Codes for Information Retrieval With Small Uncertainty

In a recent paper by Yaakobi and Bruck, the problem of information retrieval in associative memories has been considered. In an associative memory, each memory entry is associated to the neighboring entries. When searching information, a fixed number of input clues are given and the output set is formed by the entries associated to all the input clues. The maximum size of an output set is called the uncertainty of the associative memory. In this paper, we study the problem of information retrieval in associative memories with small uncertainty. In particular, we concentrate on the cases where the memory entries and their associations form a binary Hamming space or an infinite square grid. Particularly, we focus on minimizing the number of input clues needed to retrieve information with small uncertainty and present good constructions some of which are optimal, i.e., use the smallest possible number of clues.