  In this paper, we consider a few iterative decoding schemes for the joint
source-channel coding of correlated sources. Specifically, we consider the
joint source-channel coding of two erasure correlated sources with transmission
over different erasure channels. Our main interest is in determining whether or
not various code ensembles can achieve the capacity region universally over
varying channel conditions. We consider two ensembles in the class of
low-density generator-matrix (LDGM) codes known as Luby-Transform (LT) codes
and one ensemble of low-density parity-check (LDPC) codes. We analyze them
using density evolution and show that optimized LT codes can achieve the
extremal symmetric point of the capacity region. We also show that LT codes are
not universal under iterative decoding for this problem because they cannot
simultaneously achieve the extremal symmetric point and a corner point of the
capacity region. The sub-universality of iterative decoding is characterized by
studying the density evolution for LT codes.
