Can iterative decoding for erasure correlated sources be universal?

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.