arXiv subjects

Xiaoqiang Wang

Publications and source records attributed to Xiaoqiang Wang.

At least 55 records · Page 3Linked to original sources

arXiv2022

Generalized Hamming Weights of Linear Codes from Quadratic Forms over Finite Fields of Even Characteristic

The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one of important research topics in coding theory. Recently, Li (IEEE Trans. Inf. Theory, 67(1): 124-129, 2021) and Li and Li (Discrete Math., 345: 112718, 2022) obtained the complete weight hierarchy of linear codes from a quadratic form over a finite field of odd characteristic by analysis of the solutions of the restricted quadratic equation in its subspace. In this paper, we further determine the complete weight hierarchy of linear codes from a quadratic form over a finite field of even characteristic by carefully studying the behavior of the quadratic form on the subspaces of this field and its dual space, and complement the results of Li and Li.

cs.IT↗

arXiv2022

Two classes of narrow-sense BCH codes and their duals

BCH codes and their dual codes are two special subclasses of cyclic codes and are the best linear codes in many cases. A lot of progress on the study of BCH cyclic codes has been made, but little is known about the minimum distances of the duals of BCH codes. Recently, a new concept called dually-BCH code was introduced to investigate the duals of BCH codes and the lower bounds on their minimum distances in \cite{GDL21}. For a prime power $q$ and an integer $m \ge 4$, let $n=\frac{q^m-1}{q+1}$ \ ($m$ even), or $n=\frac{q^m-1}{q-1}$ \ ($q>2$). In this paper, some sufficient and necessary conditions in terms of the designed distance will be given to ensure that the narrow-sense BCH codes of length $n$ are dually-BCH codes, which extended the results in \cite{GDL21}. Lower bounds on the minimum distances of their dual codes are developed for $n=\frac{q^m-1}{q+1}$ \ ($m$ even). As byproducts, we present the largest coset leader $δ_1$ modulo $n$ being of two types, which proves a conjecture in \cite{WLP19} and partially solves an open problem in \cite{Li2017}. We also investigate the parameters of the narrow-sense BCH codes of length $n$ with design distance $δ_1$. The BCH codes presented in this paper have good parameters in general.

cs.IT↗

arXiv2022

Towards Contextual Spelling Correction for Customization of End-to-end Speech Recognition Systems

Contextual biasing is an important and challenging task for end-to-end automatic speech recognition (ASR) systems, which aims to achieve better recognition performance by biasing the ASR system to particular context phrases such as person names, music list, proper nouns, etc. Existing methods mainly include contextual LM biasing and adding bias encoder into end-to-end ASR models. In this work, we introduce a novel approach to do contextual biasing by adding a contextual spelling correction model on top of the end-to-end ASR system. We incorporate contextual information into a sequence-to-sequence spelling correction model with a shared context encoder. Our proposed model includes two different mechanisms: autoregressive (AR) and non-autoregressive (NAR). We propose filtering algorithms to handle large-size context lists, and performance balancing mechanisms to control the biasing degree of the model. We demonstrate the proposed model is a general biasing solution which is domain-insensitive and can be adopted in different scenarios. Experiments show that the proposed method achieves as much as 51% relative word error rate (WER) reduction over ASR system and outperforms traditional biasing methods. Compared to the AR solution, the proposed NAR model reduces model size by 43.2% and speeds up inference by 2.1 times.

cs.CL↗

arXiv2022

Two Classes of Constacyclic Codes with Variable Parameters

Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes are of theoretical importance. On the other hand, constacyclic codes are important in practice, as they have rich algebraic structures and may have efficient decoding algorithms. In this paper, two classes of constacyclic codes are constructed using a general construction of constacyclic codes with cyclic codes. The first class of constacyclic codes is motivated by the punctured Dilix cyclic codes and the second class is motivated by the punctured generalised Reed-Muller codes. The two classes of constacyclic codes contain optimal linear codes. The parameters of the two classes of constacyclic codes are analysed and some open problems are presented in this paper.

