# Shannon Shakes Hands with Chernoff: Big Data Viewpoint On Channel Information Measures

## TL;DR

This paper reexamines Shannon, Renyi, and Chernoff information measures from a big data perspective using the ACE algorithm, revealing their similarities and proposing a conjecture about channel information.

## Contribution

It introduces a big data viewpoint to compare Shannon, Renyi, and Chernoff measures and proposes a conjecture on channel information depending solely on channel parameters.

## Key findings

- Shannon and Chernoff mutual information decompositions are nearly identical.
- Shannon and Chernoff measures effectively represent the same information.
- A conjecture that channel information is determined solely by channel parameters.

## Abstract

Shannon entropy is the most crucial foundation of Information Theory, which has been proven to be effective in many fields such as communications. Renyi entropy and Chernoff information are other two popular measures of information with wide applications. The mutual information is effective to measure the channel information for the fact that it reflects the relation between output variables and input variables. In this paper, we reexamine these channel information measures in big data viewpoint by means of ACE algorithm. The simulated results show us that decomposition results of Shannon and Chernoff mutual information with respect to channel parametersare almost the same. In this sense, Shannon shakes hands with Chernoff since they are different measures of the same information quantity. We also propose a conjecture that there is nature of channel information which is only decided by the channel parameters.