The broadcast of repetition coding achieves the capacity bounds of decode-and-forward

In FD-AWGN relay channel, the source sends the superposition of many capacity-achieving codewords. The relay decodes them using successive interference cancellation (SIC) and sends the superposition of the same codewords multiplied by random dither sequences and with a new power distribution among the codewords. The destination node decodes all code-words by removing the dithering and then applying maximal ratio combining and SIC in the same order used at the relay. We call this scheme the broadcast of repetition coding (BRC). We demonstrate that the achievable rate by the BRC scheme increases as the number of layers of the superposition coding increases and it achieves the capacity bounds of decode-forward when the number of layers grows to infinity. The design task of the BRC scheme is to optimize the power distribution over the added layers. This is obtained by solving first-order differential equations. We propose also a different two-layer scheme based on reverse order of SIC at the destination. This scheme is practical for implementation and achieves close-to-capacity rates. Our proposed schemes provide flexible alternatives to the cooperative coding schemes over relay channels.