Reviewerly/exHarmony huggingface dataset:
Exponents in smoothing the max-relative entropy and of randomness extraction against quantum side information

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award.The smooth max-relative entropy is a basic tool in quantum information theory and cryptography. In this paper, we derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy. We then apply this result to the problem of privacy amplification against quantum side information and obtain an upper bound for the exponent of the decreasing of the insecurity, measured using either purified distance or relative entropy. Our upper bound complements the earlier lower bound established by Hayashi, and the two bounds match when the rate of randomness extraction is above a critical value. Thus, for the case of high rate, we have determined the exact security exponent. Following this, we give examples and show that in the low-rate case, neither the upper bound nor the lower bound is tight in general.Lastly, we investigate the asymptotics of equivocation and its exponent under the security measure using the sandwiched Rényi divergence of order between 1 and 2, which has not been addressed previously in the quantum setting.
On Zero-Error Capacity of "One-Edge" Binary Channels with Two Memories

In this paper, we study the zero-error capacity of binary channels with two memories. Among all 11 categories of "one-edge" channels, we solve 10 of them and give a lower and an upper bound on the capacity of the remaining one.
Quantum codes construction from skew polycyclic codes

This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> -polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of "MDS (Maximum Distance Separable)" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.
Universal Randomized Guessing Subject to Distortion

Consider the problem of guessing a sequence subject to a distortion constraint. Specifically, assume the following game between Alice and Bob: Alice has a sequence x of length n. Bob wishes to guess x, yet he is satisfied with finding any sequence $\hat x$ which is within a given distortion D from x. Thus, he successively submits queries to Alice, until receiving an affirmative answer, stating that his guess was within the required distortion. Finding guessing strategies which minimize the number of guesses and analyzing its properties has applications in information security, source and channel coding. Guessing subject to a distortion constraint is especially useful when considering biometrically-secured systems, where the "password" which protects the data is not a single, fixed vector but rather a ball of feature vectors centered at some x, and any feature vector within the ball results in acceptance. We formally define the guessing problem under distortion in four different setups: memoryless sources, guessing through a noisy channel, sources with memory, and individual sequences. We suggest a randomized guessing strategy which is asymptotically optimal for all setups and is five–fold universal, as it is independent of the source statistics, the channel, the moment to be optimized, the distortion measure and the distortion level.
Non-standard linear recurring sequence subgroups and automorphisms of irreducible cyclic codes

Let ${{\mathcal{U}}_n}$ be the multiplicative group of order n in the splitting field ${{\mathbb{F}}_{{q^m}}}$ of x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> − 1 over a finite field ${{\mathbb{F}}_q}$. Any map of the form x → cx <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> with $c \in {{\mathcal{U}}_n}$ and t = q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sup> , 0 ≤ i < m, is ${{\mathbb{F}}_q}$-linear on ${{\mathbb{F}}_{{q^m}}}$ and fixes ${{\mathcal{U}}_n}$ set-wise; maps of this type will be called standard. Occasionally there are other, non-standard ${{\mathbb{F}}_q}$-linear maps on ${{\mathbb{F}}_{{q^m}}}$ fixing ${{\mathcal{U}}_n}$ set-wise, and in that case we say that the pair (n, q) is non-standard. We show that an irreducible cyclic code of length n over ${{\mathbb{F}}_q}$ has “extra” permutation automorphisms (others than the standard permutations generated by the cyclic shift and the Frobenius mapping that every such code has) precisely when the pair (n, q) is non-standard; we refer to such irreducible cyclic codes as non-standard or NSIC-codes. In addition, we relate these concepts to that of a non-standard linear recurring sequence subgroup as investigated in a sequence of papers by Brison and Nogueira. We present several families of NSIC-codes, and two constructions called “lifting” and “extension” to create new NSIC-codes from existing ones. We show that all NSIC-codes of dimension two can be obtained in this way, thus completing the classification for this case started by Brison and Nogueira.
Coding with Cyclic PAM and Vector Quantization for the RLWE/MLWE Channel

