A note on outer bounds for broadcast channel

TL;DR

This paper simplifies the understanding of the New-Jersey outer bound for broadcast channels by proving its equivalence to a more computable region and showing it matches the UV-outerbound when private information is absent.

Contribution

It demonstrates the equivalence of the New-Jersey outer bound to a simpler computable region and its coincidence with the UV-outerbound under certain conditions.

Findings

New-Jersey outer bound is equivalent to a simpler computable region.

In absence of private information, the bound matches the UV-outerbound.

Provides a clearer understanding of outer bounds for broadcast channels.

Abstract

In this note we establish two facts concerning the so-called {\em New-Jersey} outer bound. We show that this outer bound is equivalent to a much simpler {\em computable} region; and secondly we show that in the absence of private information this bound is exactly same as the $UV$-outerbound.