On Marton's Inner Bound for the General Broadcast Channel

TL;DR

This paper investigates Marton's coding scheme for the general broadcast channel, revealing its limitations, properties, and potential for improvement, thereby advancing understanding of capacity bounds.

Contribution

It demonstrates Marton's scheme is not always optimal, analyzes properties of its inner bound, and proposes a new coding scheme to potentially enlarge the achievable region.

Findings

Marton's scheme is suboptimal for some degraded channels

Properties of Marton's inner bound help narrow the search for capacity

A new coding scheme may achieve larger inner bounds

Abstract

We establish several new results on Marton's coding scheme and its corresponding inner bound on the capacity region of the general broadcast channel. We show that unlike the Gaussian case, Marton's coding scheme without superposition coding is not optimal in general even for a degraded broadcast channel with no common message. We then establish properties of Marton's inner bound that help restrict the search space for computing the sum-rate. Next, we show that the inner bound is optimal along certain directions. Finally, we propose a coding scheme that may lead to a larger inner bound.