Problem
Research questions and friction points this paper is trying to address.
symbol-pair errors
data protection
function-correcting codes
Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles
🤖 AI Summary
研究通过引入功能纠正符号对码并结合数据保护，解决了存储系统中相邻符号联合错误的问题，并给出了冗余度界限及构造方法。
📝 Abstract
In several storage systems, including DNA storage and flash memory, errors affect neighbouring symbols jointly, and the Hamming metric does not adequately capture such error patterns. The symbol-pair read channel, introduced by Cassuto and Blaum~\cite{cassuto2011codes}, addresses this by reading consecutive pairs of symbols rather than individual symbols. Motivated by this, we introduce function-correcting symbol-pair codes with data protection (FCSPC-DP), which guarantee reliable recovery of a desired function of the message while simultaneously protecting the message itself against symbol-pair errors. We derive bounds on the optimal redundancy of such codes and establish a relationship with joint-pair distance matrices. We also give explicit constructions of FCSPC-DP for locally pair-bounded functions and symbol-pair weight functions. We introduce the pair-separation constant of a function, the minimum symbol-pair distance between messages sharing a function value, and show that when it is sufficiently large, data protection requires no additional redundancy: the optimal redundancy coincides with that of the corresponding code without data protection. Considering the symbol-pair analogue of the $α$-distance graph, we introduce two code invariants, the generation profile and the disconnection threshold, and use them to characterise a code's protection properties. Relating the two metrics through these invariants yields upper and lower bounds on the symbol-pair threshold in terms of its Hamming counterpart, both of which are attained. We further extend the classical Plotkin and sphere-packing bounds to this setting.
Innovation
Methods, ideas, or system contributions that make the work stand out.
function-correcting symbol-pair codes
data protection
redundancy bounds
pair-separation constant
protection profiles
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