# Side Information Design in Zero-Error Coding for Computing

## TL;DR

This paper studies how to design encoder side information to minimize communication rates in zero-error computing tasks.

## Contribution

The paper introduces two greedy algorithms for optimizing side information design in zero-error coding.

## Key findings

- A condition for computing the optimal rate R*(g) was derived for full-support PX,Y.
- Two greedy algorithms are proposed for the side information design problem.
- One of the algorithms runs in polynomial time.

## Abstract

We investigate the zero-error coding for computing problems with encoder side information. An encoder provides access to a source X and is furnished with side information g(Y). It communicates with a decoder that possesses side information Y and aims to retrieve f(X,Y) with zero probability of error, where f and g are assumed to be deterministic functions. In previous work, we determined a condition that yields an analytic expression for the optimal rate R*(g); in particular, it covers the case where PX,Y is full support. In this article, we review this result and study the side information design problem, which consists of finding the best trade-offs between the quality of the encoder’s side information g(Y) and R*(g). We construct two greedy algorithms that give an achievable set of points in the side information design problem, based on partition refining and coarsening. One of them runs in polynomial time.