  In this paper, we deal with low-complexity near-optimal
detection/equalization in large-dimension multiple-input multiple-output
inter-symbol interference (MIMO-ISI) channels using message passing on
graphical models. A key contribution in the paper is the demonstration that
near-optimal performance in MIMO-ISI channels with large dimensions can be
achieved at low complexities through simple yet effective
simplifications/approximations, although the graphical models that represent
MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1)
use of Markov Random Field (MRF) based graphical model with pairwise
interaction, in conjunction with {\em message/belief damping}, and 2) use of
Factor Graph (FG) based graphical model with {\em Gaussian approximation of
interference} (GAI). The per-symbol complexities are $O(K^2n_t^2)$ and
$O(Kn_t)$ for the MRF and the FG with GAI approaches, respectively, where $K$
and $n_t$ denote the number of channel uses per frame, and number of transmit
antennas, respectively. These low-complexities are quite attractive for large
dimensions, i.e., for large $Kn_t$. From a performance perspective, these
algorithms are even more interesting in large-dimensions since they achieve
increasingly closer to optimum detection performance for increasing $Kn_t$.
Also, we show that these message passing algorithms can be used in an iterative
manner with local neighborhood search algorithms to improve the
reliability/performance of $M$-QAM symbol detection.
