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 for integrity authentication. Reversible data hiding (RDH) methods offer a potential solution, but existing approaches suffer from limitations in usability, capacity, and fidelity, hindering their practical adoption. In this paper, we propose a secure static DNN watermarking scheme called Secure Difference Contraction (SDC). Our scheme utilizes a one-dimensional quantizer for watermark embedding and employs dithering to ensure key-dependent security, i.e., the watermark cannot be correctly extracted without the secret key used during embedding. Additionally, we design two schemes to address the challenges of integrity protection and legitimate authentication for DNNs. Simulation results on training loss and classification accuracy demonstrate the feasibility and effectiveness of our proposed methods, highlighting their advantages in capacity and fidelity over existing techniques.

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. The existence of such lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.

Federated learning faces challenges associated with privacy breaches, client communication efficiency, stragglers’ effect, and heterogeneity. To address these challenges, this paper reformulates the optimal client selection problem as a sparse optimization task, proposes a secure and efficient optimal client selection method for federated learning, named secure orthogonal matching pursuit federated learning (SecOMPFL). Therein, we first introduce a method to identify correlations in the local model parameters of participating clients, addressing the issue of duplicated client contributions highlighted in recent literature. Next, we establish a secure variant of the OMP algorithm in compressed sensing using secure multiparty computation and propose a novel secure aggregation protocol. This protocol enhances the global model’s convergence rate through sparse optimization techniques while maintaining privacy and security. It relies entirely on the local model parameters as inputs, minimizing client communication requirements. We also devise a client sampling strategy without requiring additional communication, resolving the bottleneck encountered by the optimal client selection policy. Finally, we introduce a strict yet inclusive straggler penalty strategy to minimize the impact of stragglers. Theoretical analysis confirms the security and convergence of SecOMPFL, highlighting its resilience to stragglers’ effect and systematic/statistical heterogeneity with high client communication efficiency. Numerical experiments were conducted to compare the convergence rate and client communication efficiency of SecOMPFL with those of FedAvg, FOLB, and BN2. These experiments used natural and synthetic with statistical heterogeneity datasets, considering varying numbers of clients and client sampling scales. The results demonstrate that SecOMPFL achieves a competitive convergence rate, with communication overhead 39.96% lower than that of FOLB and 28.44% lower than that of BN2. Furthermore, SecOMPFL shows good resilience to statistical heterogeneity.

In this paper, we propose three Griesmer type bounds for the minimum Hamming weight of complementary codes of linear codes. Infinite families of complementary codes meeting the three Griesmer type bounds are given to show these bounds are tight. The Griesmer type bounds proposed in this paper are significantly stronger than the classical Griesmer bound for linear codes. As a by-product, we construct some optimal few-weight codes and determine their weight distributions. As an application, Griesmer type bounds for the column distance of convolutional codes are presented. These Griesmer type bounds are stronger than the Singleton bound for convolutional codes.

Syndrome Trellis Code (STC) stands out as one of the nearly optimal steganographic coding methods to date. Its superior efficiency and performance have garnered significant attention. However, STC has a limitation: it struggles to handle unevenly distributed host signals and messages, preventing it from achieving the theoretical minimum distortion. To address this flaw, we introduce an enhanced STC scheme called Content-Aware STC (CA-STC). In our work, we propose modifying the codebook based on the statistical relationship between host signals and messages. This adjustment aims to reduce overall distortion. Additionally, we introduce a new parameter to strike a balance between complexity and embedding efficiency in the proposed method. Simulation results, including scenarios involving random data, demonstrate that our approach outperforms STC in terms of global distortion, effectively adapting to diverse scenarios. Code available: https://github.com/shx-lyu/CA-STC/.

The rising complexity and cost of training DNN models underscore the need for intellectual property protection. In this regard, DNN watermarking has emerged as a crucial safeguarding technique. This paper introduces FedReverse, a multiparty reversible watermarking method that ensures robust copyright protection and minimal performance impact. FedReverse is reversible, allowing collaborative watermark embedding post-training and enables complete removal with unanimous consent. It is resistant to Known Original Attacks (KOA), making watermark forgery and key inference difficult. Comprehensive simulations with MLP and CNN models on varying parameters show FedReverse’s robustness, reversibility, and minimal accuracy impact.

