Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2405.05845 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916240456417280 |
|---|---|
| author | Ramkumar, Vinayak Raviv, Netanel Tamo, Itzhak |
| author_facet | Ramkumar, Vinayak Raviv, Netanel Tamo, Itzhak |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Binary Covering Codes for Low-Access Computations Ramkumar, Vinayak Raviv, Netanel Tamo, Itzhak Information Theory 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. |
| title | Non-Binary Covering Codes for Low-Access Computations |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.05845 |