Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs

Per Austrin; Petteri Kaski; Mikko Koivisto; Jesper Nederlof

doi:10.1109/ISIT.2016.7541316

Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference contribution › Scientific › vertaisarvioitu

1 Sitaatiot (Scopus)

Abstrakti

Two sets A, B ⊆ {0, 1}ⁿ form a Uniquely Decodable Code Pair (UDCP) if every pair a ⋯ A, b ⋯ B yields a distinct sum a+b, where the addition is over ℤⁿ. We show that every UDCP A, B, with |A| = 2^(1-ϵ)n and |B| = 2^βn, satisfies equation. For sufficiently small ϵ, this bound significantly improves previous bounds by Urbanke and Li [Information Theory Workshop ′98] and Ordentlich and Shayevitz [2014, arXiv:1412.8415], which upper bound β by 0.4921 and 0.4798, respectively, as ϵ approaches 0.

Alkuperäiskieli	Englanti
Otsikko	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Kustantaja	IEEE
Sivut	335-339
Sivumäärä	5
Vuosikerta	2016-August
ISBN (elektroninen)	9781509018062
DOI - pysyväislinkit	https://doi.org/10.1109/ISIT.2016.7541316
Tila	Julkaistu - 10 elok. 2016
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisuussa
Tapahtuma	IEEE International Symposium on Information Theory - Barcelona, Espanja Kesto: 10 heinäk. 2016 → 15 heinäk. 2016 http://www.isit2016.org/

Conference

Conference	IEEE International Symposium on Information Theory
Lyhennettä	ISIT
Maa/Alue	Espanja
Kaupunki	Barcelona
Ajanjakso	10/07/2016 → 15/07/2016
www-osoite	http://www.isit2016.org/

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10.1109/ISIT.2016.7541316

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@inproceedings{317840250ceb472785c4609e0a57002f,

title = "Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs",

abstract = "Two sets A, B ⊆ {0, 1}n form a Uniquely Decodable Code Pair (UDCP) if every pair a ⋯ A, b ⋯ B yields a distinct sum a+b, where the addition is over ℤn. We show that every UDCP A, B, with |A| = 2(1-ϵ)n and |B| = 2βn, satisfies equation. For sufficiently small ϵ, this bound significantly improves previous bounds by Urbanke and Li [Information Theory Workshop ′98] and Ordentlich and Shayevitz [2014, arXiv:1412.8415], which upper bound β by 0.4921 and 0.4798, respectively, as ϵ approaches 0.",

author = "Per Austrin and Petteri Kaski and Mikko Koivisto and Jesper Nederlof",

year = "2016",

month = aug,

day = "10",

doi = "10.1109/ISIT.2016.7541316",

language = "English",

volume = "2016-August",

pages = "335--339",

booktitle = "Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory",

publisher = "IEEE",

address = "United States",

note = "IEEE International Symposium on Information Theory, ISIT ; Conference date: 10-07-2016 Through 15-07-2016",

url = "http://www.isit2016.org/",

}

Austrin, P, Kaski, P, Koivisto, M & Nederlof, J 2016, Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs. julkaisussa Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Vuosikerta 2016-August, 7541316, IEEE, Sivut 335-339, IEEE International Symposium on Information Theory, Barcelona, Espanja, 10/07/2016. https://doi.org/10.1109/ISIT.2016.7541316

Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs. / Austrin, Per; Kaski, Petteri; Koivisto, Mikko et al.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Vuosikerta 2016-August IEEE, 2016. s. 335-339 7541316.

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference contribution › Scientific › vertaisarvioitu

TY - GEN

T1 - Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs

AU - Austrin, Per

AU - Kaski, Petteri

AU - Koivisto, Mikko

AU - Nederlof, Jesper

PY - 2016/8/10

Y1 - 2016/8/10

N2 - Two sets A, B ⊆ {0, 1}n form a Uniquely Decodable Code Pair (UDCP) if every pair a ⋯ A, b ⋯ B yields a distinct sum a+b, where the addition is over ℤn. We show that every UDCP A, B, with |A| = 2(1-ϵ)n and |B| = 2βn, satisfies equation. For sufficiently small ϵ, this bound significantly improves previous bounds by Urbanke and Li [Information Theory Workshop ′98] and Ordentlich and Shayevitz [2014, arXiv:1412.8415], which upper bound β by 0.4921 and 0.4798, respectively, as ϵ approaches 0.

AB - Two sets A, B ⊆ {0, 1}n form a Uniquely Decodable Code Pair (UDCP) if every pair a ⋯ A, b ⋯ B yields a distinct sum a+b, where the addition is over ℤn. We show that every UDCP A, B, with |A| = 2(1-ϵ)n and |B| = 2βn, satisfies equation. For sufficiently small ϵ, this bound significantly improves previous bounds by Urbanke and Li [Information Theory Workshop ′98] and Ordentlich and Shayevitz [2014, arXiv:1412.8415], which upper bound β by 0.4921 and 0.4798, respectively, as ϵ approaches 0.

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U2 - 10.1109/ISIT.2016.7541316

DO - 10.1109/ISIT.2016.7541316

M3 - Conference contribution

AN - SCOPUS:84986000922

VL - 2016-August

SP - 335

EP - 339

BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory

PB - IEEE

T2 - IEEE International Symposium on Information Theory

Y2 - 10 July 2016 through 15 July 2016

ER -

Sharper upper bounds for unbalanced Uniquely Decodable Code Pairs

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