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About 10,000 papers for “Convolutional code”

Convolutional-Code-Specific CRC Code Design

Chung-Yu Lou, Babak Daneshrad, Richard D. Wesel · IEEE Transactions on Communications · 2015

Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The algorithm utilizes two distinct approaches to computing undetected error probability of a CRC code used with a specific convolutional code. The first approach enumerates the error patterns of the convolutional code and tests if each of them is detectable. The second approach reduces complexity significantly by exploiting the equivalence of the undetected error probability to the frame error rate of an equivalent catastrophic convolutional code. The error events of the equivalent convolutional code are exactly the undetectable errors for the original concatenation of CRC and convolutional codes. This simplifies the computation because error patterns do not need to be individually checked for detectability. As an example, we optimize CRC codes for a commonly used 64-state convolutional code for information length k=1024, demonstrating significant reduction in undetected error probability compared to the existing CRC codes with the same degrees. For a fixed target undetected error probability, the optimized CRC codes typically require 2 fewer bits.

Cited by 45

Code underlying: Simplicial Convolutional Filters

Yang, Maosheng · 4TU.ResearchData · 2025

This implements the simplicial convolutional filters in Matlab, together with their design and applications. In this work, we have developed filters of processing data defined on the edge space of a simplicial 2-complex, and Fourier analysis of such signals. To achieve certain filtering, we proposed different ways of designing the required filters.

Cited by 0Open access

Description of a Quantum Convolutional Code

H Ollivier, Jean–Pierre Tillich · Physical Review Letters · 2003

We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances in classical communication. The particular example shown here uses the stabilizer formalism. We provide an explicit encoding circuit and its associated error estimation algorithm. The latter gives the most likely error over any memoryless quantum channel, with a complexity growing only linearly with the number of encoded qubits.

Cited by 110Open access

Convolutional Code Theory based Steganography Technique

María Isabel García Planas, Laurence Emilie Um · International Journal of Circuits Systems and Signal Processing · 2022

Steganography, as it is known, is a technique to hide a secret message within a message or collection of data that is not secret, and a problem in mathematics is to decipher the secret included in the message, to solve this problem a good tool It is the theory of codes. Unlike the existing works that use block codes to hide information using the steganographic process, in this work, we propose the use of convolutional coding theory in steganography to encrypt and decrypt messages methods to decrypt messages. Here, we suggest a steganographic protocol based on convolutional codes in which they are defined as discrete linear dynamical systems with which the properties on controllability and observability characteristic of linear systems theory can be applied, in particular the properties of output observability character which can be easily described using matrix language. The proposed decoding algorithm used for dissimulation is a linear decoding method, which has decreased both the time and space complexity, compared to the Viterbi decoding algorithm, sometimes used in other cases; indeed, we go from 2h.n to 2h=2.n, in memory space (with h: constraint height, and n: length of cover object). Moreover, the time complexity is better, while we can also denote that with the convolutional approach, we intend to take advantage of the time-depending transaction.

Cited by 0Open access

Complex-shaped convolutional sparse code dictionary.

Ziniu Wu (11604297), Harold Rockwell (11604300), Yimeng Zhang (283704) et al. · Figshare · 2021

<p>Learned feature dictionaries from the CSC algorithm applied to grayscale natural images with 64, 128, and 256 elements, each with a kernel size of 9px.</p>

Cited by 0Open access

Convolutional coding for code multiplexing of channels

A V Rabin, Steven Rabin, А. В. Овчинников · EPJ Web of Conferences · 2025

This paper explores the application of convolutional codes and their extensions in the context of binary channel code division. A novel method for channel division utilizing convolutional coding is presented, alongside a comparative analysis with block coding techniques. While the approach for implementing convolutional codes in channel division shares similarities with block coding methods, it possesses distinct characteristics. The study introduces the use of elements from the field of formal power Laurent series, with coefficients drawn from a finite field, as components of both the transmitted message and code word. This innovative approach enhances the flexibility and efficiency of the coding process. Furthermore, the research investigates the feasibility and conditions for simultaneous error correction during the code division of channels. This dual functionality has the potential to significantly improve the reliability and performance of communication systems. By examining these advanced coding techniques, the paper contributes to the ongoing development of more robust and efficient channel division methods in digital communications.

