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.

中文翻译：

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计算零错误编码中的辅助信息设计

我们研究了用于编码器辅助信息计算问题的零错误编码。编码器提供对源X的访问并配备辅助信息g(Y)。它与拥有辅助信息 Y 的解码器通信，旨在以零错误概率检索 f(X,Y)，其中 f 和 g 被假定为确定性函数。在之前的工作中，我们确定了一个条件，可以产生最佳速率 R*(g) 的解析表达式；特别是，它涵盖了 PX,Y 完全支持的情况。在本文中，我们回顾了这一结果并研究了辅助信息设计问题，其中包括找到编码器辅助信息 g(Y) 和 R*(g) 质量之间的最佳权衡。我们构建了两种贪婪算法，基于分区细化和粗化，给出辅助信息设计问题中可实现的点集。其中之一在多项式时间内运行。