Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels

@misc{hareesh2026functioncorrecting,
  title = {{Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels}},
  author = {Hareesh K. and B. Sundar Rajan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09491},
  eprint = {2610.09491},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09491},
}

TY  - UNPB
TI  - Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels
AU  - Hareesh K.
AU  - B. Sundar Rajan
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09491
UR  - https://arxiv.org/abs/2610.09491
AB  - Function-correcting codes (FCCs) protect specified function evaluations of messages against errors while reducing the redundancy required for reliable communication. We study FCCs for symbol-pair read channels, motivated by high-density storage systems that read overlapping symbol pairs. Phase-shift keying (PSK) modulation is well-suited to such systems due to its bandwidth efficiency and noise robustness. While FCCs for symbol-pair read channels have been studied under the Hamming metric, the Lee metric is a more appropriate error model for q-ary PSK and, hence for q-ary symbol-pair read channels. We generalize the symbol-pair Lee distance, previously defined only over ℤ_4, to ℤ_q, q≥2, and introduce function-correcting symbol-pair Lee-distance codes (FCSPLCs) over ℤ_q, specializing to q=2^m, m≥1, for 2^m-ary PSK constellations. We investigate their redundancy requirements by introducing irregular-pair Lee-distance codes and relating the optimal redundancy of FCSPLCs to the shortest length of such codes. We derive Plotkin-type and Gilbert--Varshamov-type bounds on the optimal redundancy through lower and upper bounds on the shortest length of irregular-pair Lee-distance codes. For bijective functions, we obtain corresponding Plotkin-type and Gilbert--Varshamov-type bounds for classical Lee metric codes for symbol-pair read channels over ℤ_q, which, to the best of our knowledge, are the first such bounds for the Lee metric symbol-pair setting. We then specialize the FCSPLC framework to pair-locally bounded functions, the Pair-Lee weight function, and the Pair-Lee weight distribution function, giving explicit constructions and corresponding bounds on the optimal redundancy. Finally, for linear functions, we derive a Plotkin-type lower bound on the optimal redundancy.
ER  -