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In a parallel concatenated convolutional code, an information sequence is encoded by a convolutional encoder, and an interleaved version of the information sequence is encoded by another convolutional encoder. We discuss the situation in which we require both convolutional encoders to end in the all-zero state. To do so, we have to split an information word in two parts. One part contains the true information bits, and the second part contains the so-called tail bits, which are special bits with values computed such that both encoders end in the all-zero state. Depending on the interleaver, a different number of tail bits are needed. By using a constructive method, we give a characterization of all interleavers for a prescribed number of tail bits. We explain the method of encoding. In addition, simulations have been carried out to investigate the performance of codes resulting from simultaneous zero-tailing. This shows that simultaneous zero-tailing is similar in performance as compared to previously known zero-tailing methods (but with fewer trellis termination bits) and that it is better than zero-tailing just one of the encoders.