A noisy network coding scheme for sending multiple sources over a general
noisy network is presented. For multi-source multicast networks, 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 and
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 scheme
involves message repetition coding, relay signal compression, and simultaneous
decoding. Unlike previous compress--forward schemes, where independent messages
are sent over multiple blocks, the same message is sent multiple times using
independent codebooks as in the network coding scheme for cyclic networks.
Furthermore, the relays do not use Wyner--Ziv binning as in previous
compress-forward schemes, and each decoder performs simultaneous joint
typicality decoding on the received signals from all the blocks without
explicitly decoding the compression indices. A consequence of this new scheme
is that achievability is proved simply and more generally without resorting to
time expansion to extend results for acyclic networks to networks with cycles.
The noisy network coding scheme is then extended to general multi-source
networks by combining it with decoding techniques for interference channels.
For the Gaussian multicast network, noisy network coding improves the
previously established gap to the cutset bound. We also demonstrate through two
popular AWGN network examples that noisy network coding can outperform
conventional compress-forward, amplify-forward, and hash-forward schemes.Comment: 33 pages, 4 figures, submitted to IEEE Transactions on Information
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