arXiv subjects

Chunlei Li

Publications and source records attributed to Chunlei Li.

At least 55 records · Page 3Linked to original sources

arXiv2024

New Correlation Bound and Construction of Quasi-Complementary Code Sets

Quasi-complementary sequence sets (QCSSs) have attracted sustained research interests for simultaneously supporting more active users in multi-carrier code-division multiple-access (MC-CDMA) systems compared to complete complementary codes (CCCs). In this paper, we investigate a novel class of QCSSs composed of multiple CCCs. We derive a new aperiodic correlation lower bound for this type of QCSSs, which is tighter than the existing bounds for QCSSs. We then present a systematic construction of such QCSSs with a small alphabet size and low maximum correlation magnitude, and also show that the constructed aperiodic QCSSs can meet the newly derived bound asymptotically.

cs.IT↗

arXiv2023

A Unified Particle-Based Solver for Non-Newtonian Behaviors Simulation

In this paper, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.

cs.GR↗

arXiv2023

Novel Power-Imbalanced Dense Codebooks for Reliable Multiplexing in Nakagami Channels

This paper studies enhanced dense code multiple access (DCMA) system design for downlink transmission over the Nakagami-$m$ fading channels. By studying the DCMA pairwise error probability (PEP) in a Nakagami-$m$ channel, a novel design metric called minimum logarithmic sum distance (MLSD) is first derived. With respect to the proposed MLSD, we introduce a new family of power-imbalanced dense codebooks by deleting certain rows of a special non-unimodular circulant matrix. Simulation results demonstrate that our proposed dense codebooks lead to both larger minimum Euclidean distance and MLSD, thus yielding significant improvements of error performance over the existing sparse code multiple access and conventional unimodular DCMA schemes in Nakagami-$m$ fading channels under different overloading factors.

cs.IT↗

arXiv2023

Two new algorithms for error support recovery of low rank parity check codes

Due to their weak algebraic structure, low rank parity check (LRPC) codes have been employed in several post-quantum cryptographic schemes. In this paper we propose new improved decoding algorithms for (n, k) LRPC codes of dual rank weight d. The proposed algorithms can efficiently decode LRPC codes with the parameters satisfying n - k = rd - c, where r is the dimension of the error support and c <= d - 2. They outperform the original decoding algorithm of LRPC codes when d > 2 and allow for decoding LRPC codes with a higher code rate and smaller values m.

cs.IT↗

arXiv2023

Generalized LRPC codes

In this paper we generalize the notion of low-rank parity check (LRPC) codes by introducing a bilinear product over F^m q based on a generic 3-tensor in Fq^mxmxm, where Fq is the finite field with q elements. The generalized LRPC codes are Fq -linear codes in general and a particular choice of the 3-tensor corresponds to the original Fqm -linear LRPC codes. For the generalized LRPC codes, we propose two probabilistic polynomial-time decoding algorithms by adapting the decoding method for LRPC codes and also show that the proposed algorithms have a decoding failure rate similar to that of decoding LRPC codes

cs.IT↗

arXiv2023

Sparse Complementary Pairs with Additional Aperiodic ZCZ Property

This paper presents a novel class of complex-valued sparse complementary pairs (SCPs), each consisting of a number of zero values and with additional zero-correlation zone (ZCZ) property for the aperiodic autocorrelations and crosscorrelations of the two constituent sequences. Direct constructions of SCPs and their mutually-orthogonal mates based on restricted generalized Boolean functions are proposed. It is shown that such SCPs exist with arbitrary lengths and controllable sparsity levels, making them a disruptive sequence candidate for modern low-complexity, low-latency, and low-storage signal processing applications.

cs.IT↗

arXiv2022

Bivariate functions with low $c$-differential uniformity

Starting with the multiplication of elements in $\mathbb{F}_{q}^2$ which is consistent with that over $\mathbb{F}_{q^2}$, where $q$ is a prime power, via some identification of the two environments, we investigate the $c$-differential uniformity for bivariate functions $F(x,y)=(G(x,y),H(x,y))$. By carefully choosing the functions $G(x,y)$ and $H(x,y)$, we present several constructions of bivariate functions with low $c$-differential uniformity. Many P$c$N and AP$c$N functions can be produced from our constructions.

cs.IT↗

arXiv2022

Low c-differentially uniform functions via an extension of Dillon's switching method

In this paper we generalize Dillon's switching method to characterize the exact $c$-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known $c$-differential uniformity in a controllable number of coordinates to render more such functions. We present several applications of the method in constructing PcN and APcN functions with respect to all $c\neq 1$. As a byproduct, we generalize some result of [Y. Wu, N. Li, X. Zeng, {\em New PcN and APcN functions over finite fields}, Designs Codes Crypt. 89 (2021), 2637--2651]. Computational results rendering functions with low differential uniformity, as well as, other good cryptographic properties are sprinkled throughout the paper.

cs.IT↗

arXiv2022

On the Differential Properties of the Power Mapping $x^{p^m+2}$

Let $m$ be a positive integer and $p$ a prime. In this paper, we investigate the differential properties of the power mapping $x^{p^m+2}$ over $\mathbb{F}_{p^n}$, where $n=2m$ or $n=2m-1$. For the case $n=2m$, by transforming the derivative equation of $x^{p^m+2}$ and studying some related equations, we completely determine the differential spectrum of this power mapping. For the case $n=2m-1$, the derivative equation can be transformed to a polynomial of degree $p+3$. The problem is more difficult and we obtain partial results about the differential spectrum of $x^{p^m+2}$.