This paper aims to build a bridge between the probabilistic shaping and the geometric shaping for lattice codes from the perspective of polar lattices. We prove that when performing the lattice Gaussian shaping on polar lattices, a shaping lattice As which is good for the so-called discrete additive white Gaussian noise (AWGN) channel is constructed indeed, and the shaping process is equivalent to the modulo As operation within a multi-level decoding manner. To achieve the power-constraint AWGN channel capacity or the rate distortion bound of the i.i.d. Gaussian source, one classical approach is to construct two nested lattices where the fine lattice takes care of the Gaussian noise or the target distortion, and the coarse lattice is responsible for the boundary of the lattice codewords. Another approach is to construct a single lattice and then perform the lattice Gaussian shaping. The former approach falls into the category of geometric shaping, while the latter one is regarded as a type of probabilistic shaping. This work proposes a unified perspective of these two approaches, and provides new evidence on why they are both able to achieve the optimal performance of Gaussian channel coding and source coding problems.

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$\frac{1}{2\pi e}$as the dimension of lattices increases. It has been predicted by Zamir et al. [1] 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 [2], 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.

This paper introduces a privacy-preserving distributed learning framework via private-key homomorphic encryption. Using randomness in the quantization of gradients, our encryption replaces the Gaussian error term of Learning With Errors (LWE) with quantized gradients, thus reducing the error expansion speed in conventional LWE-based homomorphic en-cryption. The proposed system allows a large number of learning participants to engage in distributed learning collaboratively over an honest-but-curious server, while ensuring the cryptographic security of participants' uploaded gradients.

Existing reversible audio watermarking (RAW) techniques are often vulnerable to intentional or even unintentional attacks on the cover object. This paper proposes a robust RAW scheme based on lattices, which is referred to as Meet-in-the-Middle Embedding (MME). In MME, the lattice quantization errors are properly scaled and added back to the quantized host signals such that the receiver can estimate the cover. Scaling factor serves as a key factor to the reversibility of MME, whose feasible range is rigorously justified. Both theoretically and experimentally, we demonstrate the superiority of MME to improved quantization index modulation (IQIM) in terms of signal-to-watermark ratio (SWR) and generalized signal-to-noise ratio (GSNR). Moreover, simulations show that MME also outperforms other state-of-the-arts in SWR, objective difference grade (ODG), and bit error rate (BER).

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. Both schemes can be categorized as (key-aided) semi-blind watermarking. 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.

This paper delves into the challenges of spread spectrum (SS) watermarking extraction, considering both reference-free and referential extraction scenarios, within the framework of lattice decoding. The orthogonality of carriers plays a crucial role in the accuracy of extraction, impacting the bit error rate (BER). When carriers lack sufficient orthogonality, conventional reference-free extraction methods such as multi-carrier iterative generalized least-squares (M-IGLS) and referential extraction techniques like MMSE-based schemes encounter performance degradation, posing difficulties in accurately recovering hidden data at the receiver end. To address these challenges, we propose two novel SS watermarking extraction approaches by integrating precise lattice decoding algorithms. Firstly, we introduce the highly accurate yet computationally efficient successive interference cancellation (SIC) algorithm to augment M-IGLS, resulting in a new method termed multi-carrier iterative successive interference cancellation (M-ISIC). Secondly, we adapt the near-optimal sphere decoding (SD) technique for referential extraction in SS watermarking. Theoretical analysis and experimental simulations showcase that our proposed M-ISIC and SD methods outperform M-IGLS and MMSE-based detectors, particularly in scenarios where carrier orthogonality is limited, achieving lower BER. Our code is available athttps://github.com/shx-lyu/M_ISIC.