cs.IT↗

arXiv2022

Infinite families of cyclic and negacyclic codes supporting 3-designs

Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been constructed in the past 50 years. However, no infinite family of negacyclic codes supporting an infinite family of $3$-designs has been reported in the literature. This is the main motivation of this paper. Let $q=p^m$, where $p$ is an odd prime and $m \geq 2$ is an integer. The objective of this paper is to present an infinite family of cyclic codes over $\gf(q)$ supporting an infinite family of $3$-designs and two infinite families of negacyclic codes over $\gf(q^2)$ supporting two infinite families of $3$-designs. The parameters and the weight distributions of these codes are determined. The subfield subcodes of these negacyclic codes over $\gf(q)$ are studied. Three infinite families of almost MDS codes are also presented. A constacyclic code over GF($4$) supporting a $4$-design and six open problems are also presented in this paper.

cs.IT↗

arXiv2022

Several Families of Irreducible Constacyclic and Cyclic Codes

In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several families of irreducible constacyclic codes with a few weights and several families of optimal constacyclic codes are constructed. As by-products, a family of $[2n, (n-1)/2, d \geq 2(\sqrt{n}+1)]$ irreducible cyclic codes over $\gf(q)$ and a family of $[(q-1)n, (n-1)/2, d \geq (q-1)(\sqrt{n}+1)]$ irreducible cyclic codes over $\gf(q)$ are presented, where $n$ is a prime such that $\ord_n(q)=(n-1)/2$. The results in this paper complement earlier works on irreducible constacyclic and cyclic codes over finite fields.

cs.IT↗

arXiv2022

Two families of negacyclic BCH codes

Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let $q$ be an odd prime power and $m$ be a positive integer. The objective of this paper is to study negacyclic BCH codes with length $\frac{q^m-1}{2}$ and $\frac{q^m+1}{2}$ over the finite field $\mathbf(q)$ and analyse their parameters. The negacyclic BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes. For certain $q$ and $m$, compared with cyclic codes with the same dimension and length, the negacyclic BCH codes presented in this paper have a larger minimum distance in some cases.

cs.IT↗

arXiv2022

RetrieverTTS: Modeling Decomposed Factors for Text-Based Speech Insertion

This paper proposes a new "decompose-and-edit" paradigm for the text-based speech insertion task that facilitates arbitrary-length speech insertion and even full sentence generation. In the proposed paradigm, global and local factors in speech are explicitly decomposed and separately manipulated to achieve high speaker similarity and continuous prosody. Specifically, we proposed to represent the global factors by multiple tokens, which are extracted by cross-attention operation and then injected back by link-attention operation. Due to the rich representation of global factors, we manage to achieve high speaker similarity in a zero-shot manner. In addition, we introduce a prosody smoothing task to make the local prosody factor context-aware and therefore achieve satisfactory prosody continuity. We further achieve high voice quality with an adversarial training stage. In the subjective test, our method achieves state-of-the-art performance in both naturalness and similarity. Audio samples can be found at https://ydcustc.github.io/retrieverTTS-demo/.

eess.AS↗

arXiv2022

Strict Half-Singleton Bound, Strict Direct Upper Bound for Linear Insertion-Deletion Codes and Optimal Codes

Insertion-deletion codes (insdel codes for short) are used for correcting synchronization errors in communications, and in other many interesting fields such as DNA storage, date analysis, race-track memory error correction and language processing, and have recently gained a lot of attention. To determine the insdel distances of linear codes is a very challenging problem. The half-Singleton bound on the insdel distances of linear codes due to Cheng-Guruswami-Haeupler-Li is a basic upper bound on the insertion-deletion error-correcting capabilities of linear codes. On the other hand the natural direct upper bound $d_I(\mathcal C) \leq 2d_H(\mathcal C)$ is valid for any insdel code. In this paper, for a linear insdel code $\mathcal C$ we propose a strict half-Singleton upper bound $d_I(\mathcal C) \leq 2(n-2k+1)$ if $\mathcal C$ does not contain the codeword with all 1s, and a stronger direct upper bound $d_I(\mathcal C) \leq 2(d_H(\mathcal C)-t)$ under a weak condition, where $t\geq 1$ is a positive integer determined by the generator matrix. We also give optimal linear insdel codes attaining our strict half-Singleton bound and direct upper bound, and show that the code length of optimal binary linear insdel codes with respect to the (strict) half-Singleton bound is about twice the dimension. Interestingly explicit optimal linear insdel codes attaining the (strict) half-Singleton bound, with the code length being independent of the finite field size, are given.

