MacKay-Neal Codes for DNA Channels under Block-MAP Decoding
Abstract
We prove achievability below the symmetric information rate (SIR) under block maximum a posteriori (MAP) decoding for a fixed-degree MacKay-Neal (MN) socket ensemble on the quaternary insertion-deletion-substitution channel used to model DNA reads. For every integer ℓ≥4, the (ℓ,3,3) socket ensemble, with one transmitted bit fixed and an independent uniform known offset, has limiting rate r⋆=6/ℓ bits per stored nucleotide. If the joint SIR Jt of a fixed number t of reads under independent, uniformly distributed input nucleotides exceeds r⋆, the ensemble-average full extended-word block error is O(1/n), and deterministic graph-offset sequences attain the same limiting rate and message-average error bound. This result concerns the discrete rate family 6/ℓ, not arbitrary rates approaching a given SIR. The channel permits arbitrarily many insertions and unbounded drift, with no alignment supplied to the receiver. The proof combines established MN parity and distance estimates with a strict arbitrary-candidate-list bound and a list construction that accounts for hidden output boundaries.
Related
- Spatially Coupled MacKay-Neal Codes on Symmetric Markov Noise: A Reduction to BMS Channels
- MacKay-Neal Codes Achieve Capacity under MAP Decoding
- Spatially Coupled MacKay-Neal Codes Achieve Capacity on BMS Channels at Fixed Degrees
- Spatially Coupled MacKay-Neal/Hsu-Anastasopoulos CSS Codes Achieve the Quantum-Erasure Hashing Bound by Seeded BP Decoding
- Log Density Spectrum Based Decoding of Polar Codes for Channels with Strong Phase Noise
BibTeX
@misc{kasai2026mackayneal,
title = {{MacKay-Neal Codes for DNA Channels under Block-MAP Decoding}},
author = {Kenta Kasai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38440},
eprint = {2610.38440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38440},
}
RIS
TY - UNPB
TI - MacKay-Neal Codes for DNA Channels under Block-MAP Decoding
AU - Kenta Kasai
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38440
UR - https://arxiv.org/abs/2610.38440
AB - We prove achievability below the symmetric information rate (SIR) under block maximum a posteriori (MAP) decoding for a fixed-degree MacKay-Neal (MN) socket ensemble on the quaternary insertion-deletion-substitution channel used to model DNA reads. For every integer ℓ≥4, the (ℓ,3,3) socket ensemble, with one transmitted bit fixed and an independent uniform known offset, has limiting rate r_⋆=6/ℓ bits per stored nucleotide. If the joint SIR J_t of a fixed number t of reads under independent, uniformly distributed input nucleotides exceeds r_⋆, the ensemble-average full extended-word block error is O(1/n), and deterministic graph-offset sequences attain the same limiting rate and message-average error bound. This result concerns the discrete rate family 6/ℓ, not arbitrary rates approaching a given SIR. The channel permits arbitrarily many insertions and unbounded drift, with no alignment supplied to the receiver. The proof combines established MN parity and distance estimates with a strict arbitrary-candidate-list bound and a list construction that accounts for hidden output boundaries.
ER -