Function-Correcting Codes

Andreas Lenz; Rawad Bitar; Antonia Wachter-Zeh; Eitan Yaakobi

doi:10.1109/TIT.2023.3279768

Function-Correcting Codes

Andreas Lenz, Rawad Bitar, Antonia Wachter-Zeh, Eitan Yaakobi

Computer Science

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

1 Scopus citations

Abstract

In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes, which protect the whole message.

Original language	English
Pages (from-to)	5604-5618
Number of pages	15
Journal	IEEE Transactions on Information Theory
Volume	69
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2023.3279768
State	Published - 1 Sep 2023

Keywords

Forward error correction
error correction codes
information theory

ASJC Scopus subject areas

Information Systems
Library and Information Sciences
Computer Science Applications

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10.1109/TIT.2023.3279768

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title = "Function-Correcting Codes",

abstract = "In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes, which protect the whole message.",

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N2 - In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes, which protect the whole message.

AB - In this paper we study function-correcting codes, a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes, i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance codes and derive general upper and lower bounds on their optimal redundancy. Since these bounds heavily depend on the specific function, we provide simplified, suboptimal bounds that are easier to evaluate. We further employ our general results to specific functions of interest and compare our results to standard error-correcting codes, which protect the whole message.

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JF - IEEE Transactions on Information Theory

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Function-Correcting Codes

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Keywords

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