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A finite-sample, distribution-free, probabilistic lower bound on mutual information.

Nathan D VanderKraats¹, Arunava Banerjee

¹Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA. ndv@cise.ufl.edu

Neural Computation

|April 16, 2011

Summary

This study introduces a novel, distribution-free lower bound for mutual information in binary input channels. The new method offers superior accuracy compared to existing techniques, enhancing communication channel analysis.

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Area of Science:

Information Theory
Communication Systems Engineering

Background:

Estimating mutual information is crucial for understanding communication channel capacity.
Existing methods, like Fano's inequality with discretization, can introduce inaccuracies for continuous variables.

Purpose of the Study:

To develop a novel, distribution-free probabilistic lower bound for mutual information in memoryless binary input channels.
To introduce an efficient algorithm for computing this bound and associated distribution functions.
To demonstrate the superiority of the proposed bound over existing methods.

Main Methods:

Utilizing the Dvoretzky-Kiefer-Wolfowitz inequality to establish a probabilistic lower bound.
Developing a quadratic time algorithm for computing the bound and class-conditional distribution functions.
Comparing the proposed bound against a Fano's inequality-based approach using discretization.

Main Results:

A new, distribution-free lower bound on mutual information for binary input channels was successfully derived.
An efficient quadratic time algorithm for computing the bound and distribution functions was presented.
The proposed bound demonstrated superior performance compared to the discretized Fano's inequality method.

Conclusions:

The novel probabilistic lower bound provides a more accurate and robust estimation of mutual information in binary input channels.
The developed algorithm offers computational efficiency for practical applications.
This work advances the analysis of communication channels by offering a superior alternative to discretization-based methods.