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In this paper, we propose a joint design of serially concatenated source channel coding for binary Markov sources over AWGN channels. To exploit the memory structure inherent within the sequence output from the source, modifications are made on the BCJR algorithm. To decode the outer code, the modified version of the BCJR algorithm is used, while the inner code by the standard version of the algorithm. Since optimal design of serially concatenated convolutional code falls into the problem of curve matching between the extrinsic information transfer (EXIT) curves of the inner and outer codes, we first evaluate the EXIT curve of the outer code decoded by the modified BCJR algorithm. It is then shown that the EXIT curve obtained by the modified BCJR algorithm is better matched with short memory inner convolutional code, which significantly reduces coding/decoding complexity. Numerical results demonstrate significant gains over the systems in which source statistics are not exploited (i.e., the standard BCJR algorithm is used for the both codes), and thereby narrowing the performance gap to the Shannon limit. We also compare in this paper the performance of the proposed design with the algorithm presented in , designed also for transmission of binary Markov source using parallel concatenated convolutional code (the authors of Ref.  refer the technique as Joint Source Channel Turbo Code (JSCTC)). It is shown that our proposed system is superior in both system complexity and BER performance to the JSCTC technique presented in .