Fine asymptotics for approximate simulation of symmetric channels
Abstract
We study the approximate channel simulation problem in the normal approximation regime. Our starting point is the fact established by Cao et al.~\cite{Cao_channel_simulation}, that the minimal codebook size Mε*(W) for a fixed error tolerance ε>0 is closely related to the ε-smooth channel max-information, Imaxε(W). Using this, we refine earlier large-blocklength approximations to Mε*(W⊗ n) for discrete memoryless channels. Specifically, we provide tight third-order expansions for Gallager-symmetric channels and demonstrate that the third-order term is channel-dependent. As in corresponding channel coding expansions, we identify a substantial rate gap between singular and nonsingular channels. Notably, the direction of this gap is reversed relative to channel coding: The third-order term is −1/2log n for singular channels but O(loglog n) for nonsingular channels.
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BibTeX
@misc{lungu2026fine,
title = {{Fine asymptotics for approximate simulation of symmetric channels}},
author = {Valentinian Lungu and Aaron B. Wagner and Ioannis Kontoyiannis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15877},
eprint = {2610.15877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15877},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fine asymptotics for approximate simulation of symmetric channels
AU - Valentinian Lungu
AU - Aaron B. Wagner
AU - Ioannis Kontoyiannis
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15877
UR - https://arxiv.org/abs/2610.15877
AB - We study the approximate channel simulation problem in the normal approximation regime. Our starting point is the fact established by Cao et al.~\cite{Cao_channel_simulation}, that the minimal codebook size M_ε^*(W) for a fixed error tolerance ε>0 is closely related to the ε-smooth channel max-information, I_max^ε(W). Using this, we refine earlier large-blocklength approximations to M_ε^*(W^⊗ n) for discrete memoryless channels. Specifically, we provide tight third-order expansions for Gallager-symmetric channels and demonstrate that the third-order term is channel-dependent. As in corresponding channel coding expansions, we identify a substantial rate gap between singular and nonsingular channels. Notably, the direction of this gap is reversed relative to channel coding: The third-order term is −1/2log n for singular channels but O(loglog n) for nonsingular channels.
ER -