arXiv subjects

Shanxiang Lyu

Publications and source records attributed to Shanxiang Lyu.

At least 19 recordsLinked to original sources

arXiv2026

Symplectic Barnes-Wall GKP Codes: Deterministic $O(N \log^2 N)$ Decoding and Logarithmic Rate Scaling

We construct an explicit symplectic realization of the Barnes-Wall lattice that yields a family of multimode Gottesman-Kitaev-Preskill (GKP) codes with encoding rate $R = \frac{1}{2}\log_2 N$ and a deterministic $O(N\log^2 N)$ bounded-distance decoder. The recursive generator $G_{m+1} = \bigl(\begin{smallmatrix} G_m & 0 \\ G_m & R_m G_m \end{smallmatrix}\bigr)$ with $R_m = I + Ω$ simultaneously guarantees symplectic integrality for valid quantum stabilizers and preserves the exact Barnes-Wall decoding structure through a chain of isometric isomorphisms. The code distance is constant at $Δ^2 = 1$ (in units of $2π$), representing an explicit distance--rate tradeoff in which logarithmic encoding efficiency is achieved at the cost of non-scaling protection. This construction provides a deterministic, space-efficient paradigm for GKP error correction in platforms supporting non-local modular connectivity.

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arXiv2026

Forging the Unforgeable: On the Feasibility of Counterfeit Watermarks in Backdoor-Based Dataset Ownership Verification

Backdoor watermarking has emerged as the predominant approach for protecting public datasets, enabling dataset ownership verification (DOV) through embedded triggers that induce predefined model behaviors. While existing works assume that DOV results can serve as reliable evidence for copyright infringement claims, we argue that this assumption is fundamentally flawed. In this paper, we expose critical vulnerabilities in current backdoor watermarking schemes by demonstrating that attackers can forge watermarks that are statistically indistinguishable from the original ones, thereby evading infringement allegations. Specifically, we propose a Forged Watermark Generator (FW-Gen), a lightweight variational autoencoder-based framework that generates forged watermarks preserving the statistical properties of original watermarks while exhibiting distinct visual patterns. Our attack operates under a realistic threat model where an accused attacker, upon receiving an infringement claim, extracts watermark information from the protected dataset and produces counterfeit evidence to refute the allegation. Extensive experiments across six backdoor watermarking methods, two benchmark datasets, and two model architectures demonstrate that forged watermarks achieve equivalent or superior statistical significance in hypothesis testing compared to original watermarks. These findings reveal that current DOV mechanisms are insufficient as standalone evidence for copyright disputes and call for more robust dataset protection schemes.

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arXiv2026

On the Optimal Integer-Forcing Precoding: A Geometric Perspective and a Polynomial-Time Algorithm

The joint optimization of the integer matrix $\mathbf{A}$ and the power scaling matrix $\mathbf{D}$ is central to achieving the capacity-approaching performance of Integer-Forcing (IF) precoding. This problem, however, is known to be NP-hard, presenting a fundamental computational bottleneck. In this paper, we reveal that the solution space of this problem admits a intrinsic geometric structure: it can be partitioned into a finite number of conical regions, each associated with a distinct full-rank integer matrix $\mathbf{A}$. Leveraging this decomposition, we transform the NP-hard problem into a search over these regions and propose the Multi-Cone Nested Stochastic Pattern Search (MCN-SPS) algorithm. Our main theoretical result is that MCN-SPS finds a near-optimal solution with a computational complexity of $\mathcal{O}\left(K^4\log K\log_2(r_0)\right)$, which is polynomial in the number of users $K$. Numerical simulations corroborate the theoretical analysis and demonstrate the algorithm's efficacy.

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arXiv2026

Decoding Golay Codes and their Related Lattices: A PAC Code Perspective

In this work, we propose a decoding method of Golay codes from the perspective of Polarization Adjusted Convolutional (PAC) codes. By invoking Forney's cubing construction of Golay codes and their generators $G^*(8,7)/(8,4)$, we found different construction methods of Golay codes from PAC codes, which result in an efficient parallel list decoding algorithm with near-maximum likelihood performance. Compared with existing methods, our method can get rid of index permutation and codeword puncturing. Using the new decoding method, some related lattices, such as Leech lattice $Λ_{24}$ and its principal sublattice $H_{24}$, can be also decoded efficiently.

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arXiv2025

Revisit the AWGN-goodness of Polar-like Lattices

This paper aims to provide a comprehensive introduction to lattices constructed based on polar-like codes and demonstrate some of their key properties, such as AWGN goodness. We first present polar lattices directly from the perspective of their generator matrix. Next, we discuss their connection with the recently proposed PAC (polarization adjusted convolutional) lattices and analyze the structural advantages of PAC lattices, through which the AWGN-goodness of PAC lattices can be conveniently demonstrated.

