PHY-layer network coding for broadcast channel with side information

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 the joint design achieves capacity regions for both Cases i) and ii). For Case i), each link achieves the same error probability as that of one-to-one single-link transmission using the constituent code. For Case ii), an embedded coding structure is used, and upper bounds on decoding error probability are characterized. For Cases iii) and iv), the scheme resembles super-position coding.