We consider the problem of transmitting correlated data after independent
encoding to a central receiver through orthogonal channels. We assume that the
channel state information is not known at the transmitter. The receiver has
access to both the source correlation and the channel state information. We
provide a generic framework for analyzing the performance of joint iterative
decoding, using density evolution. Using differential evolution, we design
punctured systematic LDPC codes to maximize the region of achievable channel
conditions, with joint iterative decoding.

Algorithms based on multiple decoding attempts of Reed-Solomon (RS)codes have
recently attracted new attention. Choosing decoding candidates based on
rate-distortion (R-D) theory, as proposed previously by the authors, currently
provides the best performance-versus-complexity trade-off. In this paper, an
analysis based on the rate-distortion exponent (RDE) is used to directly
minimize the exponential decay rate of the error probability. This enables
rigorous bounds on the error probability for finite-length RS codes and leads
to modest performance gains.

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.