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arXiv2025

On the edge densities of normal, convex mosaics

In this paper we investigate the problem of finding the minimum edge density in families of convex, normal mosaics with unit volume cells in $n$-dimensional Euclidean space. In the first part of the paper we solve this problem for mosaics whose cells are Minkowski sums of cells of $1$ or $2$-dimensional mosaics. We show that while for $n=2$ this minimum is attained by a mosaic with regular hexagon cells, this is not true in any dimension $n > 2$, where the minimum is attained by a mosaic whose cells are Minkowski sums of pairwise orthogonal regular triangles, and possibly a segment. In the second part we investigate $3$-dimensional convex mosaics whose cells are translates of a given convex polyhedron, and show that within this family, mosaics with cubes as cells have minimum edge density. In addition, using our method, in the family of $3$-dimensional convex polyhedra whose translates tile the space, we find the unit volume polyhedra with minimal total edge length.

math.MG↗

arXiv2025

A Failure-Free and Efficient Discrete Laplace Distribution for Differential Privacy in MPC

In an MPC-protected distributed computation, although the use of MPC assures data privacy during computation, sensitive information may still be inferred by curious MPC participants from the computation output. This can be observed, for instance, in the inference attacks on either federated learning or a more standard statistical computation with distributed inputs. In this work, we address this output privacy issue by proposing a discrete and bounded Laplace-inspired perturbation mechanism along with a secure realization of this mechanism using MPC. The proposed mechanism strictly adheres to a zero failure probability, overcoming the limitation encountered on other existing bounded and discrete variants of Laplace perturbation. We provide analyses of the proposed differential privacy (DP) perturbation in terms of its privacy and utility. Additionally, we designed MPC protocols to implement this mechanism and presented performance benchmarks based on our experimental setup. The MPC realization of the proposed mechanism exhibits a complexity similar to the state-of-the-art discrete Gaussian mechanism, which can be considered an alternative with comparable efficiency while providing stronger differential privacy guarantee. Moreover, efficiency of the proposed scheme can be further enhanced by performing the noise generation offline while leaving the perturbation phase online.

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arXiv2025

Construction of Simultaneously Good Polar Codes and Polar Lattices

In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of such kind of lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.

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arXiv2025

On the quantization goodness of polar lattices

In this work, we prove that polar lattices, when tailored for lossy compression, are quantization-good in the sense that their normalized second moments approach $\frac{1}{2πe}$ as the dimension of lattices increases. It has been predicted by Zamir et al. \cite{ZamirQZ96} that the Entropy Coded Dithered Quantization (ECDQ) system using quantization-good lattices can achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous work \cite{LingQZ}, we established that polar lattices are indeed capable of attaining the same objective. It is reasonable to conjecture that polar lattices also demonstrate quantization goodness in the context of lossy compression. This study confirms this hypothesis.

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arXiv2024

Towards Quantum-Safe Federated Learning via Homomorphic Encryption: Learning with Gradients

This paper introduces a privacy-preserving distributed learning framework via private-key homomorphic encryption. Thanks to the randomness of the quantization of gradients, our learning with error (LWE) based encryption can eliminate the error terms, thus avoiding the issue of error expansion in conventional LWE-based homomorphic encryption. The proposed system allows a large number of learning participants to engage in neural network-based deep learning collaboratively over an honest-but-curious server, while ensuring the cryptographic security of participants' uploaded gradients.

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arXiv2023

FedReverse: Multiparty Reversible Deep Neural Network Watermarking

The proliferation of Deep Neural Networks (DNN) in commercial applications is expanding rapidly. Simultaneously, the increasing complexity and cost of training DNN models have intensified the urgency surrounding the protection of intellectual property associated with these trained models. In this regard, DNN watermarking has emerged as a crucial safeguarding technique. This paper presents FedReverse, a novel multiparty reversible watermarking approach for robust copyright protection while minimizing performance impact. Unlike existing methods, FedReverse enables collaborative watermark embedding from multiple parties after model training, ensuring individual copyright claims. In addition, FedReverse is reversible, enabling complete watermark removal with unanimous client consent. FedReverse demonstrates perfect covering, ensuring that observations of watermarked content do not reveal any information about the hidden watermark. Additionally, it showcases resistance against Known Original Attacks (KOA), making it highly challenging for attackers to forge watermarks or infer the key. This paper further evaluates FedReverse through comprehensive simulations involving Multi-layer Perceptron (MLP) and Convolutional Neural Networks (CNN) trained on the MNIST dataset. The simulations demonstrate FedReverse's robustness, reversibility, and minimal impact on model accuracy across varying embedding parameters and multiple client scenarios.

