A comparison of superposition coding schemes

There are two variants of superposition coding schemes. Cover's original superposition coding scheme has code clouds of identical shape, while Bergmans's superposition coding scheme has code clouds of independently generated shapes. These two schemes yield identical achievable rate regions in several scenarios, such as the capacity region for degraded broadcast channels. This paper shows that under optimal decoding, these two superposition coding schemes can result in different rate regions. In particular, it is shown that for the two-receiver broadcast channel, Cover's scheme achieves a larger rate region than Bergmans's scheme in general.