In some lattice-based cryptosystems, the encryption and decryption processes can be interpreted as a noisy communication channel. In this work, we focus on cryptosystems based on the ring learning with errors (RLWE) and module learning with errors (MLWE) problems, e.g. Kyber. We provide new coding schemes for the communication channel involved in these cryptosystems. For encoding we use an error-correction code (ECC) along with modulo Q pulse amplitude modulation (PAM) (for some fixed small prime power Q), and vector dequantization. For decoding we perform vector quantization followed by hard/soft decision decoding (HDD/SDD) for the ECC. This construction provides remarkable reduction in the decryption failure rate (DFR), compared to some earlier proposed coding schemes for the same bitrate. For example, in Kyber encryption scheme, we reduce the DFR from 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−174</sup> (uncoded) to 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1325</sup> (using HDD) or 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1414</sup> (using SDD).
Chain rules for quantum channels

Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if the same channel is applied to both inputs then the divergence cannot increase. Based on direct matrix analysis methods, we derive several Rényi divergence chain rules for channels in the quantum setting. Our results simplify and in some cases generalise previous derivations in the literature.
A Mathematical Framework to Characterize the Dependency Structures in Multimodal Learning with Minimax Principle

Multimodal learning is an increasingly important research topic. Exploiting conditional dependency across multiple modalities has been shown useful for estimating of the multimodal joint distribution, especially when the number of training samples is insufficient. However, it is difficult to theoretically characterize such conditional dependency structure. To address this issue, we establish a mathematical framework and formulate the estimation problem based on the minimax principle. Then, we propose an estimator which is close to the analytical solution of the problem under a mild assumption on the sample size. Moreover, the proposed estimator is a linear combination of the learning results from the true dependency structure and the conditional one. The combining coefficient is related to three aspects: the number of training samples, the fitness of the conditional dependency structure, and the cardinality of each modality. Finally, numerical simulations are provided to verify our theoretical results that the proposed estimator is close to the optimal solution of the formulated problem.
Speeding Up AIFV-m Dynamic Programs by m–1 Orders of Magnitude

AIFV-m coding is a method for constructing lossless codes for memoryless sources that provide better worst-case redundancy than Huffman codes. It achieves this by using m code trees instead of one and also by allowing some bounded delay in the decoding process. The process for constructing optimal AIFV-m on n source symbols is based on multiple calls to a local optimization subroutine. Local optimization was originally performed using Integer Linear Programming, which was later replaced by an O(mn <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m+1</sup> )-time Dynamic Program. The running time for m = 2 was further improved to O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), but the speedup technique was not applicable to m > 2. This paper introduces a new dynamic programming approach that yields a general O(mn <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+2</sup> )-time algorithm.
Distributed Attribute-based Private Access Control

In attribute-based access control, users with specific verified attributes will gain access to some particular data. Concerning the privacy of the users’ attributes, we study the problem of distributed attribute-based private access control (DAPAC) with multiple authorities. Each authority will learn and verify only one of the attributes.To investigate its fundamental limits, we introduce an information-theoretic DAPAC framework, with $N \in {\mathbb{N}},N \geq 2$, replicated non-colluding servers (authorities), and some users. Each user has an attribute vector ${{\mathbf{v}}^{\ast}} = \left( {v_1^{\ast}, \ldots,v_N^{\ast}} \right)$ of dimension N and is eligible to retrieve a message ${W^{{{\text{v}}^{\ast}}}}$, available on all servers. Each server n ∈ [N] can only observe and verify the n’th attribute of a user. In response, it sends a function of its authorized messages to the user. The system must satisfy the following conditions: (1) Correctness: the user with attribute vector v <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> can retrieve his intended message ${W^{{{\text{v}}^{\ast}}}}$ from the servers’ responses, (2) Data Secrecy: the user will not learn anything about the other messages, (3) Attribute Privacy: each Server n learns nothing beyond attribute n of the user. The capacity of the DAPAC is defined as the ratio of the file size and the aggregated size of the responses, maximized over all feasible schemes. We obtain a lower bound on the capacity of this problem by proposing an achievable algorithm with rate $\frac{1}{{2K}}$, where K is the size of the alphabet of each attribute.
Stabilizer codes and Symbol-Pair Metric are Related

In [3], the relation between stabilizer codes and binary codes over the symplectic inner product and symplectic weight was established. In the current work, we present a relation between the symplectic weight and symbol-pair weight and use it to construct stabilizer codes of length n from binary codes of length n defined over the symbol-pair metric and Euclidean inner product. In particular, we use certain length n binary LCD codes over the symbol-pair metric to obtain stabilizer codes of length n. We also present the Modified CSS construction which outperforms the CSS construction in the given setup.
Statistical Minimax Lower Bounds for Transfer Learning in Linear Binary Classification

