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.

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.