Improved Constructions and Lower Bounds for Maximally Recoverable Grid Codes

IF 2.6 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2026-06-01 Epub Date: 2026-04-20 DOI:10.1109/TIT.2026.3685533

Joshua Brakensiek;Manik Dhar;Sivakanth Gopi

{"title":"Improved Constructions and Lower Bounds for Maximally Recoverable Grid Codes","authors":"Joshua Brakensiek;Manik Dhar;Sivakanth Gopi","doi":"10.1109/TIT.2026.3685533","DOIUrl":null,"url":null,"abstract":"In this paper, we continue the study of Maximally Recoverable (MR) Grid Codes initiated by Gopalan et al. [SODA 2017]. More precisely, we study codes over an <inline-formula> <tex-math>$m \\times n$ </tex-math></inline-formula> grid topology with one parity check per row and column of the grid along with <inline-formula> <tex-math>$h \\ge 1$ </tex-math></inline-formula> global parity checks. Previous works have largely focused on the setting in which <inline-formula> <tex-math>$m = n$ </tex-math></inline-formula>, where explicit constructions require field size which is exponential in <inline-formula> <tex-math>$n$ </tex-math></inline-formula>. Motivated by practical applications, we consider the regime in which <inline-formula> <tex-math>$m,h$ </tex-math></inline-formula> are constants and <inline-formula> <tex-math>$n$ </tex-math></inline-formula> is growing. In this setting, we provide a number of new explicit constructions whose field size is polynomial in <inline-formula> <tex-math>$n$ </tex-math></inline-formula>. We further complement these results with new field size lower bounds.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3820-3829"},"PeriodicalIF":2.6000,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/11488385/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2026/4/20 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper, we continue the study of Maximally Recoverable (MR) Grid Codes initiated by Gopalan et al. [SODA 2017]. More precisely, we study codes over an

$m \times n$

grid topology with one parity check per row and column of the grid along with

$h \ge 1$

global parity checks. Previous works have largely focused on the setting in which

$m = n$

, where explicit constructions require field size which is exponential in

$n$

. Motivated by practical applications, we consider the regime in which

$m,h$

are constants and

$n$

is growing. In this setting, we provide a number of new explicit constructions whose field size is polynomial in

$n$

. We further complement these results with new field size lower bounds.

查看原文本刊更多论文

最大可恢复网格码的改进结构和下界

在本文中，我们继续研究由Gopalan等人[SODA 2017]发起的最大化可恢复（MR）网格代码。更准确地说，我们研究了$m \ * n$网格拓扑上的代码，网格的每行和列都有一次奇偶校验以及$h \ge 1$全局奇偶校验。以前的工作主要集中在$m = n$的设置上，其中显式结构需要在$n$中呈指数级增长的字段大小。在实际应用的激励下，我们考虑$m,h$是常数，$n$是递增的情况。在这种情况下，我们提供了一些新的显式结构，其字段大小是$n$的多项式。我们进一步用新的字段大小下界来补充这些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.