Linear Programming Bounds for Multi-level Unequal Protection Codes

Tomohiko Saito; Toshiyasu Matsushima; Shigeichi Hirasawa

doi:10.1109/SMC.2018.00496

Linear Programming Bounds for Multi-level Unequal Protection Codes

Tomohiko Saito, Toshiyasu Matsushima, Shigeichi Hirasawa

School of Fundamental Science and Engineering

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

Abstract

In coding theory, it is important to find upper bounds for the code size given a code length and minimum distance. The Hamming bounds and Linear Programming (LP) bounds were proposed in previous works. On the other hand, Masnick et al. proposed Unequal Error Protection (UEP) codes and modified Hamming bounds as upper bounds for the code size of UEP codes. In our previous work, we defined 2-level UEP codes as a subclass of UEP codes, and derived LP bounds for 2-level UEP codes. In this paper, we define multi-level UEP codes by extending 2-level UEP codes, and derive LP bounds for multi-level UEP codes. Moreover, we show that LP bounds for UEP codes are tighter upper bound than modified Hamming bounds.

Original language	English
Title of host publication	Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2917-2922
Number of pages	6
ISBN (Electronic)	9781538666500
DOIs	https://doi.org/10.1109/SMC.2018.00496
Publication status	Published - 2019 Jan 16
Event	2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018 - Miyazaki, Japan Duration: 2018 Oct 7 → 2018 Oct 10

Publication series

Name	Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018

Conference

Conference	2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018
Country/Territory	Japan
City	Miyazaki
Period	18/10/7 → 18/10/10

ASJC Scopus subject areas

Information Systems
Information Systems and Management
Health Informatics
Artificial Intelligence
Computer Networks and Communications
Human-Computer Interaction

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10.1109/SMC.2018.00496

Cite this

Saito, T., Matsushima, T., & Hirasawa, S. (2019). Linear Programming Bounds for Multi-level Unequal Protection Codes. In Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018 (pp. 2917-2922). [8616492] (Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SMC.2018.00496

Linear Programming Bounds for Multi-level Unequal Protection Codes. / Saito, Tomohiko; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2917-2922 8616492 (Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018).

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

Saito, T, Matsushima, T & Hirasawa, S 2019, Linear Programming Bounds for Multi-level Unequal Protection Codes. in Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018., 8616492, Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018, Institute of Electrical and Electronics Engineers Inc., pp. 2917-2922, 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018, Miyazaki, Japan, 18/10/7. https://doi.org/10.1109/SMC.2018.00496

Saito T, Matsushima T, Hirasawa S. Linear Programming Bounds for Multi-level Unequal Protection Codes. In Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2917-2922. 8616492. (Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018). https://doi.org/10.1109/SMC.2018.00496

Saito, Tomohiko ; Matsushima, Toshiyasu ; Hirasawa, Shigeichi. / Linear Programming Bounds for Multi-level Unequal Protection Codes. Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2917-2922 (Proceedings - 2018 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2018).

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abstract = "In coding theory, it is important to find upper bounds for the code size given a code length and minimum distance. The Hamming bounds and Linear Programming (LP) bounds were proposed in previous works. On the other hand, Masnick et al. proposed Unequal Error Protection (UEP) codes and modified Hamming bounds as upper bounds for the code size of UEP codes. In our previous work, we defined 2-level UEP codes as a subclass of UEP codes, and derived LP bounds for 2-level UEP codes. In this paper, we define multi-level UEP codes by extending 2-level UEP codes, and derive LP bounds for multi-level UEP codes. Moreover, we show that LP bounds for UEP codes are tighter upper bound than modified Hamming bounds.",

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Linear Programming Bounds for Multi-level Unequal Protection Codes

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