In this paper, we give many new Singleton type upper bounds on the sizes of codes with given minimum Hamming distances. 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 are presented. Our generalized Singleton type upper bounds have wide applications to symbol-pair codes, insertion-deletion codes and locally recoverable codes. The generalized Singleton type upper bounds on symbol-pair codes and insertion-deletion codes are much stronger than the direct Singleton bounds on symbol-pair codes and insertion-deletion codes when the lengths are large and the Hamming minimum distances are small. Upper bounds on the lengths of small dimension optimal locally recoverable codes and small dimension optimal$(r, \delta)$locally recoverable codes with any given minimum distance are also presented.

In this paper, we study low-complexity linear precoding for downlink massive multiple-input multiple-output (MIMO) systems, exploiting a statistical method. In sharp contrast to traditional linear precoding algorithms, our proposed efficient randomized iterative precoding algorithm (ERIPA) not only avoids costly matrix inversion but also considers the complexity reduction of matrix multiplication involved, thus enabling more efficient linear precoding. Additionally, ERIPA is demonstrated to have both exponentially fast and global convergence, making it adaptable to various practical scenarios of massive MIMO. We also investigate the convergence phenomenon of ERIPA in relation to the selection of the sampling distribution during random iterations. After that, the concept of conditional sampling is introduced to ERIPA such that significant system potential can be beneficially exploited in terms of both precoding performance and computational complexity. Finally, simulation results regarding the downlink massive MIMO are presented to confirm the superiorities of the proposed ERIPA.

Conventional Quantization Index Modulation (QIM) has been tailored for diverse data hiding applications, yet it lacks the ability to achieve minimal distortion in physical layer steganography. To address this, we introduce an enhanced QIM scheme, Content-Aware QIM (CA-QIM). By adapting the codebook to the probability distribution of embedded messages and host signals, CA-QIM excels at handling non-uniformly distributed messages, resulting in significantly reduced distortion. Our approach outperforms other QIM variants in terms of mean square error (MSE), peak signal-to-noise ratio (PSNR), and percentage residual difference (PRD), as demonstrated through simulation results. CA-QIM offers a promising solution for achieving improved perceptual transparency and robustness in steganography applications.

Quantization index modulation (QIM) is a popular data hiding paradigm due to its considerable performance advantages over spread spectrum techniques. Nevertheless, the random dithering procedure in QIM suffers from the synchronization and distortion issues. From the perspective of lattices, this work shows that using fixed optimized dithering is beneficial for achieving a smaller amount of distortion to the cover object. This can be translated into better Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) for the multimedia.

Due to the openness of wireless communication, information transmitted in the multiple access channel is vulnerable to eavesdropping by illegitimate users. Classic artificial noise-assisted schemes can improve security but are not suitable for power-constrained users. To address this problem, we propose a cross-time interference injection scheme in this paper, which improves security by introducing cross-time self-interference and inter-user interference, and does not require artificial noise. The proposed scheme exploits the properties of the Hadamard matrix and the wireless channels, so that the eavesdropping channel suffers from stronger interference than the legitimate channel. We analyze the security performance when both the legitimate receiver and the eavesdropper exploit the successive interference cancellation (SIC) scheme, including the secrecy sum rate, the secrecy capacity, and the secrecy outage probability. We further investigate the effect of the number of eavesdropper’s antennas, the number of legitimate users, and the number of time slots used by the scheme on the security performance, and obtain the corresponding relationship between these parameters when achieving a positive secrecy rate. Finally, simulation results corroborate our theoretical analysis.

One of the main problems of subspace coding is to determine the maximal size of a constant dimension subspace code with given parameters. In this paper, we show that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. We introduce a new class of subspace codes called mixed dimension/distance subspace codes. Using such codes, we present two constructions for large constant dimension subspace codes. The problem about the sizes of our constant dimension subspace codes is transformed into finding mixed dimension/distance subspace codes with large dimension distributions. The new constructed codes are the largest known for many sets of parameters. Our method gives at least 136 new lower bounds on the sizes of constant dimension subspace codes.