cs.CR↗

arXiv2022

Encoding and Decoding of Several Optimal Rank Metric Codes

This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right choice for these codes and then we provide easily reversible encoding methods for each family. Later unique decoding algorithms for the codes are described. The decoding algorithms are interpolation-based and can uniquely correct errors for each code with rank up to $\lfloor(d-1)/2\rfloor$ in polynomial-time, where $d$ is the minimum distance of the code.

cs.IT↗

arXiv2021

The Differential Spectrum of the Power Mapping $x^{p^n-3}$

Let $n$ be a positive integer and $p$ a prime. The power mapping $x^{p^n-3}$ over $\mathbb{F}_{p^n}$ has desirable differential properties, and its differential spectra for $p=2,\,3$ have been determined. In this paper, for any odd prime $p$, by investigating certain quadratic character sums and some equations over $\mathbb{F}_{p^n}$, we determine the differential spectrum of $x^{p^n-3}$ with a unified approach. The obtained result shows that for any given odd prime $p$, the differential spectrum can be expressed explicitly in terms of $n$. Compared with previous results, a special elliptic curve over $\mathbb{F}_{p}$ plays an important role in our computation for the general case $p \ge 5$.

cs.IT↗

arXiv2021

The resolution of Niho's last conjecture concerning sequences, codes, and Boolean functions

A new method is used to resolve a long-standing conjecture of Niho concerning the crosscorrelation spectrum of a pair of maximum length linear recursive sequences of length $2^{2 m}-1$ with relative decimation $d=2^{m+2}-3$, where $m$ is even. The result indicates that there are at most five distinct crosscorrelation values. Equivalently, the result indicates that there are at most five distinct values in the Walsh spectrum of the power permutation $f(x)=x^d$ over a finite field of order $2^{2 m}$ and at most five distinct nonzero weights in the cyclic code of length $2^{2 m}-1$ with two primitive nonzeros $α$ and $α^d$. The method used to obtain this result proves constraints on the number of roots that certain seventh degree polynomials can have on the unit circle of a finite field. The method also works when $m$ is odd, in which case the associated crosscorrelation and Walsh spectra have at most six distinct values.

math.NT↗

arXiv2021

Decoding a class of maximum Hermitian rank metric codes

Maximum Hermitian rank metric codes were introduced by Schmidt in 2018 and in this paper we propose both interpolation-based encoding and decoding algorithms for this family of codes when the length and the minimum distance of the code are both odd.

cs.IT↗

arXiv2021

Two new infinite classes of APN functions

In this paper, we present two new infinite classes of APN functions over $\gf_{2^{2m}}$ and $\gf_{2^{3m}}$, respectively. The first one is with bivariate form and obtained by adding special terms, $\sum(a_ix^{2^i}y^{2^i},b_ix^{2^i}y^{2^i})$, to a known class of APN functions by {G{ö}lo{ǧ}lu} over $\gf_{2^m}^2$. The second one is of the form $L(z)^{2^m+1}+vz^{2^m+1}$ over $\gf_{2^{3m}}$, which is a generalization of one family of APN functions by Bracken et al. [Cryptogr. Commun. 3 (1): 43-53, 2011]. The calculation of the CCZ-invariants $Γ$-ranks of our APN classes over $\gf_{2^8}$ or $\gf_{2^9}$ indicates that they are CCZ-inequivalent to all known infinite families of APN functions. Moreover, by using the code isomorphism, we see that our first APN family covers an APN function over $\gf_{2^8}$ obtained through the switching method by Edel and Pott in [Adv. Math. Commun. 3 (1): 59-81, 2009].

cs.IT↗

arXiv2021

On interpolation-based decoding of a class of maximum rank distance codes

In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with a linearized polynomial with a given rank and the modified Berlekamp-Massey algorithm in decoding. When the rank of the error vector attains the unique decoding radius, the problem is converted to solving a quadratic polynomial, which ensures that the proposed decoding algorithm has polynomial-time complexity.

cs.IT↗

arXiv2021

Low Row Rank Parity Check Codes

In this paper we present an extended variant of low rank parity check matrix (LRPC) codes that have received significant interests in recent years. It is shown that the extension indeed yields a superfamily of LRPC codes, which are termed low row rank parity check codes. The decoding method of the proposed codes is also investigated.

cs.IT↗

arXiv2021

Self-Amplification of Coherent Energy Modulation in Seeded Free-Electron Lasers

The spectroscopic techniques for time-resolved fine analysis of matter require coherent X-ray radiation with femtosecond duration and high average brightness. Seeded free-electron lasers (FELs), which use the frequency up-conversion of an external seed laser to improve temporal coherence, are ideal for providing fully coherent soft X-ray pulses. However, it is difficult to operate seeded FELs at a high repetition rate due to the limitations of present state-of-the-art laser systems. Here, we report the novel self-modulation method for enhancing laser-induced energy modulation, thereby significantly reducing the requirement of an external laser system. Driven by this scheme, we experimentally realize high harmonic generation in a seeded FEL using an unprecedentedly small energy modulation. An electron beam with a laser-induced energy modulation as small as 1.8 times the slice energy spread is used for lasing at the 7th harmonic of a 266-nm seed laser in a single-stage high-gain harmonic generation (HGHG) setup and the 30th harmonic of the seed laser in a two-stage HGHG setup. The results mark a major step towards a high-repetition-rate, fully coherent X-ray FEL.

physics.acc-ph↗

arXiv2020

A complete characterization of the APN property of a class of quadrinomials

In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients $a_1,a_2,a_3\in\mathbb{F}_{2^n}$ with $n=2m$ such that $f(x) = {x}^{3\cdot2^m} + a_1x^{2^{m+1}+1} + a_2 x^{2^m+2} + a_3x^3$ is an APN function over $\mathbb{F}_{2^n}$. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.

cs.IT↗