LDGM lattices is computationally feasible for dimensions of a few thousand.

The generalized algorithm maintains low complexity suitable for practical high-dimensional lattice decoding.

Abstract

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.