Abstract We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

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.

In this paper, the random iterative method is introduced to massive multiple-input multiple-output (MIMO) systems for the efficient downlink linear precoding. By adopting the random sampling into the traditional iterative methods, the matrix inversion within the linear precoding schemes can be approximated statistically, which not only achieves a faster exponential convergence with low complexity but also experiences a global convergence without suffering from the various convergence requirements. Specifically, based on the random iterative method, the randomized iterative precoding algorithm (RIPA) is firstly proposed and we show its approximation error decays exponentially and globally along with the number of iterations. Then, with respect to the derived convergence rate, the concept of conditional sampling is introduced, so that further optimization and enhancement are carried out to improve both the convergence and the efficiency of the randomized iterations. After that, based on the equivalent iteration transformation, the modified randomized iterative precoding algorithm (MRIPA) is presented, which achieves a better precoding performance with low-complexity for various scenarios of massive MIMO. Finally, simulation results based on downlink precoding in massive MIMO systems are given to show the system gains of RIPA and MRIPA in terms of performance and complexity.

Conventional hybrid precoding and combining based transceivers require a large number of high-resolution radio frequency (RF) phase shifters (PSs), which impose prohibitive hardware costs and power consumption. To address the above issue, both partially connected RF PSs and low-resolution PSs have been proposed. However, the performance limits of these low-cost designs have not been investigated theoretically. Furthermore, there is room for improvement in their spectral efficiency. To fill this knowledge gap, we derive the mean square error performance discrepancy between an optimal precoder/combiner and the hybrid analog-digital precoder/combiner under the constraint of 1-bit PSs relying on lattice theory. Then, by observing that this performance gap can be reduced by deactivating parts of the PSs whilst improving both the spectral and energy efficiency, we develop an adaptive RF PS connection network. To resolve the associated hybrid precoding and combining problems, we appropriately adapt Babai's algorithm from the lattice decoding literature. Our simulation results demonstrate the superiority of the proposed scheme both in terms of its spectral and energy efficiency.

In current vector perturbation (VP) precoding architecture, the optimum perturbation vector is found with a closest lattice vector search for a given query point. In this work, we show that the query point should be judiciously chosen such that the effective noise power is minimized. The reduced noise power results in a better error rate performance for VP. The crux in the design is to decode an integer-multiple of lattice point within a modulo lattice architecture, where the integer- multiple can be a prime or a product of primes. Simulations show that around 2 dBs' performance gain can be observed even in the small-scale systems.

In this paper, we continue our previous work on the reduction of algebraic lattices over imaginary quadratic fields for the special case when the lattice is spanned over a two dimensional basis. In particular, we show that the algebraic variant of Gauss's algorithm returns a basis that corresponds to the successive minima of the lattice in polynomial time if the chosen ring is Euclidean.

The compute-and-forward (C&F) protocol in quasi-static channels normally employs lattice codes based on the rational integers ℤ, the Gaussian integers ℤ[i], or the Eisenstein integers ℤ[ω], while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for C&F in block-fading channels without CSIT, which is referred to as ring C&F because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Owing to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic-integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional C&F based on the ℤ-lattices. By investigating the effect of the Diophantine approximation by algebraic conjugates, we prove that the degrees of freedom (DoFs) of the optimized computation rate are n/L, where n is the number of blocks and L is the number of users.

Bases in the complex field, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we examine the properties and reduction of such lattices. Focusing on algebraic Lenstra-Lenstra-Lovász (ALLL) reduction, we show that to satisfy Lovás condition requires the ring to be Euclidean. The proposed algorithm can be used to design network coding matrices in compute-and-forward (C & F).

Previous approaches to compute-and-forward (C&F) are mostly based on quantizing channel coefficients to integers. In this work, we investigate the C&F strategy over block fading channels using Construction A over rings, so as to allow better quantization for the channels. Advantages in decoding error probabilities and computation rates are demonstrated, and the construction is shown to outperform the C&F strategy over the integers Z.