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This paper proposes a novel combination of network coding and channel coding for a two-receiver Gaussian broadcast channel under practical modulation. We assume that one receiver may know the message for the other receiver, called the side information (SI). This models relaying in dense wireless networks where destination nodes may have received packets intended for other nodes in previous transmissions. Four cases are considered: i) both receivers have SI; ii) only the weak receiver has SI; iii) only the strong receiver has SI; and iv) neither receiver has SI. We propose a simple adaptive coding scheme that combines channel coding with network coding, which greatly reduces coding/decoding complexity as compared to pure random coding. The scheme first designs channel codes independently for each channel, then combines them with simple network coding. Analysis is also presented showing that …