We propose a novel joint decoding technique for distributed source-channel (DSC) coded systems for transmission of correlated binary Markov sources over additive white Gaussian noise (AWGN) channels. In the proposed scheme, relatively short-length, low-density parity-check (LDPC) codes are independently used to encode the bit sequences of each source. To reconstruct the original bit sequence, a joint source-channel decoding (JSCD) technique is proposed which exploits the knowledge of both temporal and source correlations. The JSCD technique is composed of two stages, which are iteratively performed. First, a sum-product (SP) decoder is serially concatenated with a BCJR decoder, where the knowledge of source memory is utilized during {\em local (horizontal) iterations}. Then, the estimate of correlation between the sources is used to update the concatenated decoder during {\em global (vertical) iterations}. Therefore, the correlation of the sources is assumed as side information in the subsequent global iteration of each concatenated decoder. From the simulation results of frame/bit error rate (FER/BER), we note that significant gains are achieved by the proposed decoding scheme with respect to the case where the correlation knowledge is not completely utilized at the decoder.