Spatially Coupled MacKay-Neal Codes on Symmetric Markov Noise: A Reduction to BMS Channels
Abstract
We prove a capacity criterion for fixed-degree spatially coupled MacKay--Neal codes on additive symmetric Markov noise. The noise bit flips with probability p, so the channel has one parameter and capacity 1−h2(p). For every integer ℓ≥4 with 3/ℓ<1−h2(p), matched finite-window BCJR and sum-product decoding admit code sequences, possibly depending on p, with actual rate tending to 3/ℓ and vanishing average information-bit error. The proof parallels the GEC-to-BEC argument: a conditional-entropy correction transfers BMS fixed-point positivity to the channel with memory. The correction also covers a capacity deficit of the effective BMS channel. A two-state posterior contraction supplies the additional derivative bound needed for threshold saturation. The result uses the cited BMS positivity theorem, with an analytic proof for ℓ≥33 and exact interval certificates for 4≤ℓ≤32.
Related
- 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
- MacKay-Neal Codes for DNA Channels under Block-MAP Decoding
- Exact Degrees of Freedom of Spatially Sparse MIMO Channels Without Prior CSI
- Finite BSC-Decomposition of Binary-Input Symmetric-Output Channels and Applications to Channel Simulation
BibTeX
@misc{kasai2026spatially,
title = {{Spatially Coupled MacKay-Neal Codes on Symmetric Markov Noise: A Reduction to BMS Channels}},
author = {Kenta Kasai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00227},
eprint = {2610.00227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00227},
}
RIS
TY - UNPB
TI - Spatially Coupled MacKay-Neal Codes on Symmetric Markov Noise: A Reduction to BMS Channels
AU - Kenta Kasai
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00227
UR - https://arxiv.org/abs/2610.00227
AB - We prove a capacity criterion for fixed-degree spatially coupled MacKay--Neal codes on additive symmetric Markov noise. The noise bit flips with probability p, so the channel has one parameter and capacity 1−h_2(p). For every integer ℓ≥4 with 3/ℓ<1−h_2(p), matched finite-window BCJR and sum-product decoding admit code sequences, possibly depending on p, with actual rate tending to 3/ℓ and vanishing average information-bit error. The proof parallels the GEC-to-BEC argument: a conditional-entropy correction transfers BMS fixed-point positivity to the channel with memory. The correction also covers a capacity deficit of the effective BMS channel. A two-state posterior contraction supplies the additional derivative bound needed for threshold saturation. The result uses the cited BMS positivity theorem, with an analytic proof for ℓ≥33 and exact interval certificates for 4≤ℓ≤32.
ER -