Improved Constructions of Skew-Tolerant Gray Codes

Gabriel Sac Himelfarb; Moshe Schwartz

doi:10.1109/TIT.2025.3592490

Improved Constructions of Skew-Tolerant Gray Codes

Gabriel Sac Himelfarb
, Moshe Schwartz

School of Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Skew-tolerant Gray codes are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over previous work. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete m-ary skew-tolerant Gray codes for every base m ≥ 3 .

Original language	English
Pages (from-to)	8017-8028
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	71
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2025.3592490
State	Published - 1 Jan 2025

Keywords

Gray codes
graph-compatible gray codes
skew tolerance

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2025.3592490

Cite this

@article{7cca359adc6e4f65b3d5f0c6005b8e5d,

title = "Improved Constructions of Skew-Tolerant Gray Codes",

abstract = "Skew-tolerant Gray codes are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over previous work. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete m-ary skew-tolerant Gray codes for every base m ≥ 3 .",

keywords = "Gray codes, graph-compatible gray codes, skew tolerance",

author = "\{Sac Himelfarb\}, Gabriel and Moshe Schwartz",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2025",

month = jan,

day = "1",

doi = "10.1109/TIT.2025.3592490",

language = "English",

volume = "71",

pages = "8017--8028",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers",

number = "10",

}

TY - JOUR

T1 - Improved Constructions of Skew-Tolerant Gray Codes

AU - Sac Himelfarb, Gabriel

AU - Schwartz, Moshe

PY - 2025/1/1

Y1 - 2025/1/1

N2 - Skew-tolerant Gray codes are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over previous work. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete m-ary skew-tolerant Gray codes for every base m ≥ 3 .

AB - Skew-tolerant Gray codes are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over previous work. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete m-ary skew-tolerant Gray codes for every base m ≥ 3 .

KW - Gray codes

KW - graph-compatible gray codes

KW - skew tolerance

UR - https://www.scopus.com/pages/publications/105011756171

U2 - 10.1109/TIT.2025.3592490

DO - 10.1109/TIT.2025.3592490

M3 - Article

AN - SCOPUS:105011756171

SN - 0018-9448

VL - 71

SP - 8017

EP - 8028

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 10

ER -

Improved Constructions of Skew-Tolerant Gray Codes

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this