Network coding is a hot research topic due to its ability to improve network throughput and robustness. Most existing research on network coding assumes that the transmission between two nodes in a network is free of errors. Accompanying with this assumption is that nodes in the network always perform hard decisions regarding the received data bits. In this paper, however, we deal with the fact that data transmission is noisy in reality. Only binary networks are considered. The communication channel between two nodes is treated as either BSC or AWGN. Two issues are addressed. First, with all network branches treated as BSC, we investigate the problem of how a transmitter node should allocate its available energy among the branches connected to it so that the intended receivers get the best result (in some sense). Secondly, by treating the branches connected to a receiver node as AWGN, we develop a soft decoding scheme for obtaining the soft decisions (in terms of probabilities) regarding the received data bits at a receiver node. We then show how these soft decisions can be exploited in some belief-propagation decoding schemes. We claim that if error correcting codes are to be incorporated into network coding, then soft decoding is either indispensable or much preferred.