Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1
Fractional repetition (FR) codes are a class of distributed storage codes that replicate and distribute information data over several nodes for easy repair, as well as efficient reconstruction. In this paper, we propose three new constructions of FR codes based on relative difference sets (RDSs) wit...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-10-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/19/10/563 |
| _version_ | 1818033452085149696 |
|---|---|
| author | Young-Sik Kim Hosung Park Jong-Seon No |
| author_facet | Young-Sik Kim Hosung Park Jong-Seon No |
| author_sort | Young-Sik Kim |
| collection | DOAJ |
| description | Fractional repetition (FR) codes are a class of distributed storage codes that replicate and distribute information data over several nodes for easy repair, as well as efficient reconstruction. In this paper, we propose three new constructions of FR codes based on relative difference sets (RDSs) with λ = 1 . Specifically, we propose new ( q 2 - 1 , q , q ) FR codes using cyclic RDS with parameters ( q + 1 , q - 1 , q , 1 ) constructed from q-ary m-sequences of period q 2 - 1 for a prime power q, ( p 2 , p , p ) FR codes using non-cyclic RDS with parameters ( p , p , p , 1 ) for an odd prime p or p = 4 and ( 4 l , 2 l , 2 l ) FR codes using non-cyclic RDS with parameters ( 2 l , 2 l , 2 l , 1 ) constructed from the Galois ring for a positive integer l. They are differentiated from the existing FR codes with respect to the constructable code parameters. It turns out that the proposed FR codes are (near) optimal for some parameters in terms of the FR capacity bound. Especially, ( 8 , 3 , 3 ) and ( 9 , 3 , 3 ) FR codes are optimal, that is, they meet the FR capacity bound for all k. To support various code parameters, we modify the proposed ( q 2 - 1 , q , q ) FR codes using decimation by a factor of the code length q 2 - 1 , which also gives us new good FR codes. |
| first_indexed | 2024-12-10T06:23:29Z |
| format | Article |
| id | doaj.art-ba162644aa9a4de7b75181d5b09bc7ba |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T06:23:29Z |
| publishDate | 2017-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ba162644aa9a4de7b75181d5b09bc7ba2022-12-22T01:59:16ZengMDPI AGEntropy1099-43002017-10-01191056310.3390/e19100563e19100563Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1Young-Sik Kim0Hosung Park1Jong-Seon No2Department of Information and Communication Engineering, Chosun University, Gwangju 61452, KoreaSchool of Electronics and Computer Engineering, Chonnam National University, Gwangju 61186, KoreaDepartment of Electrical and Computer Engineering, Institute of New Media and Communications, Seoul National University, Seoul 08826, KoreaFractional repetition (FR) codes are a class of distributed storage codes that replicate and distribute information data over several nodes for easy repair, as well as efficient reconstruction. In this paper, we propose three new constructions of FR codes based on relative difference sets (RDSs) with λ = 1 . Specifically, we propose new ( q 2 - 1 , q , q ) FR codes using cyclic RDS with parameters ( q + 1 , q - 1 , q , 1 ) constructed from q-ary m-sequences of period q 2 - 1 for a prime power q, ( p 2 , p , p ) FR codes using non-cyclic RDS with parameters ( p , p , p , 1 ) for an odd prime p or p = 4 and ( 4 l , 2 l , 2 l ) FR codes using non-cyclic RDS with parameters ( 2 l , 2 l , 2 l , 1 ) constructed from the Galois ring for a positive integer l. They are differentiated from the existing FR codes with respect to the constructable code parameters. It turns out that the proposed FR codes are (near) optimal for some parameters in terms of the FR capacity bound. Especially, ( 8 , 3 , 3 ) and ( 9 , 3 , 3 ) FR codes are optimal, that is, they meet the FR capacity bound for all k. To support various code parameters, we modify the proposed ( q 2 - 1 , q , q ) FR codes using decimation by a factor of the code length q 2 - 1 , which also gives us new good FR codes.https://www.mdpi.com/1099-4300/19/10/563distributed storage systems (DSS)fractional repetition (FR) codesFR capacityminimum bandwidth regenerating (MBR) codesrelative difference sets (RDSs)q-ary m-sequences |
| spellingShingle | Young-Sik Kim Hosung Park Jong-Seon No Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1 Entropy distributed storage systems (DSS) fractional repetition (FR) codes FR capacity minimum bandwidth regenerating (MBR) codes relative difference sets (RDSs) q-ary m-sequences |
| title | Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1 |
| title_full | Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1 |
| title_fullStr | Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1 |
| title_full_unstemmed | Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1 |
| title_short | Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1 |
| title_sort | construction of new fractional repetition codes from relative difference sets with λ 1 |
| topic | distributed storage systems (DSS) fractional repetition (FR) codes FR capacity minimum bandwidth regenerating (MBR) codes relative difference sets (RDSs) q-ary m-sequences |
| url | https://www.mdpi.com/1099-4300/19/10/563 |
| work_keys_str_mv | AT youngsikkim constructionofnewfractionalrepetitioncodesfromrelativedifferencesetswithl1 AT hosungpark constructionofnewfractionalrepetitioncodesfromrelativedifferencesetswithl1 AT jongseonno constructionofnewfractionalrepetitioncodesfromrelativedifferencesetswithl1 |