Noisy network coding

A new coding scheme for multicasting multiple sources over a general noisy network is presented. The scheme naturally extends both network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover-El Gamal to general discrete memoryless and Gaussian networks. The scheme also recovers as special cases the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The key idea is to use block Markov message repetition coding and simultaneous decoding. Instead of sending multiple independent messages over several blocks and decoding them sequentially as in previous relaying schemes, the same message is sent multiple times using independent codebooks and the decoder performs joint typicality decoding on the received signals from all the blocks without explicitly decoding the compression indices. New results on semideterministic relay networks and Gaussian networks demonstrate the potential of noisy network coding as a robust and scalable scheme for communication over wireless networks.