# A Regression Approach to Certain Information Transmission Problems

## TL;DR

This paper explores a regression-based approach to information transmission, demonstrating optimal channel output processing via conditional expectation and proposing a data-driven inference algorithm validated through experiments.

## Contribution

It introduces a regression-inspired framework for information transmission problems, including a data-driven algorithm and extensions to broader models.

## Key findings

- Optimal processing function is the conditional expectation.
- Proposed algorithm effectively solves the formulated problem.
- Extensions to general models are feasible.

## Abstract

A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual information. When the encoder and the decoder know the statistical channel model, it is found that the optimal channel output processing function is the conditional expectation operator, thus hinting a potential role of regression, a classical topic in machine learning, for this model. Without utilizing the statistical channel model, a problem formulation inspired by machine learning principles is established, with suitable performance metrics introduced. A data-driven inference algorithm is proposed to solve the problem, and the effectiveness of the algorithm is validated via numerical experiments. Extensions to more general information transmission models are also discussed.