Encoding and Decoding Construction D' Lattices for Power-Constrained Communications

TL;DR

This paper introduces new encoding and decoding methods for Construction D' lattices, enabling efficient power-constrained communication with improved shaping gains using specific lattice structures.

Contribution

It presents novel encoding/decoding algorithms and a QC-LDPC code design for Construction D' lattices, enhancing power efficiency and low complexity in lattice-based communication.

Findings

Shaping gains of 0.65 dB, 0.86 dB, and 1.03 dB achieved with specific lattices.

New encoding and decoding algorithms for Construction D' lattices.

Design of QC-LDPC codes for nested lattice constructions.

Abstract

This paper focuses on the encoding and decoding of Construction D' coding lattices that can be used with shaping lattices for power-constrained channels. Two encoding methods and a decoding algorithm for Construction D' lattices are given. A design of quasi-cyclic low-density parity-check (QC-LDPC) codes to form Construction D' lattices is presented. This allows construction of nested lattice codes which are good for coding, good for shaping, and have low complexity encoding and decoding. Numerical results of using $E_8$, $BW_{16}$ and Leech lattices for shaping a Construction D' lattice indicate that the shaping gains 0.65 dB, 0.86 dB and 1.03 dB are preserved, respectively.