Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles

@misc{singh2026data,
  title = {{Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles}},
  author = {Anamika Singh and Abhay Kumar Singh},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10989},
  eprint = {2609.10989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10989},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles
AU  - Anamika Singh
AU  - Abhay Kumar Singh
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.10989
UR  - https://arxiv.org/abs/2609.10989
AB  - 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.
ER  -