arXiv subjects

Xiaohu Tang

Publications and source records attributed to Xiaohu Tang.

At least 19 recordsLinked to original sources

arXiv2026

Convertible Polynomial Evaluation Codes in the Merge Regime: A Skew-Polynomial Framework

In this paper, we develop an algebraic framework for merge-regime convertible codes that works directly with the polynomial-evaluation structure of the underlying codes. We characterize the minimal skew polynomials associated with unions of conjugacy classes, establish an evaluation-compatible product rule, and derive a special Chinese Remainder Theorem (sCRT) tailored to these evaluation sets. Based on this machinery, we propose two conversion templates for skew polynomial evaluation codes (PECs). The first applies to distinct initial PECs, whose different evaluation sets naturally provide the moduli required by sCRT. The second treats identical initial PECs, for which distinct auxiliary evaluation sets and explicit algebraic compatibility conditions are introduced to preserve unchanged symbols and to generate written symbols from designated read symbols. When instantiated with the standard basis $1,x,\ldots,x^{k-1}$, both constructions yield merge conversions for linearized Reed--Solomon codes whose final codes are equivalent to linearized Reed--Solomon codes and achieve per-symbol access-optimal cost. The framework further specializes to the commutative ring $\mathbb{F}_q[x]$, yielding corresponding conversion constructions for ordinary PECs and recovering the known polynomial-form constructions for Reed--Solomon and Tamo--Barg codes as special cases. As a further application, to the best of our knowledge, this specialization gives the first merge-regime convertible construction with Gabidulin initial codes and a final code equivalent to a Gabidulin code, while attaining per-symbol optimal access under the symbol-access model considered in this paper.

cs.IT↗

arXiv2026

Lightweight Adaptive ReduNet via Hyperspherical Manifold Learning

In recent years, a white-box neural network called ReduNet has been proposed, which employs the maximal coding rate reduction (MCR$^2$) principle to transform raw data into low-dimensional discriminative features via a forward layer-wise construction process. Unlike traditional deep networks that rely on backpropagation, ReduNet explicitly derives the parameters of each layer from the features of its preceding layer, offering a mathematically interpretable paradigm. However, this layer-wise construction often requires a large number of layers for the MCR$^2$ objective to reach a stable value, which increases the parameter storage of the unfolded module. To address this issue, we propose LA-ReduNet, a lightweight adaptive architecture that refines the layer-wise update rule and enables discriminative feature representations to be obtained with substantially fewer unfolded layers. Specifically, LA-ReduNet employs hyperspherical manifold learning and adaptive step sizes, thereby reducing by an order of magnitude the number of layers required for the MCR$^2$ objective to reach a stable value. Simulation results demonstrate that, while maintaining comparable classification accuracy, LA-ReduNet requires significantly fewer layers for the MCR$^2$ objective to reach a stable value. Remarkably, under the considered experimental settings, LA-ReduNet requires only approximately $1/29$ of the parameter storage of the unfolded ReduNet module for the MCR$^2$ objective to reach a stable value.

cs.LG↗

arXiv2026

Convertible Codes: MSR-to-MSR Conversion with Optimal Access and Bandwidth

In this paper, we study convertible codes in the merge regime and focus on the minimum storage regenerating (MSR) setting, where both the initial codes and the final code admit optimal single-node repair. We propose explicit MSR-to-MSR conversion schemes and analyze their performance in terms of access cost and conversion bandwidth. We first construct convertible MSR codes in the irregular setting, where the $m$ initial codes may have different parameters, achieving optimal access cost. We further consider the practically important same-code setting, where all initial codewords are drawn from the same MSR code. By introducing a row-matching technique, we obtain constructions simultaneously achieving optimal access cost and conversion bandwidth in most parameter regimes.

cs.IT↗

arXiv2026

Secure Aggregation with Top-K Sparsification in Decentralized Federated Learning

Secure aggregation is a vital component for mitigating gradient leakage in federated learning, but its communication cost conventionally scales with the gradient dimension. This becomes prohibitive for large models and even more pronounced in decentralized federated learning with limited bandwidth and unreliable nodes. Top-K gradient sparsification is an effective approach to reduce communication by transmitting only a few entries of the full gradient, while maintaining competitive model accuracy. Nevertheless, the top-K entries selected by each user are unpredictable and vary across users, which poses a challenge for efficient sparse secure aggregation. This paper studies information-theoretic secure aggregation with top-K sparsification in decentralized federated learning under user dropouts and user collusion. We propose a communication-efficient sparse secure aggregation scheme that offloads dimension-dependent overhead to an offline phase and protects private gradients using random masks and permutations. Experimental results demonstrate that our scheme preserves accuracy comparable to full-gradient aggregation even with only 1% gradient sparsification, while substantially reducing the communication cost.

