A Comparison of Superposition Coding Schemes

TL;DR

This paper compares two variants of superposition coding schemes, showing that under optimal decoding, Cover's scheme can achieve higher rates than Bergmans's scheme for two-receiver broadcast channels.

Contribution

It demonstrates that the two superposition coding schemes differ in achievable rate regions under maximum likelihood decoding, highlighting the superiority of Cover's scheme in certain scenarios.

Findings

Cover's scheme achieves strictly larger rates than Bergmans's scheme for two-receiver broadcast channels.

Both schemes have identical achievable rate regions under some scenarios like degraded broadcast channels.

Optimal maximum likelihood decoding reveals differences not apparent in traditional analyses.

Abstract

There are two variants of superposition coding schemes. Cover's original superposition coding scheme has code clouds of the 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 the optimal maximum likelihood 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 superposition coding scheme can achieve rates strictly larger than Bergmans's scheme.