Non-Binary Covering Codes for Low-Access Computations (2405.05845v1)

Abstract: Given a real dataset and a computation family, we wish to encode and store the dataset in a distributed system so that any computation from the family can be performed by accessing a small number of nodes. In this work, we focus on the families of linear computations where the coefficients are restricted to a finite set of real values. For two-valued computations, a recent work presented a scheme that gives good feasible points on the access-redundancy tradeoff. This scheme is based on binary covering codes having a certain closure property. In a follow-up work, this scheme was extended to all finite coefficient sets, using a new additive-combinatorics notion called coefficient complexity. In the present paper, we explore non-binary covering codes and develop schemes that outperform the state-of-the-art for some coefficient sets. We provide a more general coefficient complexity definition and show its applicability to the access-redundancy tradeoff.