Cited by 0Open access

Code for Pseudo-Riemannian Graph Convolutional Networks

Xiong, Bo, Zhu, Shichao, Potyka, Nico et al. · Universitätsbibliothek Stuttgart · 2024

<p>This dataset is the official implementation of Pseudo-Riemannian Graph Convolutional Networks in PyTorch, based on <a href="https://github.com/HazyResearch/hgcn">HGCN implementation</a>. </p> <p>This code is used to reproduce the experiments of the paper. Datasets are provided in the /data directly. To execute the code, follow the instructions in the <a href="https://darus.uni-stuttgart.de/file.xhtml?fileId=300076">README.md</a> file. </p> <p>For more info, please check the paper or feel free to contact the authors for any inquiries. <p>

Cited by 0Open access

On Syndrome Decoding of Convolutional Code Cosets

Vladimir Sidorenko, Gerhard Kramer · 2024

Consider the following problem. Given a syndrome <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$s$</tex> of a terminated convolutional (or linear block) code <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$c$</tex> of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> over the field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{F}$</tex> with the parity check matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H$</tex> and a vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x\in \mathbb{F}^{n}$</tex>, find a vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$e\in \mathbb{F}^{n}$</tex> such that i) it has the syndrome <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$eH^{T}=5$</tex> and ii) minimizes the distortion <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d(x, e^{\backslash }$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d(x,\ e)$</tex> is a distance function. This problem is an instance of vector quantization and is called also trellis-coded quantization. Solution of this problem has many practical applications including telecommunication, data compression, and steganography. To solve the problem some publications suggest to use the minimal trellis of the coset and the trellis is designed for every given syndrome, which is complicated. In this paper, we propose using only one trellis of the original code <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$c$</tex> for all syndromes and a representative <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$e$</tex> of the coset, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$e$</tex> satisfies the condition i) only. We show a simple method to find a representative <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$e$</tex> of the coset for every given syndrome <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$s$</tex>.

Cited by 0

Viterbi decoder architecture for interleaved convolutional code

Jun Jin Kong, Keshab K. Parhi · 2003

Sn area efficient high speed Veterbi decoder architecture, which is based on the state-parallel architecture with register exchange path memory structure, for interleaved convolutional code is proposed By replacing each delay (or storage) element in state metrics memory (or path metrics memory) and path memory (or survival memory) with I delays, interleaved Viterbi decoder is obtained. The decoding speed of this decoder architecture is as fast as the operating clock speed. The latency of proposed interleaved Viterbi decoder is "decoding depth (DD) /spl times/ interleaving degree (I)', which is linearly increased with the interleaving degree I.

Cited by 2

The Golay convolutional code-some application aspects

S. Riedel, C. Weiss · IEEE Transactions on Information Theory · 1999

The Golay convolutional code and related block codes are investigated from an application point of view. We calculate the distance spectrum of the Golay convolutional code and the weight distributions of the block codes using the transfer-matrix method. The performance of the considered codes is shown and discussed. Moreover, the codes are applied as component codes of parallel concatenated codes which are iteratively decoded.

