Side Information Design in Zero-Error Coding for Computing

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.