An information inequality and evaluation of Marton's inner bound for binary input broadcast channels

TL;DR

This paper proves a new information inequality related to Marton's inner bound for binary input broadcast channels, showing that randomized time-division achieves the sum rate for all such channels.

Contribution

It generalizes a previous inequality to all binary input broadcast channels, confirming the optimality of randomized time-division strategies.

Findings

Randomized time-division achieves Marton's sum rate for all binary input broadcast channels.

The established inequality extends previous results from specific channels to all binary input cases.

The work provides theoretical validation for a simple strategy in complex broadcast channel scenarios.

Abstract

We establish an information inequality that is intimately connected to the evaluation of the sum rate given by Marton's inner bound for two receiver broadcast channels with a binary input alphabet. This generalizes a recent result where the inequality was established for a particular channel, the binary skew-symmetric broadcast channel. The inequality implies that randomized time-division strategy indeed achieves the sum rate of Marton's inner bound for all binary input broadcast channels.