Abstract:We study finite-blocklength bounds for noisy permutation channels whose reachable output polytope may be lower-dimensional than the output simplex. Existing Gaussian achievability analyses focus on strictly positive full-rank square DMC transition matrices. The capacity result for arbitrary strictly positive DMCs is established through a weak converse, while available strong converse bounds in the lower-dimensional setting can scale with the dimension of the output simplex rather than with that of the reachable output polytope. On the achievability side, messages are placed on a simplex lattice in affine coordinates, and decoding is performed by projecting the empirical output distribution onto the reachable affine hull followed by Euclidean nearest-neighbor decoding. Writing $d$ for the affine dimension of the reachable output polytope, a geometric reduction converts decoding errors into $d(d+1)$ one-dimensional transfer events, yielding a refined Gaussian achievability lower bound based on averaged local coordinate variances and a relative volume ratio. On the converse side, a modified meta-converse, a Kullback--Leibler divergence covering, and a local binary-testing bound yield a strong converse whose blocklength-dependent term is $d\log\sqrt n$, up to a bounded additive remainder.
| Comments: | 27 pages, 2 figures |
| Subjects: | Information Theory (cs.IT) |
| Cite as: | arXiv:2605.25699 [cs.IT] |
| (or arXiv:2605.25699v1 [cs.IT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25699 arXiv-issued DOI via DataCite (pending registration) |
From: Lugaoze Feng [view email]
[v1]
Mon, 25 May 2026 10:57:35 UTC (121 KB)
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