cs.IT↗

arXiv2026

The Capacity of Information-Theoretic Secure Aggregation in Federated Learning

Secure aggregation allows a server to aggregate users' local updates while preserving update privacy. Existing information-theoretic problems typically assume that correlated random keys are provided by a trusted third party (TTP) or generated via prescribed groupwise structures, while the communication cost for establishing such correlated keys is often ignored. Consequently, the fundamental limits under general key-distribution mechanisms remain unknown. In this paper, we study the $T$-colluding information-theoretic secure aggregation problem with $N$ users under a general two-phase framework consisting of a key distribution phase and an update aggregation phase. Unlike prior work, we model key distribution through user-to-user communication and allow arbitrary user-generated key-distribution mechanisms, eliminating TTP or prescribed structures. This enables a joint characterization of three resources: randomness for security, key-distribution communication, and aggregation communication. We completely characterize the capacity region among these three resources by constructing a novel secure aggregation scheme together with a matching information-theoretic converse. In particular, we develop an explicit deterministic capacity-achieving construction over any finite field of size at least $N$, whereas most existing schemes either rely on TTP or employ randomized or existential constructions over sufficiently large finite fields. We further show that the optimal performance can be achieved using only pairwise shared keys, enabling implementation via Diffie--Hellman key exchange. Compared with Google's seminal secure aggregation scheme, the proposed scheme requires fewer random masking keys while preserving the same aggregation communication overhead.

cs.IT↗

arXiv2026

Repurposing Backdoors for Good: Ephemeral Intrinsic Proofs for Verifiable Aggregation in Cross-silo Federated Learning

While Secure Aggregation (SA) protects update confidentiality in Cross-silo Federated Learning, it fails to guarantee aggregation integrity, allowing malicious servers to silently omit or tamper with updates. Existing verifiable aggregation schemes rely on heavyweight cryptography (e.g., ZKPs, HE), incurring computational costs that scale poorly with model size. In this paper, we propose a lightweight architecture that shifts from extrinsic cryptographic proofs to \textit{Intrinsic Proofs}. We repurpose backdoor injection to embed verification signals directly into model parameters. By harnessing Catastrophic Forgetting, these signals are robust for immediate verification yet ephemeral, naturally decaying to preserve final model utility. We design a randomized, single-verifier auditing framework compatible with SA, ensuring client anonymity and preventing signal collision without trusted third parties. Experiments on SVHN, CIFAR-10, and CIFAR-100 demonstrate high detection probabilities against malicious servers. Notably, our approach achieves over $1000\times$ speedup on ResNet-18 compared to cryptographic baselines, effectively scaling to large models.

cs.CR↗

arXiv2026

Secure Joint Source-Channel Coding for the AWGN Channel with Feedback: A Finite Blocklength Analysis

In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.

cs.IT↗

arXiv2025

Orthogonal Soft Pruning for Efficient Class Unlearning

Efficient and controllable data unlearning in federated learning remains challenging, due to the trade-off between forgetting and retention performance. Especially under non-independent and identically distributed (non-IID) settings, where deep feature entanglement exacerbates this dilemma. To address this challenge, we propose FedOrtho, a federated unlearning framework that combines orthogonalized deep convolutional kernels with an activation-driven controllable one-shot soft pruning (OSP) mechanism. FedOrtho enforces kernel orthogonality and local-global alignment to decouple feature representations and mitigate client drift. This structural independence enables precise one-shot pruning of forgetting-related kernels while preserving retained knowledge. FedOrtho achieves SOTA performance on CIFAR-10, CIFAR100 and TinyImageNet with ResNet and VGG frameworks, verifying that FedOrtho supports class-, client-, and sample-level unlearning with over 98% forgetting quality. It reduces computational and communication costs by 2-3 orders of magnitude in federated settings and achieves subsecond-level erasure in centralized scenarios while maintaining over 97% retention accuracy and mitigating membership inference risks.

cs.LG↗

arXiv2025

Efficient Repair of (k+2, k) Degraded Read Friendly MDS Array Codes With Sub-packetization 2

In this paper, we present two constructions of degraded read friendly (DRF) MDS array codes with two parity nodes and a sub-packetization level of 2 over small finite fields, applicable for any arbitrary code length. The first construction achieves the smallest repair bandwidth among all existing constructions with the same parameters, and is asymptotically optimal with respect to the lower bound on the average repair bandwidth characterized by Zhang et al. The second construction supports two repair mechanisms, depending on whether computation within the helper nodes is permitted or not during the node repair process, thereby optimizing either the repair bandwidth or the rebuilding access.

