Bounds on Mixed Codes with Finite Alphabets

Yonatan Yehezkeally; Haider Al Kim; Sven Puchinger; Antonia Wachter-Zeh

doi:10.1109/ITW55543.2023.10161655

Bounds on Mixed Codes with Finite Alphabets

Yonatan Yehezkeally, Haider Al Kim, Sven Puchinger, Antonia Wachter-Zeh

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Mixed codes, which are error-correcting codes in the Cartesian product of different-sized spaces, model degrading storage systems well. While such codes have previously been studied for their algebraic properties (e.g., existence of perfect codes) or in the case of unbounded alphabet sizes, we focus on the case of finite alphabets, and generalize the Gilbert-Varshamov, sphere-packing, Elias-Bassalygo, and first linear programming bounds to that setting. In the latter case, our proof is also the first for the non-symmetric mono-alphabetic q-ary case using Navon and Samorodnitsky's Fourier-analytic approach.

Original language	English
Title of host publication	2023 IEEE Information Theory Workshop, ITW 2023
Publisher	Institute of Electrical and Electronics Engineers
Pages	389-394
Number of pages	6
ISBN (Electronic)	9798350301496
DOIs	https://doi.org/10.1109/ITW55543.2023.10161655
State	Published - 1 Jan 2023
Externally published	Yes
Event	2023 IEEE Information Theory Workshop, ITW 2023 - Saint-Malo, France Duration: 23 Apr 2023 → 28 Apr 2023

Publication series

Name	2023 IEEE Information Theory Workshop, ITW 2023

Conference

Conference	2023 IEEE Information Theory Workshop, ITW 2023
Country/Territory	France
City	Saint-Malo
Period	23/04/23 → 28/04/23

ASJC Scopus subject areas

Artificial Intelligence
Computational Theory and Mathematics
Computer Networks and Communications
Signal Processing
Control and Optimization

Access to Document

10.1109/ITW55543.2023.10161655

Cite this

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title = "Bounds on Mixed Codes with Finite Alphabets",

abstract = "Mixed codes, which are error-correcting codes in the Cartesian product of different-sized spaces, model degrading storage systems well. While such codes have previously been studied for their algebraic properties (e.g., existence of perfect codes) or in the case of unbounded alphabet sizes, we focus on the case of finite alphabets, and generalize the Gilbert-Varshamov, sphere-packing, Elias-Bassalygo, and first linear programming bounds to that setting. In the latter case, our proof is also the first for the non-symmetric mono-alphabetic q-ary case using Navon and Samorodnitsky's Fourier-analytic approach.",

author = "Yonatan Yehezkeally and Kim, {Haider Al} and Sven Puchinger and Antonia Wachter-Zeh",

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doi = "10.1109/ITW55543.2023.10161655",

language = "English",

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Yehezkeally, Y, Kim, HA, Puchinger, S & Wachter-Zeh, A 2023, Bounds on Mixed Codes with Finite Alphabets. in 2023 IEEE Information Theory Workshop, ITW 2023. 2023 IEEE Information Theory Workshop, ITW 2023, Institute of Electrical and Electronics Engineers, pp. 389-394, 2023 IEEE Information Theory Workshop, ITW 2023, Saint-Malo, France, 23/04/23. https://doi.org/10.1109/ITW55543.2023.10161655

Bounds on Mixed Codes with Finite Alphabets. / Yehezkeally, Yonatan; Kim, Haider Al; Puchinger, Sven et al.
2023 IEEE Information Theory Workshop, ITW 2023. Institute of Electrical and Electronics Engineers, 2023. p. 389-394 (2023 IEEE Information Theory Workshop, ITW 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Bounds on Mixed Codes with Finite Alphabets

AU - Yehezkeally, Yonatan

AU - Kim, Haider Al

AU - Puchinger, Sven

AU - Wachter-Zeh, Antonia

PY - 2023/1/1

Y1 - 2023/1/1

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AB - Mixed codes, which are error-correcting codes in the Cartesian product of different-sized spaces, model degrading storage systems well. While such codes have previously been studied for their algebraic properties (e.g., existence of perfect codes) or in the case of unbounded alphabet sizes, we focus on the case of finite alphabets, and generalize the Gilbert-Varshamov, sphere-packing, Elias-Bassalygo, and first linear programming bounds to that setting. In the latter case, our proof is also the first for the non-symmetric mono-alphabetic q-ary case using Navon and Samorodnitsky's Fourier-analytic approach.

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T3 - 2023 IEEE Information Theory Workshop, ITW 2023

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BT - 2023 IEEE Information Theory Workshop, ITW 2023

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ER -

Bounds on Mixed Codes with Finite Alphabets

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