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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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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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The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
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Related Experiment Video

Updated: May 10, 2025

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues
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Quasi-Optimal Path Convergence-Aided Automorphism Ensemble Decoding of Reed-Muller Codes.

Kairui Tian1, He Sun1,2, Yukai Liu1

  • 1School of Electronic and Information Engineering, Beihang University, Beijing 100191, China.

Entropy (Basel, Switzerland)
|April 26, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a quasi-optimal path convergence (QOPC) technique to reduce the complexity of Automorphism Ensemble (AE) Successive Cancellation (SC) decoding for Reed-Muller (RM) codes. The method significantly cuts computational cost with minimal performance impact, enhancing decoding efficiency.

Keywords:
Reed–Muller codesautomorphism ensemble decodingearly terminationsuccessive cancellation decoding

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Area of Science:

  • Coding Theory
  • Information Theory
  • Digital Communications

Background:

  • Automorphism Ensemble (AE) Successive Cancellation (SC) decoders offer near-maximum-likelihood (ML) performance for Reed-Muller (RM) codes.
  • The high decoding complexity of AE-SC decoders stems from the need for multiple decoding attempts to achieve diversity gain.

Purpose of the Study:

  • To propose a novel quasi-optimal path convergence (QOPC)-aided early termination (ET) technique for AE-SC decoding.
  • To reduce the computational complexity of AE-SC decoding without significant performance degradation.

Main Methods:

  • Developed a QOPC technique to detect convergence of partial path metrics (PPMs) in SC constituent decoders.
  • Implemented an early termination strategy based on the QOPC criterion to prune non-optimal decoding paths.
  • Evaluated performance and complexity reduction in both fully and partially parallel AE-SC decoding frameworks.

Main Results:

  • The QOPC-aided ET method achieved negligible performance loss for medium-to-high-rate RM codes in the short-length regime.
  • Complexity reduction ranged from 35.9% to 47.4% at a block error rate (BLER) of 10-3, outperforming existing methods.
  • Under a partially parallel framework, complexity reduction reached 81.3% to 86.7% at a BLER of 10-5, maintaining near-ML performance.

Conclusions:

  • The proposed QOPC-aided ET technique effectively reduces AE-SC decoding complexity for RM codes.
  • This method offers a practical solution for improving the efficiency of high-performance decoders.
  • The technique demonstrates superior performance and complexity reduction compared to state-of-the-art methods.