Distributed decode-forward for multicast

TLDR

The authors introduce a distributed decode‑forward coding scheme for multicasting over general relay networks, extending network coding and partial decode‑forward, and adaptable to broadcasting multiple messages. The scheme employs multicoding at the source, has relays recover an auxiliary index that carries partial message information, and forwards it using block Markov coding, building on Marton coding and partial decode‑forward. For an N‑node Gaussian multicast network, the scheme attains within 0.5 N bits of capacity, improving the best known capacity‑gap bounds.

Abstract

A new coding scheme for multicasting a message over a general relay network is presented that extends both network coding for graphical networks by Ahlswede, Cai, Li, and Yeung, and partial decode-forward for relay channels by Cover and El Gamal. For the N-node Gaussian multicast network, the scheme achieves within 0.5N bits from the capacity, improving upon the best known capacity gap results. The key idea is to use multicoding at the source as in Marton coding for broadcast channels. Instead of recovering a specific part of the message as in the original partial decode-forward scheme, a relay in the proposed distributed decode-forward scheme recovers an auxiliary index that implicitly carries some information about the message and forwards it in block Markov coding. This scheme can be adapted to broadcasting multiple messages over a general relay network, extending and refining a recent result by Kannan, Raja, and Viswanath.