  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.
