Non-Binary Covering Codes for Low-Access Computations
<|reference_start|>Non-Binary Covering Codes for Low-Access Computations: 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.<|reference_end|>
@article{ramkumar2024non-binary,
    title={Non-Binary Covering Codes for Low-Access Computations},
    author={Vinayak Ramkumar, Netanel Raviv, Itzhak Tamo},
    journal={arXiv preprint arXiv:2405.05845},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.05845},
    primaryClass={cs.IT math.IT}
}