Modern machine learning models require a large amount of labeled data for training to perform well. A recently emerging paradigm for reducing the reliance of large model training on massive labeled data is to take advantage of abundantly available labeled data from a related source task to boost the performance of the model in a desired target task where there may not be a lot of data available. This approach, which is called transfer learning, has been applied successfully in many application domains. However, despite the fact that many transfer learning algorithms have been developed, the fundamental understanding of "when" and "to what extent" transfer learning can reduce sample complexity is still limited. In this work, we take a step towards foundational understanding of transfer learning by focusing on binary classification with linear models and Gaussian features and develop statistical minimax lower bounds in terms of the number of source and target samples and an appropriate notion of similarity between source and target tasks. To derive this bound, we reduce the transfer learning problem to hypothesis testing via constructing a packing set of source and target parameters by exploiting Gilbert-Varshamov bound, which in turn leads to a lower bound on sample complexity. We also evaluate our theoretical results by experiments on real data sets.
Smoothed InfoNCE: Breaking the log N Curse without Overshooting

We revisit the log N bound of InfoNCE (N is the sample size), which sets an upper limit on the estimator, thereby often causing the estimator to return an under-estimate of the mutual information. We show that the existing solution of excluding data samples from the reference set causes an equally debilitating problem, namely, it causes the estimator to overshoot, often with no sign of convergence, thereby leading to an overestimate of the mutual information. We mitigate both issues by introducing a classifier to smooth out the data labels and propose a new mutual information neural estimator called Smoothed InfoNCE. We conduct experiments on high-dimensional Gaussian data and demonstrate that the proposed model can break the log N curse without suffering from overshooting.
Improved Adversarial Robustness by Hardened Prediction

We find a way to harden the decision of a neural network. Combining such a hardening effect with another adversarial training method would further improve its adversarial robustness. By suppressing the logit corresponding to the class that the model has highest confidence during training, the model is encouraged to make harder predictions. This significantly improves a model’s robustness against gradient-based adversarial attacks. The simplicity of our method makes it very easy to be deployed on existing adversarial training schemes with almost no computational overhead. The experimental results show that a model trained with TRADES benefits from hardening. It shows a greatly improved robustness against the PGD attack while retaining similar performance against decision-based attacks. How the hardening effect effectively defends the models from gradient-based attacks is worth further investigation.
An Upper Bound of the Set Size of Perfect Sequences with Optimal Cross-correlation

The set of perfect sequences with optimal cross-correlation has applications in communication and radar systems. Many different constructions, which are called optimal sets of perfect sequences according to Sarwate bound, have been studied in the literature. However, Song et al. and Zhang et al. recently showed that the set size of these constructions can be improved, since the term related to size vanishes for perfect sequences in Sarwate bound. Until now, we don’t know whether the set size of these constructions is optimal, though they are all called optimal sets. We studied the problem of the set size of perfect sequences with optimal cross-correlation, and showed that the set size must be upper bounded by the length of the perfect sequences in this paper.
Communication with Unreliable Entanglement Assistance

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance.
Sequential Quantum Channel Discrimination

We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that, by using adaptive strategies for the discrimination problem, both types of error probabilities decrease to zero exponentially fast and the rates are characterized by the measured relative entropy between two quantum channels. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. We also characterize the error exponents in the discrimination problem if non-adaptive strategies are used.
Joint Coding for Discrete Sources and Finite-State Noiseless Channels

We propose a joint coding scheme using multiple code tables to efficiently transmit a sequence of messages of a discrete memoryless source (DMS) through a finite-state noiseless channel with unequal costs of code letters, which includes a noiseless (d, k)-constrained channel as a particular case. This paper presents a methodology for code design based on two methods. The first method, integer programming, is used to optimize a prefix-free code at each channel state when codeword costs are unequal and vary with each state. The second method is an iterative optimization that minimizes the average cost of the joint coding scheme using multiple code tables. The proposed coding scheme achieves the optimal average cost in the class of joint coding schemes using multiple code tables of prefix-free codes for a given pair of DMS and finite-state channel.
A New Coding Scheme for Matrix-Vector Multiplication via Universal Decodable Matrices

