Full Rate Network Coding via Nesting Modulation Constellations

Network coding is an effective method to improving relay efficiency, by reducing the number of transmissions required to deliver data from source(s) to destination(s). However, its performance may be greatly degraded by rate mismatch, which is seldom touched in previous works and remains a challenge. In this paper, we reinterpret network coding as a mapping of modulation constellation. On this basis, we extend the mapping to support full rate network coding (FRNC), enabling simultaneous use of different modulations by nesting the low level constellation as a subset of the high level constellation. When relay links have different qualities, the messages of different flows are combined via network coding in such a way that for each relay link, its desired message is transmitted at its own highest rate. The limit in constellation size is also addressed. Compared with the stateof-the-art solutions to rate mismatch, the proposed scheme achieves the full rate of all relay links on the broadcast channel.