Absorbing sets of codes from finite geometries

Allison Beemer; Kathryn Haymaker; Christine A. Kelley

doi:10.1007/s12095-019-0353-6

Absorbing sets of codes from finite geometries

Allison Beemer, Kathryn Haymaker, Christine A. Kelley

Mathematics

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

Abstract

We examine the presence of absorbing sets, fully absorbing sets, and elementary absorbing sets in low-density parity-check (LDPC) codes arising from certain classes of finite geometries. In particular, we prove the parameters of the smallest absorbing sets for finite geometry codes using a tree-based argument. Moreover, we obtain the parameters of the smallest absorbing sets for a special class of codes whose graphs are d-left-regular with girth g = 6 or g = 8.

Original language	English (US)
Pages (from-to)	1115-1131
Number of pages	17
Journal	Cryptography and Communications
Volume	11
Issue number	5
DOIs	https://doi.org/10.1007/s12095-019-0353-6
State	Published - Sep 15 2019

Keywords

Absorbing sets
Finite geometry LDPC codes
Tree bounds

ASJC Scopus subject areas

Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s12095-019-0353-6

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AU - Kelley, Christine A.

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AB - We examine the presence of absorbing sets, fully absorbing sets, and elementary absorbing sets in low-density parity-check (LDPC) codes arising from certain classes of finite geometries. In particular, we prove the parameters of the smallest absorbing sets for finite geometry codes using a tree-based argument. Moreover, we obtain the parameters of the smallest absorbing sets for a special class of codes whose graphs are d-left-regular with girth g = 6 or g = 8.

KW - Absorbing sets

KW - Finite geometry LDPC codes

KW - Tree bounds

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JF - Cryptography and Communications

IS - 5

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Absorbing sets of codes from finite geometries

Abstract

Keywords

ASJC Scopus subject areas

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