Rate-splitting in the presence of multiple receivers

In the presence of multiple senders, one of the simplest decoding strategies that can be employed by a receiver is successive decoding. In a successive decoding strategy, the receiver decodes the messages one at a time using the knowledge of the previously decoded messages as side information. Recently, there have been two separate attempts to construct codes for the interference channel using successive decoding based on the idea of rate-splitting. In this note, we highlight a difficulty that arises when a rate-splitting codebook is to be decoded by multiple receivers. The main issue is that the rates of the split codebook are tightly coupled to the properties of the channel to the receiver, thus, rates chosen for one of the receivers may not be decodable for the other. We illustrate this issue by scrutinizing two recent arguments claiming to achieve the Han-Kobayashi rate region for the interference channel using rate-splitting and successive decoding.