In this paper, we study the straggler mitigation via coded computing in distributed computations. In particular, we consider the coded matrix-vector multiplication where the matrix is sparse and coding may break the sparsity of the matrix. We construct a class of sparse universal decodable matrices (UDMs) for coded computing. In simulations, it shows that the proposed code possesses better sparsity than other schemes with randomly generated sparse matrices. Besides, the proposed code performs well in numerical stability.
Three New Constructions of 5-valued Spectrum Functions with Totally Disjoint Spectra Duals

A function $f:\mathbb{F}_2^n \to {\mathbb{F}_2}$ is called a 5-valued spectrum function if the Walsh transform W <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</inf> takes the values $0, \pm {2^{\frac{{n + {s_1}}}{2}}}, \pm {2^{\frac{{n + {s_2}}}{2}}}$ for some different non-negative integers s <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> ,i = 1,2 with n + s <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> even. In [IEEE Transactions on Information Theory, 67 (2), 2021], by spectral method, Hodžić et al. characterized the so-called basic 5-valued spectrum functions f whose duals $f_{[i]}^{\ast}(i = 1,2)$ are totally disjoint spectra functions. For a special case that the corresponding functions $\overline {f_{[i]}^{\ast}} (i = 1,2)$ are basic plateaued functions, Hodžić et al. gave a construction of basic 5-valued spectrum functions. They left open problems to provide constructions of 5-valued spectrum functions f such that f are basic and the corresponding functions $\overline {f_{[i]}^{\ast}} (i = 1,2)$ are non-basic plateaued functions, or f are non-basic. In this paper, we provide three new constructions of 5-valued spectrum functions f with totally disjoint spectra duals $f_{[i]}^{\ast}(i = 1,2)$, including the case that f are basic and the corresponding functions $\overline {f_{[i]}^{\ast}} (i = 1,2)$ are non-basic plateaued functions, and the case that f are non-basic, which provide answers to the problems proposed by Hodžić et al.. Since non-basic 5-valued spectrum functions are EA-inequivalent to basic ones, two constructions in this paper can produce 5-valued spectrum functions which are EA-inequivalent to ones in [IEEE Transactions on Information Theory, 67 (2), 2021].
Perfect Subset Privacy for Data Sharing and Learning

As the size of modern datasets grows, it becomes increasingly common to delegate computational tasks to service providers. Doing so, however, raises privacy concerns. Privatization schemes which enable learning algorithms to be executed unaltered have been recently popularized under the name instance encoding, aiming to circumvent the large overhead of traditional cryptographic primitives. In this work we take an information/coding-theoretic approach towards instance encoding. Specifically, recent works have shown that general-purpose data sharing can be achieved without leaking information about any individual datapoint (marginally), while maintaining high mutual information with the dataset in its entirety. We first extend this framework to capture the entire privacy-utility tradeoff, accounting for the privatization of any subset of the dataset, and provide a coding scheme for doing so. Second, we introduce a necessary algebraic condition for applying unaltered learning algorithms on encrypted data, termed signal preservation, and present an additional scheme which guarantees it. Both schemes achieve almost maximal mutual information with the entire dataset, under appropriate assumptions. The construction relies on some classic ideas such as Shamir secret sharing, as well as a novel technique called random Hadamard coding.
Spacecraft Components Detection Based on a Lightweight YOLOv3 Model

With the rapid development of the global aerospace industry, vision-based space target detection has become one of the hotspots of space technology. Traditional detection algorithms are mainly based on handcrafted features which have poor generalization performance. While algorithms based on deep learning, especially CNN models, can be assumed as a candidate to deal with this problem. However, it is challenging to directly deploy large neural networks on embedded devices of spacecraft due to the limited capacity. To address this problem, a lightweight YOLOv3 network structure is proposed in this paper, which reduces the number of parameters of the original by a factor of 42×, from 61M to 1.4M. And then Knowledge Distillation strategy could be used to improve the performance of the lightweight model when its accuracy drops a lot. In addition, because of the shortage of publicly available spacecraft datasets, a simulated large-scale dataset for spacecraft components detection based on a virtual environment is constructed. The experimental results show that, compared with the baseline model, the lightweight YOLOv3 model performs well on our dataset which has a smaller size and higher speed. So the lightweight model we proposed is more suitable for intelligent applications of spacecraft embedded devices.