Function-Correcting Codes for Symbol-Pair Read Channels

Function-correcting codes (FCCs) are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we develop the theory of FCCs over symbol-pair read channels. We introduce the notion of function-correcting sym...

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Bibliographic Details
Published in:IEEE transactions on information theory 2024-11, Vol.70 (11), p.7807-7819
Main Authors: Xia, Qingfeng, Liu, Hongwei, Chen, Bocong
Format: Article
Language:English
Subjects:
Codes
Function-correcting codes
lower bound
optimal redundancy
Receivers
Redundancy
symbol-pair read channels
Symbols
Termination of employment
Upper bound
Vectors
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Summary:Function-correcting codes (FCCs) are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we develop the theory of FCCs over symbol-pair read channels. We introduce the notion of function-correcting symbol-pair codes (FCSPCs) and aim to find their optimal redundancy. To this end, we introduce the notion of irregular-pair-distance codes and derive upper and lower bounds on the optimal redundancy in terms of the shortest length of the irregular-pair-distance codes. We then simplify these bounds and employ these general results to specific functions including pair-locally binary functions, pair weight functions and pair weight distribution functions. In addition, we provide some general constructions for FCSPCs. Lastly, by comparison with classical symbol-pair codes, we find that the theory of FCSPCs developed in our paper really reduces the redundancy under the condition that the receiver can recover certain attribute of the message.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2024.3451249