This paper presents a practical implementation of Noisy Network Coding (NNC) for half-duplex Two-Way Relay channels (TWRC). With Noisy Network Coding, the relay quantizes the incoming signals and forwards them digitally. The receivers do not try to recover the relay quantization index but the codewords that are embedded in the quantized signal. Our approach uses irregular repeat-accumulate low-density parity check (LDPC) codes to implement NNC. We derive the joint factor graph and the message passing rules for the corresponding joint iterative decoding scheme. Our simulation results confirm the performance advantages predicted by random coding arguments.