  This paper is concerned with the design of capacity approaching ensembles of
Low-Densiy Parity-Check (LDPC) codes for correlated sources. We consider
correlated binary sources where the data is encoded independently at each
source through a systematic LDPC encoder and sent over two independent
channels. At the receiver, a iterative joint decoder consisting of two
component LDPC decoders is considered where the encoded bits at the output of
each component decoder are used at the other decoder as the a priori
information. We first provide asymptotic performance analysis using the concept
of extrinsic information transfer (EXIT) charts. Compared to the conventional
EXIT charts devised to analyze LDPC codes for point to point communication, the
proposed EXIT charts have been completely modified to able to accommodate the
systematic nature of the codes as well as the iterative behavior between the
two component decoders. Then the developed modified EXIT charts are deployed to
design ensembles for different levels of correlation. Our results show that as
the average degree of the designed ensembles grow, the thresholds corresponding
to the designed ensembles approach the capacity. In particular, for ensembles
with average degree of around 9, the gap to capacity is reduced to about 0.2dB.
Finite block length performance evaluation is also provided for the designed
ensembles to verify the asymptotic results.
