Design of Finite-Length Irregular Protograph Codes with Low Error Floors over the Binary-Input AWGN Channel Using Cyclic Liftings

TL;DR

This paper introduces a method for designing finite-length irregular LDPC codes with low error floors over AWGN channels by cyclically lifting protographs to optimize cycle properties, resulting in practical quasi-cyclic codes.

Contribution

The paper presents a novel cyclic lifting technique to design LDPC codes with improved error floor performance based on optimizing the ACE spectrum.

Findings

Achieves low error floors in LDPC codes through ACE spectrum optimization.

Produces quasi-cyclic codes with simple encoding and decoding.

Demonstrates improved performance via simulations.

Abstract

We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.