  In this paper we explore low-complexity probabilistic algorithms for soft
symbol detection in high-dimensional multiple-input multiple-output (MIMO)
systems. We present a novel algorithm based on the Expectation Consistency (EC)
framework, which describes the approximate inference problem as an optimization
over a non-convex function. EC generalizes algorithms such as Belief
Propagation and Expectation Propagation. For the MIMO symbol detection problem,
we discuss feasible methods to find stationary points of the EC function and
explore their tradeoffs between accuracy and speed of convergence. The accuracy
is studied, first in terms of input-output mutual information and show that the
proposed EC MIMO detector greatly improves state-of-the-art methods, with a
complexity order cubic in the number of transmitting antennas. Second, these
gains are corroborated by combining the probabilistic output of the EC detector
with a low-density parity-check (LDPC) channel code.
