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Application of network coding in wireless two-way relay channels (TWRC) has received much attention recently because its ability to improve throughput significantly. In traditional designs, network coding operates at upper layers above (including) the link layer and it requires the input packets to be correctly decoded. However, this requirement may limit the performance and application of network coding due to the unavoidable fading and noise in wireless networks. In this paper, we propose a new wireless network coding scheme for TWRC, which is referred to as soft network coding (SoftNC), where the relay nodes applies symbol-by-symbol soft decisions on the received signals from the two end nodes to come up with the network coded information to be forwarded. We do not assume further channel coding on top of SoftNC at the relay node (channel coding is assumed at the end nodes). According to measures of the soft information adopted, two kinds of SoftNC are proposed: amplify-and-forward SoftNC (AF-SoftNC) and soft-bit-forward SoftNC (SBF-SoftNC). We analyze the both the ergodic capacity and the outage capacity of the two SoftNC schemes. Specifically, analytical form approximations of the ergodic capacity and the outage capacity of the two schemes are given and validated. Numerical simulation shows that our SoftNC schemes can outperform the traditional network coding based two-way relay protocol, where channel decoding and re-encoding are used at the relay node. Notable is the fact that performance improvement is achieved using only simple symbol-level operations at the relay node.