It is well known that symbol-level regenerative relay protocols suffer the error propagation problem because receiver decodes blindly and overlooks the probability of relay forwarding wrong bits. In a two-way relay networks, the problem still exists in both network coding (decode-and-forward) and physical network coding (denoise-and-forward) protocols. For today's widely adopted wide band Orthogonal frequencydivision multiplexing (OFDM) systems, error propagation will dramatically restrict the system's end-to-end performance especially when frequency selective fading exists. In this paper, we propose a bit error rate (BER) modified decoding algorithm for these OFDM-based two-way symbol-level regenerative relay strategies. By confining the confidence level of demodulated soft information according to the likelihood of relay having made an error on each bit, this proposed algorithm significantly boosts the end-to-end BER performance of the system. Gaussian superposition codes. Besides traditional exclusive-or coding method, the authors in [10] and [11] also proposed orthogonal physical network coding strategies to enable relay to decode messages from A and B in two-stage relaying (with the expense of doubling the degree of freedom). In addition, the authors in [12] examined the relay selection problem in multi-relay two-way analog network coding networks and the idea of network coding was also extended to dual-hop relay networks by the authors in [13] recently. However, for symbol-level relaying, both three-stage network coding and two-stage physical network coding suffer the error propagation problem. It is resulted by the fact that when relay regenerates new signal, errors may be introduced; lacking of ways to see those errors, node A or B can only decode what they have received. In today's wideband wireless communication systems, capacity-approaching codes such as low-density parity-check code (LDPC) and turbo code are universally in use. Commonly adopted belief propagation (BP) decoders for such codes always take soft information as input, and providing accurate likelihoods is crucial for decoding to succeed. Unfortunately, in wideband wireless links, likelihood of an erroneous bit (introduced by R) may be further magnified by frequency selective fading to make the problem severe.In this paper, we will extend the idea we proposed in [14] by presenting a low complexity and effective bit error rate (BER) modified algorithm for OFDM-based two-way relay networks to mitigate the error propagation problem. The proposed algorithm can be applied to both three-stage network coding and two-stage physical network coding for all modulation types. And we observe that symbol-level BER modified two-stage denoise-and-forward (DNF; physical network coding) protocol can outperform amplify-and-forward (analog network coding) quite a bit. Moreover, the proposed algorithm naturally suits for higher-order modulated (e.g., 16-QAM) signals, which are very common in today's wireless systems. We only concentrate our research on symbol-l...