Performance Analysis of Low-Density Parity-Check Codes over 2D Interference Channels via Density Evolution

TL;DR

This paper provides a theoretical framework using density evolution to analyze the performance of LDPC codes over 2D interference channels with AWGN, demonstrating the effectiveness of the approach through simulations.

Contribution

It introduces a modified density evolution algorithm for 2D interference channels and proves the tree-like message neighborhood for LDPC decoding systems.

Findings

Density evolution effectively predicts system performance.

The message neighborhood is tree-like for long codes.

Simulation results confirm theoretical predictions.

Abstract

The theoretical analysis of detection and decoding of low-density parity-check (LDPC) codes transmitted over channels with two-dimensional (2D) interference and additive white Gaussian noise (AWGN) is provided in this paper. The detection and decoding system adopts the joint iterative detection and decoding scheme (JIDDS) in which the log-domain sum-product algorithm is adopted to decode the LDPC codes. The graph representations of the JIDDS are explained. Using the graph representations, we prove that the message-flow neighborhood of the detection and decoding system will be tree-like for a sufficiently long code length. We further confirm that the performance of the JIDDS will concentrate around the performance in which message-flow neighborhood is tree-like. Based on the tree-like message-flow neighborhood, we employ a modified density evolution algorithm to track the message densities during the iterations. A threshold is calculated using the density evolution algorithm which can be considered as the theoretical performance limit of the system. Simulation results demonstrate that the modified density evolution is effective in analyzing the performance of 2D interference systems.