In recent years, the end-to-end (E2E) scheme based on deep learning (DL), jointly optimizes the encoder and decoder parameters located of the system. Since the center-oriented Gated Recurrent Unit (Co-GRU) network structure satisfying gradient BP while having the ability to learn and compensate for intersymbol interference (ISI) with low computation cost, it is adopted for both the channel modeling and decoder implementation in the E2E design scheme proposed. Meanwhile, to obtain the constellation with the symmetrical distribution characteristic, the encoder and decoder are first E2E joint trained through NLIN model, and further trained on the Co-GRU channel replacing the SSFM channel as well as the subsequent digital signal processing (DSP) step. After the E2EDL process, the performance of the encoder and decoder trained is tested on the SSFM channel. For the E2E system with the Co-GRU based decoder, the gain of general mutual information (GMI) and the Q2-factor relative to the conventional QAM system, are respectively improved up to 0.2 bits/sym and 0.48dB for the long-haul 5-channel dual-polarization coherent system with 960 transmission distance at around the optimal launch power point. The work paves the way for the further study of the application for the Co-GRU structure in the data-driven E2E design of the experimental system, both for the channel modeling and the decoder performance improvement.