Trellis termination of turbo codes is critical for maintaining their good performance, especially for short information blocks when the deterministic interleaver is sought to reduce the complexity of signaling the interleaver permutation. To address this problem, this paper introduces a new type of turbo code called the Return to Zero (RZ) turbo code whose both component encoders are brought to the initial (zero) state. Specifically, a general mathematical model is built in this paper to serve as the theoretical foundation of RZ turbo codes. The model is used to compute the state of a general recursive systematic convolutional (RSC) encoder. Based on this model, a unique duo property of certain class (full feedback) of RSC encoders is demonstrated which is further used to introduce a new type of interleaver called the RZ interleaver. This interleaver is capable of processing the input sequence of bits in such a way that it can bring both encoders into the initial state. Simulation results presented in this paper show that the RZ turbo code can achieve almost the same performance as that of the traditional turbo code when the interleaver size is small or medium.
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