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arXiv2023

Content-Aware Quantization Index Modulation:Leveraging Data Statistics for Enhanced Image Watermarking

Image watermarking techniques have continuously evolved to address new challenges and incorporate advanced features. The advent of data-driven approaches has enabled the processing and analysis of large volumes of data, extracting valuable insights and patterns. In this paper, we propose two content-aware quantization index modulation (QIM) algorithms: Content-Aware QIM (CA-QIM) and Content-Aware Minimum Distortion QIM (CAMD-QIM). These algorithms aim to improve the embedding distortion of QIM-based watermarking schemes by considering the statistics of the cover signal vectors and messages. CA-QIM introduces a canonical labeling approach, where the closest coset to each cover vector is determined during the embedding process. An adjacency matrix is constructed to capture the relationships between the cover vectors and messages. CAMD-QIM extends the concept of minimum distortion (MD) principle to content-aware QIM. Instead of quantizing the carriers to lattice points, CAMD-QIM quantizes them to close points in the correct decoding region. Canonical labeling is also employed in CAMD-QIM to enhance its performance. Simulation results demonstrate the effectiveness of CA-QIM and CAMD-QIM in reducing embedding distortion compared to traditional QIM. The combination of canonical labeling and the minimum distortion principle proves to be powerful, minimizing the need for changes to most cover vectors/carriers. These content-aware QIM algorithms provide improved performance and robustness for watermarking applications.

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arXiv2023

Reversible Quantization Index Modulation for Static Deep Neural Network Watermarking

Static deep neural network (DNN) watermarking techniques typically employ irreversible methods to embed watermarks into the DNN model weights. However, this approach causes permanent damage to the watermarked model and fails to meet the requirements of integrity authentication. Reversible data hiding (RDH) methods offer a potential solution, but existing approaches suffer from weaknesses in terms of usability, capacity, and fidelity, hindering their practical adoption. In this paper, we propose a novel RDH-based static DNN watermarking scheme using quantization index modulation (QIM). Our scheme incorporates a novel approach based on a one-dimensional quantizer for watermark embedding. Furthermore, we design two schemes to address the challenges of integrity protection and legitimate authentication for DNNs. Through simulation results on training loss and classification accuracy, we demonstrate the feasibility and effectiveness of our proposed schemes, highlighting their superior adaptability compared to existing methods.

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arXiv2023

Lattice-Aided Extraction of Spread-Spectrum Hidden Data

This paper discusses the problem of extracting spread spectrum hidden data from the perspective of lattice decoding. Since the conventional blind extraction scheme multi-carrier iterative generalize least-squares (M-IGLS) and non-blind extraction scheme minimum mean square error (MMSE) suffer from performance degradation when the carriers lack sufficient orthogonality, we present two novel schemes from the viewpoint of lattice decoding, namely multi-carrier iterative successive interference cancellation (M-ISIC) and sphere decoding (SD). The better performance of M-ISIC and SD are confirmed by both theoretical justification and numerical simulations.

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arXiv2023

Lattice Codes for Lattice-Based PKE

Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation technique, can substitute the naive modulation in existing lattice-based PKEs to enjoy better correction performance. We begin by modeling the FrodoPKE protocol as a noisy point-to-point communication system, where the communication channel is similar to the additive white Gaussian noise (AWGN) channel. To employ lattice codes for this special channel that hinges on hypercube shaping, we propose an efficient labeling function that converts between binary information bits and lattice codewords. The parameter sets of FrodoPKE are improved towards either higher security levels or smaller ciphertext sizes. For example, the proposed Frodo-1344-E$_\text{8}$ has a 10-bit classical security gain over Frodo-1344.

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arXiv2023

Generalized Singleton Type Upper Bounds

In this paper, we give upper bounds on the sizes of $(d, L)$ list-decodable codes in the Hamming metric space from covering codes with the covering radius smaller than or equal to $d$. When the list size $L$ is $1$, this gives many new Singleton type upper bounds on the sizes of codes with a given minimum Hamming distance. These upper bounds are stronger than the Griesmer bound when the lengths of codes are large. Some upper bounds on the lengths of general small Singleton defect codes or list-decodable codes attaining the generalized Singleton bound are given. As an application of our generalized Singleton type upper bounds on Hamming metric error-correcting codes, the generalized Singleton type upper bounds on insertion-deletion codes are given, which are much stronger than the direct Singleton bound for insertion-deletion codes when the lengths are large. We also give upper bounds on the lengths of small dimension optimal locally recoverable codes and small dimension optimal $(r, δ)$ locally recoverable codes with any fixed given minimum distance.

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arXiv2022

Better Lattice Quantizers Constructed from Complex Integers

This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$. By explicitly linking their lattice bases to various forms of $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$ cosets, we discover the $\mathcal{E}_{m,2}^+$ lattices, based on which we report the best known lattice quantizers in dimensions $14$, $15$, $18$, $19$, $22$ and $23$. Fast quantization algorithms of the generalized checkerboard lattices are proposed to enable evaluating the normalized second moment (NSM) through Monte Carlo integration.

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arXiv2022

A Lattice-Based Embedding Method for Reversible Audio Watermarking

Reversible audio watermarking (RAW) is a promising technique in various applications. To simultaneously meet the demand of achieving high imperceptibility and robustness, this paper proposes a novel RAW scheme based on lattices. The scheme is referred to as Meet-in-the-Middle Embedding (MME), in which the lattice quantization errors are properly scaled and added back to the quantized host signals. Simulations show that MME excels in a wide range of metrics including signal-to-watermark ratio (SWR), objective difference grade (ODG), and bit error rate (BER).

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