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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

1.1K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.1K
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

157
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
157
Even and Odd Signals01:17

Even and Odd Signals

630
An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as
630
Bulk Modulus01:21

Bulk Modulus

255
The bulk modulus is a scientific term used to describe a material's resistance to uniform compression. It is the proportionality constant that links a change in pressure to the resulting relative volume change.
255
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

1.6K
The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
1.6K
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

84
Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
84

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相关实验视频

Updated: May 10, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
00:07

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.3K

基于乘法重复的非二进制极点代码的比特级构造.

Rongchi Xu1, Peiyao Chen1, Ling Liu2

  • 1The State Key Laboratory of ISN, Xidian University, Xi'an 710071, China.

Entropy (Basel, Switzerland)
|April 26, 2025
PubMed
概括

这项研究引入了一种用于非二进制极性代码的新型比特级构造,提高了解码性能. 新方法优化了在合成道中的信息位分配,以获得更好的错误纠正能力.

科学领域:

  • 编码理论编码理论
  • 信息理论 信息理论
  • 数字通信数字通信

背景情况:

  • 非二进制极性代码比二进制代码有优势,但在构造方面面临挑战.
  • 传统的方法与中间极化道作斗争,限制了效率.
  • 有效地将信息位分配到合成道对于性能至关重要.

研究的目的:

  • 为基于乘法重复 (MR) 的非二进制极码提出一个比特级构造.
  • 为了解决对于有限块长度的传统非二进制极性代码构造的局限性.
  • 为了提高非二进制极性代码的解码性能.

主要方法:

  • 使用通道退化方法计算错误概率和通道容量下限.
  • 确定每个合成通道的信息位的最佳数量和索引.
  • 采用蒙特卡洛方法来计算错误概率,并最大限度地降低联合界限.
  • 引入了一种改进的基于构造的概率塑造方法.

主要成果:

  • 拟议的比特级构建有效地根据它们的容量将比特分配给合成通道.
  • 蒙特卡洛方法和概率造型优化了结构,减少了错误概率.
  • 与传统方法相比,模拟结果显示解码性能显著改善.
关键词:
频道退化 频道退化建设算法 建筑算法非二进制的极点代码.概率性塑造是一种概率性塑造.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Quasi-light Storage for Optical Data Packets

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相关实验视频

Last Updated: May 10, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
00:07

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

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结论:

  • 拟议的比特级构造方法为基于MR的非二进制极性代码提供了优越的方法.
  • 这种方法通过提高其效率和性能来增强非二进制极性代码的实际应用.
  • 进一步的研究可以探索先进的概率塑造技术,以获得更大的收益.