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Related Concept Videos

Second Order systems II01:18

Second Order systems II

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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Constraints and Statical Determinacy01:26

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In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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Routh-Hurwitz Criterion II01:19

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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...
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Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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Second Order systems I01:20

Second Order systems I

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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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Stability of Equilibrium Configuration: Problem Solving01:13

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The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
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On the Optimal File Size of Capacity-Achieving Byzantine-Resistant Private Information Retrieval Schemes.

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Evaluating the Gilbert-Varshamov Bound for Constrained Systems.

Keshav Goyal1, Han Mao Kiah1

  • 1School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637121, Singapore.

Entropy (Basel, Switzerland)
|April 26, 2024
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Summary

This study presents numerical procedures to compute Gilbert-Varshamov (GV) bounds for constrained systems. Simplified methods and explicit formulas are derived for specific graph presentations, enhancing bound computation.

Keywords:
Gilbert–Varshamov boundasymptotic ratesconstrained codessliding window constrained codes

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Area of Science:

  • Information Theory
  • Coding Theory
  • Discrete Mathematics

Background:

  • The Gilbert-Varshamov (GV) bound is a fundamental result in coding theory.
  • Previous work established connections between the GV bound and optimization problems.
  • Improvements to the GV bound were proposed by Marcus and Roth.

Purpose of the Study:

  • To provide explicit numerical procedures for computing the GV bound.
  • To simplify the computation of the GV bound through graphical methods.
  • To derive explicit formulas for the GV bound in single-state graph scenarios.

Main Methods:

  • Solving optimization problems related to the GV bound.
  • Developing numerical algorithms for bound computation.
  • Analyzing graphical representations of the optimization problems.

Main Results:

  • Explicit numerical procedures for calculating the GV bound are presented.
  • The computational procedures are simplified by plotting curves.
  • Explicit formulas for the GV bound are derived for single-state graphs.

Conclusions:

  • The study offers practical methods for computing GV bounds.
  • Graphical analysis simplifies complex optimization problems.
  • Specific formulas enhance the applicability of GV bounds in certain cases.