cs.IT↗

arXiv2022

QRelScore: Better Evaluating Generated Questions with Deeper Understanding of Context-aware Relevance

Existing metrics for assessing question generation not only require costly human reference but also fail to take into account the input context of generation, rendering the lack of deep understanding of the relevance between the generated questions and input contexts. As a result, they may wrongly penalize a legitimate and reasonable candidate question when it (i) involves complicated reasoning with the context or (ii) can be grounded by multiple evidences in the context. In this paper, we propose $\textbf{QRelScore}$, a context-aware $\underline{\textbf{Rel}}$evance evaluation metric for $\underline{\textbf{Q}}$uestion Generation. Based on off-the-shelf language models such as BERT and GPT2, QRelScore employs both word-level hierarchical matching and sentence-level prompt-based generation to cope with the complicated reasoning and diverse generation from multiple evidences, respectively. Compared with existing metrics, our experiments demonstrate that QRelScore is able to achieve a higher correlation with human judgments while being much more robust to adversarial samples.

cs.CL↗

arXiv2022

Feeding What You Need by Understanding What You Learned

Machine Reading Comprehension (MRC) reveals the ability to understand a given text passage and answer questions based on it. Existing research works in MRC rely heavily on large-size models and corpus to improve the performance evaluated by metrics such as Exact Match ($EM$) and $F_1$. However, such a paradigm lacks sufficient interpretation to model capability and can not efficiently train a model with a large corpus. In this paper, we argue that a deep understanding of model capabilities and data properties can help us feed a model with appropriate training data based on its learning status. Specifically, we design an MRC capability assessment framework that assesses model capabilities in an explainable and multi-dimensional manner. Based on it, we further uncover and disentangle the connections between various data properties and model performance. Finally, to verify the effectiveness of the proposed MRC capability assessment framework, we incorporate it into a curriculum learning pipeline and devise a Capability Boundary Breakthrough Curriculum (CBBC) strategy, which performs a model capability-based training to maximize the data value and improve training efficiency. Extensive experiments demonstrate that our approach significantly improves performance, achieving up to an 11.22% / 8.71% improvement of $EM$ / $F_1$ on MRC tasks.

cs.CL↗

arXiv2022

Amplification of optical Schrödinger cat states with implementation protocol based on frequency comb

We proposed and analyzed a scheme to generate large-size Schrödinger cat states based on linear operations of Fock states and squeezed vacuum states and conditional measurements. By conducting conditional measurements via photon number detectors, two unbalanced Schrödinger kitten states combined by a beam splitter can be amplified to a large-size cat state with the same parity. According to simulation results, two Schrödinger odd kitten states of $β=1.06$ and $β=1.11$ generated from one-photon-subtracted squeezed vacuum states of $-$3 dB, are amplified to an odd cat state of $β=1.73$ with a fidelity of $F=99\%$. A large-size Schrödinger odd cat state with $β=2.51$ and $F=97.30\%$ is predicted when the input squeezed vacuum states are increased to $-$5.91 dB. According to the analysis on the impacts of experimental imperfections in practice, Schrödinger odd cat states of $β>2$ are available. A feasible configuration based on a quantum frequency comb is developed to realize the large-size cat state generation scheme we proposed.

