# Capacity of Generalized Discrete-Memoryless Push-to-Talk Two-Way Channels

## TL;DR

This paper extends Shannon's push-to-talk two-way channel model to include full-duplex and noisy reception, deriving the capacity region and demonstrating its properties under certain symmetry conditions.

## Contribution

It introduces a generalized model of push-to-talk channels with full-duplex capability and characterizes its capacity region, which was not previously known.

## Key findings

- Capacity region is the convex hull of at most 4 rate pairs.
- Shannon's inner bound is tight under the symmetry property.
- Examples illustrate different shapes of the capacity region.

## Abstract

In this report, we generalize Shannon's push-to-talk two-way channel (PTT-TWC) by allowing reliable full-duplex transmission as well as noisy reception in the half-duplex (PTT) mode. Viewing a PTT-TWC as two state-dependent one-way channels, we introduce a channel symmetry property pertaining to the one-way channels. Shannon's TWC capacity inner bound is shown to be tight for the generalized model under this symmetry property. We also analytically derive the capacity region, which is shown to be the convex hull of (at most) 4 rate pairs. Examples that illustrate different shapes of the capacity region are given, and efficient transmission schemes are discussed via the examples.