© 2013 IEEE. We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded (using codes of fixed rate) and transmitted over two independent binary memoryless symmetric channels. The capacity of each channel is characterized by a single parameter that is not known at the transmitter. System performance is evaluated by computing the set of channel parameters for which the system can successfully decode. This set is called the achievable channel parameter region (ACPR). The goal is to design systems whose ACPRs are as large as possible. The main result is the design of irregular low-density paritycheck (LDPC) ensembles whose ACPRs are significantly larger than previous designs. Some previous attempts to achieve large ACPRs with LDPC codes failed because systematic codes were used. In this work, we start with systematic encoders but puncture all the systematic bits before transmission. We also show that additional gains are possible using a staggered structure which enables codes optimized for single-user channels to perform well under symmetric channel conditions. The main analysis tool is a generic density-evolution framework for the analysis of joint iterative decoding for this problem.