quant-ph↗

arXiv2022

Boosting RGB-D Saliency Detection by Leveraging Unlabeled RGB Images

Training deep models for RGB-D salient object detection (SOD) often requires a large number of labeled RGB-D images. However, RGB-D data is not easily acquired, which limits the development of RGB-D SOD techniques. To alleviate this issue, we present a Dual-Semi RGB-D Salient Object Detection Network (DS-Net) to leverage unlabeled RGB images for boosting RGB-D saliency detection. We first devise a depth decoupling convolutional neural network (DDCNN), which contains a depth estimation branch and a saliency detection branch. The depth estimation branch is trained with RGB-D images and then used to estimate the pseudo depth maps for all unlabeled RGB images to form the paired data. The saliency detection branch is used to fuse the RGB feature and depth feature to predict the RGB-D saliency. Then, the whole DDCNN is assigned as the backbone in a teacher-student framework for semi-supervised learning. Moreover, we also introduce a consistency loss on the intermediate attention and saliency maps for the unlabeled data, as well as a supervised depth and saliency loss for labeled data. Experimental results on seven widely-used benchmark datasets demonstrate that our DDCNN outperforms state-of-the-art methods both quantitatively and qualitatively. We also demonstrate that our semi-supervised DS-Net can further improve the performance, even when using an RGB image with the pseudo depth map.

eess.IV↗

arXiv2021

BCH codes over $\gf(q)$ with length $q^m+1$

BCH codes are an interesting class of cyclic codes due to their efficient encoding and decoding algorithms. In many cases, BCH codes are the best linear codes. However, the dimension and minimum distance of BCH codes have been seldom solved. Until now, there have been few results on BCH codes over $\gf(q)$ with length $q^m+1$, especially when $q$ is a prime power and $m$ is even. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. The BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes.

cs.IT↗

arXiv2021

The $q$-ary antiprimitive BCH codes

It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH codes are given. The BCH codes presented in this paper have good parameters in general, containing many optimal linear codes. In particular, two open problems about the minimum distance of BCH codes of this type are partially solved in this paper.

cs.IT↗

arXiv2021

Ordering-Based Causal Discovery with Reinforcement Learning

It is a long-standing question to discover causal relations among a set of variables in many empirical sciences. Recently, Reinforcement Learning (RL) has achieved promising results in causal discovery from observational data. However, searching the space of directed graphs and enforcing acyclicity by implicit penalties tend to be inefficient and restrict the existing RL-based method to small scale problems. In this work, we propose a novel RL-based approach for causal discovery, by incorporating RL into the ordering-based paradigm. Specifically, we formulate the ordering search problem as a multi-step Markov decision process, implement the ordering generating process with an encoder-decoder architecture, and finally use RL to optimize the proposed model based on the reward mechanisms designed for~each ordering. A generated ordering would then be processed using variable selection to obtain the final causal graph. We analyze the consistency and computational complexity of the proposed method, and empirically show that a pretrained model can be exploited to accelerate training. Experimental results on both synthetic and real data sets shows that the proposed method achieves a much improved performance over existing RL-based method.

cs.LG↗

arXiv2021

A Light-weight contextual spelling correction model for customizing transducer-based speech recognition systems

It's challenging to customize transducer-based automatic speech recognition (ASR) system with context information which is dynamic and unavailable during model training. In this work, we introduce a light-weight contextual spelling correction model to correct context-related recognition errors in transducer-based ASR systems. We incorporate the context information into the spelling correction model with a shared context encoder and use a filtering algorithm to handle large-size context lists. Experiments show that the model improves baseline ASR model performance with about 50% relative word error rate reduction, which also significantly outperforms the baseline method such as contextual LM biasing. The model also shows excellent performance for out-of-vocabulary terms not seen during training.

cs.CL↗

arXiv2021

Several classes of PcN power functions over finite fields

Recently, a new concept called multiplicative differential cryptanalysis and the corresponding $c$-differential uniformity were introduced by Ellingsen et al.~\cite{Ellingsen2020}, and then some low differential uniformity functions were constructed. In this paper, we further study the constructions of perfect $c$-nonlinear (PcN) power functions. First, we give a necessary and sufficient condition for the Gold function to be PcN and a conjecture on all power functions to be PcN over $\gf(2^m)$. Second, several classes of PcN power functions are obtained over finite fields of odd characteristic for $c=-1$ and our theorems generalize some results in~\cite{Bartoli,Hasan,Zha2020}. Finally, the $c$-differential spectrum of a class of almost perfect $c$-nonlinear (APcN) power functions is determined.

cs.IT↗