Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.27805

Certified Adaptive List Decoding for Error-Correcting Codes

Jaeho Hwang·Byung-Sun Won·Uiwon Hwang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Maximum-likelihood (ML) decoding of linear block codes is NP-hard, so neural decoders are evaluated by how closely they approach it. We observe that proving a candidate optimal can be far easier than finding it, and build a decoder that does both. We cast decoding as a search over an absorbing-state discrete diffusion model, whose sequential commitment of coordinates turns generation into a tree, and run a probability beam search over it. A dual bound from a linear-programming relaxation and a distance-based test, both derived from the code, then certify per frame that the current candidate is the global ML solution; because both are theorems, certified frames incur no accuracy-computation trade-off. Across $15$ codes and five operating points we certify up to $99.9\%$ of frames, the two tests dividing the space as their derivations predict, one strong for sparse parity-check matrices and the other for codes with a large minimum distance. Certification also behaves as a per-frame reliability signal, with $96.7$-$100\%$ of all frame errors falling on uncertified frames. Against an exact ML reference at $5$ dB the decoder is within one standard deviation on three of the four codes where the reference is uncensored, and against four neural baselines it attains the best bit-error rate in $71$ of $75$ cells.

Explore related subjects

cs.ITcs.LGmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jaeho Hwang, Byung-Sun Won, Uiwon Hwang. 2026-10-20. Certified Adaptive List Decoding for Error-Correcting Codes. https://arxiv.org/abs/2610.27805

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

One-weight codes in the sum-rank metric

One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics - being equivalent to (direct sums of) simplex codes - the sum-rank metric presents a far more intricate landscape. In this work, we explore the geometry of one-weight sum-rank metric codes, focusing on three distinct classes. First, we introduce and classify \emph{constant rank-list} sum-rank codes, where each nonzero codeword has the same tuple of ranks, extending results from the rank-metric setting. Next, we investigate the more general \emph{constant rank-profile} codes, where, up to reordering, each nonzero codeword has the same tuple of ranks. Although a complete classification remains elusive, we present the first examples and partial structural results for this class. Finally, we consider one-weight codes that are also MSRD (Maximum Sum-Rank Distance) codes. For dimension two, constructions arise from partitions of scattered linear sets on projective lines. For dimension three, we connect their existence to that of special $2$-fold blocking sets in the projective plane, leading to new bounds and nonexistence results over certain fields.

cs.IT↗
arXiv2026

Insertion Correcting Capability for Quantum Deletion-Correcting Codes

It is conjectured that a quantum code $C$ corrects $t$ deletion errors if and only if $C$ corrects a total of $t$ insertion and deletion errors. Although this conjecture has been proved only under certain conditions, it has not been proved in general. In this paper, we prove this conjecture for general quantum codes. Specifically, we show that a quantum state after an insertion error is represented as a product state of the original multi-qudit system and the inserted quantum state. Then, we prove this conjecture by combining the previous results and this property. In addition, we define generalized insertion errors by removing the quantum channel requirement from insertion errors and present their properties.

cs.IT↗
arXiv2026

Simultaneous Reconstruction of Shuffled Histograms from a Retained Statistic: Exact leading coefficients for finite hypothesis families

Le Cam deficiency is the largest increase in Bayes risk caused by retaining a statistic, over all priors and decision problems with losses in $[0,1]$. We compute its exact leading term for finite hypothesis families in growing shuffle models. For a bounded correlated message bundle in an iid categorical background with an observed finite tag, the coefficient is a convex program over exposed faces with Gaussian-polynomial scores; its order is set by the first differing conditional factorial-moment degree. Tag-preserving kernels can be suboptimal, and an exact example has family coefficient $4/3$ times the largest pairwise coefficient. For a critical rare-event channel along $m+1$ consecutive compositions, retaining a distinguished-symbol count has loss $n^{-1/2}κφ(0)\mathcal V_m(μ)+o(n^{-1/2})$, where $μ=θλ$, $κ^2=χ^2(q\|p)/(1-θ)>0$, and $φ$ is the standard normal density. We evaluate $\mathcal V_2$ for all $μ>0$. For every $m\ge2$, the full-chain value $e^{-μ}(1-1/\sum_{k=0}^mμ^k)$ is exact if and only if $\sum_{k=2}^{m+1}μ^k\le2$; an explicit large-mean regime is attained by the endpoint pair. Exact-arithmetic computer-assisted certificates give the complete four-composition phase diagram. At $μ=\sqrt2$, the ratio to the largest pairwise coefficient is strictly below two for every finite window and tends to two as $m\to\infty$. A universal upper bound of two and Hypothesis P, which asserts that admissible vertex paths attain every window coefficient, remain open outside the proved regimes. The comparison principle is classical; the contributions are the model-specific scores, exact coefficients, and certificates.

cs.IT↗