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In this paper, we investigate the joint design of channel and network coding with power allocation in bi-directional relaying systems and propose a combined low complexity LDPC and physical network coding scheme. For the same LDPC codes employed at both source nodes, we show that the relay can decodes the network coded code-words from the superimposed signal received from the BPSK-modulated multiple-access channel. The outage probability analysis shows that the bi- directional relaying system obtains the optimal performance while the total transmit power of the two source nodes equal to the relay node. Simulation results shown that the proposed joint LDPC and physical network coding method outperforms the existing MMSE based LDPC and network coding method over AWGN and complex MAC channel.