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This work presents an efficient structured binning scheme for solving the noiseless distributed source coding problem with parallel concatenated convolutional codes, or turbo codes. The novelty in the proposed scheme is the introduction of a syndrome former and an inverse syndrome former to efficiently and optimally exploit an existing turbo code without the need to redesign or modify the code structure and/or decoding algorithms. Extension of the proposed approach to serially concatenated codes is also briefed and examples including conventional turbo codes and asymmetric turbo codes are given to show the efficiency and the general applicability of the approach. Simulation results reveal good performance which is close to the theoretic limit.