Cited by 7

Coded QAM using a binary convolutional code

Qi Wang, L.Y. Onotera · 2002

The motivation is to utilize commercially available high-speed, low-cost, single-VLSI-chip binary-encoding/Viterbi-decoding systems (codecs). A Gray code is used to map the encoder output to the QAM constellation, transforming the large Hamming distance (HD) of the binary code into a large squared Euclidian distance of (SED) of CQAM and providing the basis for a simple, effective way to generate the binary metrics used for binary Viterbi decoding. Although the scheme may be generalized to any 2/sup 2k/-QAM, the discussion focuses on the design of 16-ary CQAM with a rate-3/4 punctured convolutional code of constraint length 7. A binary metric generation method is used so that no modification of the existing VLSI codec chips is required. This method, in conjunction with eight-level quantization for the binary metric, is shown to be suboptimum with little loss in signal-to-noise ratio compared to direct use of M-ary unquantized metric. Since the overall system is nonlinear, both worst-case and average performance are considered. Analytical and Monte Carlo simulation results are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 2

Convolutional code performance in planetary entry channels

J.W. Modestino · NASA Technical Reports Server (NASA) · 1974

The planetary entry channel is modeled for communication purposes representing turbulent atmospheric scattering effects. The performance of short and long constraint length convolutional codes is investigated in conjunction with coherent BPSK modulation and Viterbi maximum likelihood decoding. Algorithms for sequential decoding are studied in terms of computation and/or storage requirements as a function of the fading channel parameters. The performance of the coded coherent BPSK system is compared with the coded incoherent MFSK system. Results indicate that: some degree of interleaving is required to combat time correlated fading of channel; only modest amounts of interleaving are required to approach performance of memoryless channel; additional propagational results are required on the phase perturbation process; and the incoherent MFSK system is superior when phase tracking errors are considered.

Cited by 0Open access

Systematic Convolutional Low Density Generator Matrix Code

Suihua Cai, Wenchao Lin, Xinyuanmeng Yao et al. · IEEE Transactions on Information Theory · 2021

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis.

Cited by 15

Generalized LDPC Codes with Convolutional Code Constraints

Muhammad Umar Farooq, Saeedeh Moloudi, Michael Lentmaier · arXiv (Cornell University) · 2020

Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a (2), (3)-regular compact graph. In this paper, we introduce a family of (d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> , d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> )-regular GLDPC codes with convolutional code constraints (CC-GLDPC codes), which form an extension of classical BCCs to arbitrary regular graphs. In order to characterize the performance in the waterfall and error floor regions, we perform an analysis of the density evolution thresholds as well as the finite-length ensemble weight enumerators and minimum distances of the ensembles. In particular, we consider various ensembles of overall rate R = 1/3 and R = 1/2 and study the trade-off between variable node degree and strength of the component codes. We also compare the results to corresponding classical LDPC codes with equal degrees and rates. It is observed that for the considered LDPC codes with variable node degree d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> > 2, we can find a CC-GLDPC code with smaller d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> that offers similar or better performance in terms of BP and MAP thresholds at the expense of a negligible loss in the minimum distance.

Cited by 0Open access

Code Clone Detection with Convolutional Neural Networks

Harun DİŞLİ, Ayşe Tosun · Bilişim Teknolojileri Dergisi · 2020

Similar or identical code portions which are generated by copying and reusing code portions within the source code are named as code clones. While so many works have been conducted to detect these clones, they generally use string comparison techniques and very few of them take advantage of popular learning based approaches, such as deep learning. This paper proposes a new approach based on a popular and successful image classification technique named as convolutional neural network. It simply tokenizes each candidate clone pair in order to generate image files. Then, convolutional neural network is used to classify these image data with labels “clone” and “not clone”. In order to train and test the network, clone and not clone pairs are chosen from a public database including six million methods. As a result, the approach gives 99% accuracy, effectively detects clones and not clones with 2-5% false alarms rates at method granularity.

Cited by 2Open access

Key Words: Punctured Convolutional Code, Mother Code, Blocked Polynomial Generator Matrix

2014

The rate of the channel code can be controlled by various methods. Puncturing is one of the methods of increasing the code rate, and the original code before puncturing is called the mother code. Any convolutional code is obtainable by puncturing some mother codes, and the process of finding the mother code is necessary for designing the optimum channel decoder. In this paper, we proved that any convolutional code has mother codes regardless of the puncturing pattern and showed that they must be

Cited by 0