Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

482
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
482
Deconvolution01:20

Deconvolution

293
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
293
Convolution Properties I01:20

Convolution Properties I

276
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
276
First-Order Circuits01:15

First-Order Circuits

2.3K
First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
2.3K
Convolution Properties II01:17

Convolution Properties II

315
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
315
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

398
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
398

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Cryptanalysis of some nonabelian group-based key exchange protocols.

Journal of mathematical cryptology·2026
Same author

Information-set decoding for convolutional codes.

Designs, codes, and cryptography·2025
Same author

Bounds for Coding Theory over Rings.

Entropy (Basel, Switzerland)·2023
Same author

Moderate-density parity-check codes from projective bundles.

Designs, codes, and cryptography·2022
Same author

Construction of LDPC convolutional codes via difference triangle sets.

Designs, codes, and cryptography·2021
Same journal

Hierarchical controller synthesis using ( <math><mrow><mi>γ</mi> <mo>,</mo> <mi>δ</mi></mrow></math> )-Similarity.

Mathematics of control, signals, and systems : MCSS·2026
Same journal

Chebyshev centers and radii for sets induced by quadratic matrix inequalities.

Mathematics of control, signals, and systems : MCSS·2025
Same journal

Oscillator death in coupled biochemical oscillators.

Mathematics of control, signals, and systems : MCSS·2025
See all related articles

Related Experiment Video

Updated: Oct 12, 2025

Author Spotlight: Advancing Alzheimer's Research &#8211; Exploring Early Detection and Multi-Omics Approaches
09:47

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

Published on: December 15, 2023

1.3K

Erasure decoding of convolutional codes using first-order representations.

Julia Lieb1, Joachim Rosenthal1

  • 1Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.

Mathematics of Control, Signals, and Systems : MCSS
|November 22, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new decoding algorithm for convolutional codes over erasure channels, leveraging their linear system representation. The novel approach reduces decoding delay and computational effort for internet data transmission.

Keywords:
Convolutional codesDecodingErasure channelLinear systems

More Related Videos

Characterization of Anisotropic Leaky Mode Modulators for Holovideo
09:36

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

Published on: March 19, 2016

8.1K
Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

17.8K

Related Experiment Videos

Last Updated: Oct 12, 2025

Author Spotlight: Advancing Alzheimer's Research &#8211; Exploring Early Detection and Multi-Omics Approaches
09:47

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

Published on: December 15, 2023

1.3K
Characterization of Anisotropic Leaky Mode Modulators for Holovideo
09:36

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

Published on: March 19, 2016

8.1K
Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

17.8K

Area of Science:

  • Information Theory
  • Coding Theory
  • Digital Communications

Background:

  • Convolutional codes are mathematically equivalent to discrete-time linear systems over finite fields.
  • Erasure channels are crucial for internet data transmission, where symbol correctness is known upon reception.
  • Existing decoding algorithms for convolutional codes over erasure channels can be computationally intensive and introduce delays.

Purpose of the Study:

  • To develop an efficient decoding algorithm for convolutional codes over erasure channels.
  • To utilize the linear system representation of convolutional codes for improved decoding.
  • To reduce decoding delay and computational complexity in erasure recovery.

Main Methods:

  • Employing the state space description of convolutional codes.
  • Developing a novel decoding algorithm based on the linear systems representation.
  • Analyzing the properties of convolutional codes for optimal decoding performance.

Main Results:

  • A new decoding algorithm for convolutional codes over erasure channels is presented.
  • The algorithm effectively utilizes the state space representation to provide additional decoding information.
  • The proposed method demonstrates reduced decoding delay and computational effort compared to existing algorithms.

Conclusions:

  • The linear systems representation offers a powerful framework for designing efficient convolutional code decoders.
  • The developed algorithm enhances data transmission reliability and efficiency over erasure channels.
  • Specific convolutional code properties are identified to ensure superior decoding performance.