In this paper, we consider multiple access schemes with correlated sources, where a priori information, in terms of source correlation, is available at the access point (AP). In particular, we assume that each source uses a proper low-density parity-check (LDPC) code to transmit, through an additive white Gaussian noise (AWGN) channel, its information sequence to the AP. At the AP, the information sequences are recovered by an iterative decoder, with component decoders associated with the sources, which exploit the available a priori information. In order to analyze the behaviour of the considered multiple access coded system, we propose a density evolution-based approach, which allows to determine a signal-to-noise ratio (SNR) transfer chart and compute the system multi-dimensional SNR feasible region. The proposed technique, besides characterizing the performance of LDPC-coded multiple access scheme, is expedient to design optimized LDPC codes for this application.