# Joint secrecy over the K-Transmitter Multiple Access Channel

## TL;DR

This paper characterizes the achievable secure communication rates over a K-transmitter multiple access channel with an external eavesdropper, introducing new techniques for joint secrecy constraints.

## Contribution

It establishes the joint secrecy achievable rate region using novel generalizations of entropy bounds and efficient Fourier-Motzkin elimination methods.

## Key findings

- Derived the joint secrecy rate region for K-transmitter MACs.
- Introduced a generalized entropy bound for codewords with partial information.
- Developed an efficient Fourier-Motzkin elimination technique.

## Abstract

This paper studies the problem of secure communication over a K-transmitter multiple access channel in the presence of an external eavesdropper, subject to a joint secrecy constraint (i.e., information leakage rate from the collection of K messages to an eavesdropper is made vanishing). As a result, we establish the joint secrecy achievable rate region. To this end, our results build upon two techniques in addition to the standard information-theoretic methods. The first is a generalization of Chia-El Gamal's lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with properties of mutual information, leads to an efficient Fourier-Motzkin elimination. These two approaches could also be of independent interests in other contexts.