Topic
Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors proposed and experimentally demonstrated an approach to jointly enhance the physical layer security and improve an optical orthogonal frequency division multiplexing (O-OFDM) transmission in passive optical network.
Abstract: This letter proposes and experimentally demonstrates an approach to jointly enhance the physical layer security and improve an optical orthogonal frequency division multiplexing (O-OFDM) transmission in passive optical network. It is proven that the Walsh–Hadamard Transform (WHT) matrix can effectively reduce the peak-to-average power ratio (PAPR) of OFDM signals after independent row/column permutations. A hyper digital chaos is adopted to generate the chaotic permutated WHT matrix for OFDM data encryption, which provides a total key space of $\sim 10^{178}$ to enhance the physical layer confidentiality. An 8.9-Gb/s encrypted 16-QAM O-OFDM signal transmission is successfully demonstrated over 20-km standard single-mode fiber, where the receiver sensitivity is improved by $\sim 1$ dB (BER@ $10^{\mathrm {-3}}$ ) due to the PAPR reduction through the chaotic WHT precoding. Moreover, the scheme does not require any additional sideband information and provides low computational complexity.
50 citations
01 Jan 2020
TL;DR: In this article, the Hermite-Hadamard type inequalities for fractional integral integrals and Riemann-Liouville fractional integrals were extended to differentiable exponentially convex functions.
Abstract: The investigation of the proposed techniques is effective and convenient for solving the integrodifferential and difference equations. The present investigation depends on two highlights; the novel Hermite-Hadamard type inequalities for $\mathcal{K}$-conformable fractional integral operator in terms of a new parameter $\mathcal{K}>0$ and weighted version of Hermite-Hadamard type inequalities for exponentially convex functions in the classical sense. By using an integral identity together with the Holder-Iscan and improved power-mean inequality we establish several new inequalities for differentiable exponentially convex functions. This generalizes the Hadamard fractional integrals and Riemann-Liouville into a single form. Our contribution expands some innovative studies in this line. Moreover, two suitable examples are presented to demonstrate the novelty of the results established, the first one about the contributions of the modified Bessel functions and the other is about $\sigma$-digamma function. Finally, various applications for some special means as arithmetic, geometric and logarithmic are given.
50 citations
TL;DR: In this paper, the Hadamard-Fischer inequality was shown to hold for the case of BE W(n) and A E 7(1I) if A E W( n) and 0, A.
Abstract: 1) Spec A[Jl.l n IR =1= t/>, for t/> c Jl. S (n), 2) I(A[J-L]) « I(A[v]), if t/> c v S Jl. S (n), where I(A[Jl.]) = min(Spec A[Jl.l n IR). For A, BE W(n), define A «, B by I(A[J-L]) « I(B[J-L]), for t/> c Jl. S ( n ). By definition, A E7(1I) if A E W(n) and 0 «, A. For 0 « , A «t B (where A, BE W(n» it is shown that 3) 0 « det A « det B-det(B-I(A)I) « det B. For A E 7(11 ) , A «, A[Jl.l El1 A{J1.), and hence we obtain the Hadamard-Fischer inequality 4) 0 « det A « det A[Jl.l det A{J1.)
50 citations
TL;DR: In this article, it was shown that for an unknown qubit chosen either from the polar or equatorial great circles, one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement states.
Abstract: We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal superposition of the original and its complement state. Surprisingly, we find that Hadamard transformations exist for an unknown qubit chosen either from the polar or equatorial great circles. Also, we show that for an unknown qubit one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement state. We discuss why it is impossible to design a controlled-NOT gate for two unknown qubits and discuss the implications of these limitations. 03.67.Hk, 03.65.Ta.
50 citations
Posted Content•
TL;DR: In this article, the combinatorial harmonic map theory is used to study the isometric actions of discrete groups on Hadamard spaces, and the authors formulate criterions for the action to have a global fixed point.
Abstract: We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the action to have a global fixed point.
49 citations