# Low Density Lattice Codes

## TL;DR

Low density lattice codes (LDLC) are a new class of lattice codes with sparse inverse generator matrices, enabling efficient decoding and near-capacity performance on the AWGN channel, demonstrated through large-scale simulations.

## Contribution

This paper introduces LDLC, a novel lattice coding scheme with sparse inverse matrices, allowing linear-time decoding and near-capacity error performance.

## Key findings

- Decoding scheme achieves near-capacity performance within ~0.5dB.
- Efficient linear-time iterative decoding demonstrated.
- Good error performance at block length of 100,000 symbols.

## Abstract

Low density lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb, where H, the inverse of G, is restricted to be sparse. The fact that H is sparse is utilized to develop a linear-time iterative decoding scheme which attains, as demonstrated by simulations, good error performance within ~0.5dB from capacity at block length of n = 100,000 symbols. The paper also discusses convergence results and implementation considerations.