cs.IT↗

arXiv2025

Outer Channel of DNA-Based Data Storage: Capacity and Efficient Coding Schemes

In this paper, we consider the outer channel for DNA-based data storage. When transmitting over the outer channel, each DNA string is treated as a unit/symbol that would be either correctly received, or erased, or corrupted by uniformly distributed random symbol substitution errors, and all strings are randomly shuffled with each other. We first derive the capacity of the outer channel, which implies that the uniformly distributed random symbol substitution errors are only as harmful as the erasure errors (for infinite-length non-binary random linear codes with near maximum likelihood decoding). Next, we propose practically efficient coding schemes which encode the bits at the same position of different strings into a codeword. We compute the soft/hard information of each bit, which allows us to independently decode the bits within a codeword, leading to an independent decoding scheme. To improve the decoding performance, we measure the reliability of each string based on the independent decoding result, and perform a further step of decoding over the most reliable strings, leading to a joint decoding scheme. Simulations with low-density parity-check codes confirm that the joint decoding scheme can reduce the frame error rate by more than 3 orders of magnitude compared to the independent decoding scheme, and it can outperform the state-of-the-art decoding scheme in the literature across a wide range of parameter regions.

cs.IT↗

arXiv2025

Efficient Byzantine-Robust Privacy-Preserving Federated Learning via Dimension Compression

Federated Learning (FL) allows collaborative model training across distributed clients without sharing raw data, thus preserving privacy. However, the system remains vulnerable to privacy leakage from gradient updates and Byzantine attacks from malicious clients. Existing solutions face a critical trade-off among privacy preservation, Byzantine robustness, and computational efficiency. We propose a novel scheme that effectively balances these competing objectives by integrating homomorphic encryption with dimension compression based on the Johnson-Lindenstrauss transformation. Our approach employs a dual-server architecture that enables secure Byzantine defense in the ciphertext domain while dramatically reducing computational overhead through gradient compression. The dimension compression technique preserves the geometric relationships necessary for Byzantine defence while reducing computation complexity from $O(dn)$ to $O(kn)$ cryptographic operations, where $k \ll d$. Extensive experiments across diverse datasets demonstrate that our approach maintains model accuracy comparable to non-private FL while effectively defending against Byzantine clients comprising up to $40\%$ of the network.

cs.CR↗

arXiv2025

A Simple but Accurate Approximation for Multivariate Gaussian Rate-Distortion Function and Its Application in Maximal Coding Rate Reduction

The multivariate Gaussian rate-distortion (RD) function is crucial in various applications, such as digital communications, data storage, or neural networks. However, the complex form of the multivariate Gaussian RD function prevents its application in many neural network-based scenarios that rely on its analytical properties, for example, white-box neural networks, multi-device task-oriented communication, and semantic communication. This paper proposes a simple but accurate approximation for the multivariate Gaussian RD function. The upper and lower bounds on the approximation error (the difference between the approximate and the exact value) are derived, which indicate that for well-conditioned covariance matrices, the approximation error is small. In particular, when the condition number of the covariance matrix approaches 1, the approximation error approaches 0. In addition, based on the proposed approximation, a new classification algorithm called Adaptive Regularized ReduNet (AR-ReduNet) is derived by applying the approximation to ReduNet, which is a white-box classification network oriented from Maximal Coding Rate Reduction (MCR$^2$) principle. Simulation results indicate that AR-ReduNet achieves higher accuracy and more efficient optimization than ReduNet.

cs.IT↗

arXiv2025

A General Coding Framework for Adaptive Private Information Retrieval

The problem of $T$-colluding private information retrieval (PIR) enables the user to retrieve one out of $M$ files from a distributed storage system with $N$ servers without revealing anything about the index of the desired file to any group of up to $T$ colluding servers. In the considered storage system, the $M$ files are stored across the $N$ distributed servers in an $X$-secure $K$-coded manner such that any group of up to $X$ colluding servers learns nothing about the files; the storage overhead at each server is reduced by a factor of $\frac{1}{K}$ compared to the total size of the files; and the files can be reconstructed from any $K+X$ servers. However, in practical scenarios, when the user retrieves the desired file from the distributed system, some servers may respond to the user very slowly or not respond at all. These servers are referred to as \emph{stragglers}, and particularly their identities and numbers are unknown in advance and may change over time. This paper considers the adaptive PIR problem that can be capable of tolerating the presence of a varying number of stragglers. We propose a general coding method for designing adaptive PIR schemes by introducing the concept of a \emph{feasible PIR coding framework}. We demonstrate that any \emph{feasible PIR coding framework} over a finite field $\mathbb{F}_q$ with size $q$ can be used to construct an adaptive PIR scheme that achieves a retrieval rate of $1-\frac{K+X+T-1}{N-S}$ simultaneously for all numbers of stragglers $0\leq S\leq N-(K+X+T)$ over the same finite field. Additionally, we provide an implementation of the \emph{feasible PIR coding framework}, ensuring that the adaptive PIR scheme operates over any finite field $\mathbb{F}_q$ with size $q\geq N+\max\{K, N-(K+X+T-1)\}$.

