Practical Encoder and Decoder for Power Constrained QC-LDPC lattices

TL;DR

This paper introduces practical encoder and decoder methods for power-efficient QC-LDPC lattices, demonstrating their near-optimal performance with low complexity in high-dimensional settings.

Contribution

It presents a new low-complexity encoding and decoding framework for QC-LDPC lattices using shift register encoding and sum-product decoding algorithms.

Findings

Shaping gain close to the sphere bound at dimensions 40, 50, 60

Efficient linear complexity encoding via quasi cyclic generator matrices

Lattice codes perform near the theoretical limit

Abstract

LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as a special case of LDPC lattices with one binary QC-LDPC code as their underlying code. These lattices are obtained from Construction A of lattices providing us to encode them efficiently using shift registers. To benefit from an encoder with linear complexity in dimension of the lattice, we obtain the generator matrix of these lattices in "quasi cyclic" form. We provide a low-complexity decoding algorithm of QC-LDPC lattices based on sum product algorithm. To design lattice codes, QC-LDPC lattices are combined with nested lattice shaping that uses the Voronoi region of a sublattice for code shaping. The shaping gain and shaping loss of our lattice codes with dimensions $40$, $50$ and $60$ using an optimal quantizer, are presented. Consequently, we establish a family of lattice codes that perform practically close to the sphere bound.