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Noisy network coding unifies network coding by Ahlswede, Cai, Li, and Yeung for noiseless networks and compress-forward by Cover and El Gamal for noisy relay channels. In particular, it achieves the best known capacity inner bounds for multi-source multicast networks including deterministic networks by Avestimehr, Diggavi, and Tse and erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. This paper extends noisy network coding for multicast networks to networks with general message demand by combining the underlying noisy network coding scheme with decoding techniques for interference channels. At one extreme, noisy network coding is combined with simultaneous decoding, while at the other extreme interference is treated as noise. The potential of noisy network coding as a canonical building block for wireless networks is demonstrated via three examples of Gaussian networks that have drawn recent attentions.