cs.IT↗

arXiv2025

Locally Repairable Convertible Codes: Improved Lower Bound and General Construction

In this paper, we consider the convertible code with locally repairable property. We present an improved lower bound on access cost associated with $(r,\delta)$. Then, we provide a general construction of convertible codes with optimal access cost which shows that those codes can be with super-linear length or maximum repairable property. Additionally, employing the known locally repairable codes with super-linear length or maximum repairable property, we provide explicit constructions of convertible codes with super-linear length or maximum repairable property.

cs.IT↗

arXiv2025

A New Cooperative Repair Scheme with Small Finite Field for Distributed Storage Systems

In this paper, we consider the multiple failures in the distributed storage systems under the cooperative repair model. We introduce a new cooperative repair scheme for the (n,k,d,N) minimum storage regenerating (MSR) codes proposed by Ye and Barg (IEEE Transactions on Information Theory, vol. 64, no. 4, 2017), which is capable of repairing any h failed nodes by connecting any k \le d \le n - h helper nodes. Compared to prior cooperative repair schemes for (n,k,d,N) MSR codes, which require a finite field F_q with q \ge (d - k + 1)n, the proposed approach reduces the field size to q \ge n + 1.

cs.IT↗

arXiv2025

The Lee weight distributions of several classes of linear codes over $\mathbb{Z}_4$

Let $\mathbb{Z}_4$ denote the ring of integers modulo $4$. The Galois ring GR$(4,m)$, which consists of $4^m$ elements, represents the Galois extension of degree $m$ over $\mathbb{Z}_4$. The constructions of codes over $\mathbb{Z}_4$ have garnered significant interest in recent years. In this paper, building upon previous research, we utilize the defining-set approach to construct several classes of linear codes over $\mathbb{Z}_4$ by effectively using the properties of the trace function from GR$(4,m)$ to $\mathbb{Z}_4$. As a result, we have been able to obtain new linear codes over $\mathbb{Z}_4$ with good parameters and determine their Lee weight distributions. Upon comparison with the existing database of $\mathbb{Z}_4$ codes, our construction can yield novel linear codes, as well as linear codes that possess the best known minimum Lee distance.

cs.IT↗

arXiv2025

On $(\mathcal{L},\mathcal{P})$-Twisted Generalized Reed-Solomon Codes

Twisted generalized Reed-Solomon (TGRS) codes are an extension of the generalized Reed-Solomon (GRS) codes by adding specific twists, which attract much attention recently. This paper presents an in-depth and comprehensive investigation of the TGRS codes for the most general form by using a universal method. At first, we propose a more precise definition to describe TGRS codes, namely $(\mathcal{L},\mathcal{P})$-TGRS codes, and provide a concise necessary and sufficient condition for $(\mathcal{L},\mathcal{P})$-TGRS codes to be MDS, which extends the related results in the previous works. Secondly, we explicitly characterize the parity check matrices of $(\mathcal{L},\mathcal{P})$-TGRS codes, and provide a sufficient condition for $(\mathcal{L},\mathcal{P})$-TGRS codes to be self-dual. Finally, we conduct an in-depth study into the non-GRS property of $(\mathcal{L},\mathcal{P})$-TGRS codes via the Schur squares and the combinatorial techniques respectively. As a result, we obtain a large infinite families of non-GRS MDS codes.

cs.IT↗

arXiv2025

Several classes of linear codes with few weights derived from Weil sums

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with the defining sets given by the intersection, difference and union of two certain sets, where $t=3,4,5,6$ and $q$ is an odd prime power. By using Weil sums and Gauss sums, the parameters and weight distributions of these codes are determined completely. Moreover, three classes of optimal codes meeting the Griesmer bound are obtained, and computer experiments show that many (almost) optimal codes can be derived from our constructions.

cs.IT↗