arXiv subjects

Zhaienhe Zhou

Publications and source records attributed to Zhaienhe Zhou.

4 recordsLinked to original sources

arXiv2026

Incremental Directed Minimum Cut by Dynamizing Gabow's Algorithm

We give the first incremental algorithm for directed global minimum cut. Given a directed graph with $n$ vertices undergoing $m$ edge insertions, our deterministic algorithm explicitly maintains a global minimum cut or certifies that its value is at least $k$ in $O(km\log n)$ total update time. Prior work required either that $k\le2$ or that the graph is undirected. Our algorithm is a strict incremental extension of Gabow's state-of-the-art static algorithm (JCSS 1995), with no asymptotic loss in running time over the entire insertion sequence.

cs.DS↗

arXiv2026

Improved Decoding of Tanner Codes

In this paper, we present improved decoding algorithms for expander-based Tanner codes. We begin by developing a randomized linear-time decoding algorithm that, under the condition that $ δd_0 > 2 $, corrects up to $ αn $ errors for a Tanner code $ T(G, C_0) $, where $ G $ is a $ (c, d, α, δ) $-bipartite expander with $n$ left vertices, and $ C_0 \subseteq \mathbb{F}_2^d $ is a linear inner code with minimum distance $ d_0 $. This result improves upon the previous work of Shen, Shangguan, Ouyang and Cheng (IEEE TIT 2025), which required $ δd_0 > 3 $. We further derandomize the algorithm to obtain a deterministic linear-time decoding algorithm with the same decoding radius. Our algorithm improves upon the previous deterministic algorithm of Cheng et al.\ by achieving a decoding radius of $ αn $, compared with the previous radius of $ \frac{2α}{d_0(1 + 0.5cδ) }n$. Additionally, we investigate the size-expansion trade-off introduced by the recent work of Chen, Cheng, Li, and Ouyang (IEEE TIT 2023), and use it to provide new bounds on the minimum distance of Tanner codes. Specifically, we prove that the minimum distance of a Tanner code $T(G,C_0)$ is approximately $f_δ^{-1} \left( \frac{1}{d_0} \right) αn $, where $ f_δ(\cdot) $ is the Size-Expansion Function. As another application, we improve the decoding radius of our decoding algorithms from $αn$ to approximately $f_δ^{-1}\left(\frac{2}{d_0}\right)αn$. Finally, we extend Viderman's find-erasures-and-decode framework (ACM TOCT 2013) to general linear inner codes, obtaining a deterministic linear-time decoder for $δd_{0}>1.8$ when $d_0=3$, thus pushing below the $δd_0 > 2$ threshold of our general result.

cs.IT↗

arXiv2026

High-Rate Public-Key Pseudorandom Codes for Edit Errors

Pseudorandom codes (PRCs), introduced by Christ and Gunn (CRYPTO '2024), are error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings, while still being decodable by someone holding the key. They provide a natural primitive for robust and undetectable watermarking, particularly in applications to AI-generated content. Although recent works have obtained strong results for substitution errors, the edit-error setting remains much less understood, especially in the high-rate regime and over small alphabets. We study public-key pseudorandom codes against edit errors. First, we give a new reduction showing that binary zero-bit PRCs robust against a constant fraction of substitution errors can be transformed into binary zero-bit PRCs robust against edit errors. Consequently, under any assumption that yields zero-bit Hamming-robust PRCs, one also obtains zero-bit PRCs for edit channels, albeit only for the weaker class of sublinear polynomial edit channels, namely channels with edit error rate $1/n^γ$ for any constant $γ>0$. In the high-rate regime, we construct public-key PRCs with rate arbitrarily close to $1$ over sufficiently large constant alphabets, and with rate arbitrarily close to $1/2$ over the binary alphabet. Moreover, if we allow the alphabet size to be $\mathrm{poly}(λ)$, where $λ$ is the security parameter, then our public-key PRCs can attain the Singleton bound for insertion-deletion channels. Taken together, these results yield the first high-rate public-key binary PRC constructions for edit channels, under the same assumption that yields zero-bit Hamming-robust PRCs.

cs.CR↗

arXiv2025

Algorithms for Sparse LPN and LSPN Against Low-noise

We consider sparse variants of the classical Learning Parities with random Noise (LPN) problem. Our main contribution is a new algorithmic framework that provides learning algorithms against low-noise for both Learning Sparse Parities (LSPN) problem and sparse LPN problem. Different from previous approaches for LSPN and sparse LPN, this framework has a simple structure and runs in polynomial space. Let $n$ be the dimension, $k$ denote the sparsity, and $η$ be the noise rate. As a fundamental problem in computational learning theory, Learning Sparse Parities with Noise (LSPN) assumes the hidden parity is $k$-sparse. While a simple enumeration algorithm takes ${n \choose k}=O(n/k)^k$ time, previously known results stills need ${n \choose k/2} = Ω(n/k)^{k/2}$ time for any noise rate $η$. Our framework provides a LSPN algorithm runs in time $O(η\cdot n/k)^k$ for any noise rate $η$, which improves the state-of-the-art of LSPN whenever $η\in ( k/n,\sqrt{k/n})$. The sparse LPN problem is closely related to the classical problem of refuting random $k$-CSP and has been widely used in cryptography as the hardness assumption. Different from the standard LPN, it samples random $k$-sparse vectors. Because the number of $k$-sparse vectors is ${n \choose k} n^{k/2}$. However, much less is known about learning algorithms for constant $k$ like 3 and $m<n^{k/2}$ samples, except the Gaussian elimination algorithm of time $e^{ηn}$. Our framework provides a learning algorithm in $e^{O(η\cdot n^{\frac{δ+1}{2}})}$ time given $δ\in (0,1)$ and $m \approx n^{1+(1-δ)\cdot \frac{k-1}{2}}$ samples. This improves previous learning algorithms. For example, in the classical setting of $k=3$ and $m=n^{1.4}$, our algorithm would be faster than than previous approaches for any $η<n^{-0.7}$.

cs.CR↗