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Finite BSC-Decomposition of Binary-Input Symmetric-Output Channels and Applications to Channel Simulation
Abstract
We propose a finite BSC-decomposition method for representing an arbitrary binary-input symmetric-output channel (BISOC) as a mixture of binary symmetric channels (BSCs) with at most ℓ+1 distinct crossover probabilities. We show that the weighted average capacity of the component BSCs exceeds the capacity of the original BISOC by at most (π2log e)/(48ℓ2)+O(ℓ−5/2) bits, and the leading term is asymptotically optimal in the worst case. Based on the finite BSC-decomposition, we design a channel simulation scheme for arbitrary BISOCs. Combined with efficient channel simulation algorithms for BSCs, our scheme achieves a communication rate with O((log n / n)2/3) redundancy over the capacity for simulating n copies of a BISOC.
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BibTeX
@misc{zhao2026finite,
title = {{Finite BSC-Decomposition of Binary-Input Symmetric-Output Channels and Applications to Channel Simulation}},
author = {Jianguo Zhao and Cheuk Ting Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25794},
eprint = {2610.25794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25794},
}
RIS
TY - UNPB
TI - Finite BSC-Decomposition of Binary-Input Symmetric-Output Channels and Applications to Channel Simulation
AU - Jianguo Zhao
AU - Cheuk Ting Li
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25794
UR - https://arxiv.org/abs/2610.25794
AB - We propose a finite BSC-decomposition method for representing an arbitrary binary-input symmetric-output channel (BISOC) as a mixture of binary symmetric channels (BSCs) with at most ℓ+1 distinct crossover probabilities. We show that the weighted average capacity of the component BSCs exceeds the capacity of the original BISOC by at most (π^2log e)/(48ℓ^2)+O(ℓ^−5/2) bits, and the leading term is asymptotically optimal in the worst case. Based on the finite BSC-decomposition, we design a channel simulation scheme for arbitrary BISOCs. Combined with efficient channel simulation algorithms for BSCs, our scheme achieves a communication rate with O((log n / n)^2/3) redundancy over the capacity for simulating n copies of a BISOC.
ER -