Tree-codifications and convolutional codes

1980 ◽  
Vol 3 (4) ◽  
pp. 401-417
Author(s):  
Adrian Atanasiu
Keyword(s):  
Error Correction ◽  
Convolutional Code ◽  
Convolutional Codes ◽  
Convolutional Coding ◽  
New Methods

The paper deals with some C-grammars and tree-codification properties extending the result in [1]. We try to exhibit new aspects and important results, e.g. that any algebraic convolutional code is a particular case of a tree-code, as well as the finite forms of the code-sets. They can result in new methods of decodification and error correction in the case of convolutional coding.

Hybrid Arq Type I Based On Convolutional Code

2012 ◽  
Author(s):  
Hazilah Mad Kaidi ◽  
Muhammad Ibrahim
Keyword(s):  
Error Correction ◽  
Error Control ◽  
Convolutional Code ◽  
Convolutional Codes ◽  
Packet Transmission ◽  
Type I ◽  
Hybrid Arq ◽  
Convolutional Coding ◽  
Error Correction Capability ◽  
Control Scheme

Hibrid Automatik Permintaan Ulangan (HARQ), sejenis kaedah mengawal kesilapan berdasarkan pada kod konvolutional di penghantaran paket merentasi saluran tanpa wayar telah dikemukakan. Analisis prestasi daya pemprosesan dan kadar–bit–silap (BER), merujuk kepada simulasi panjang kekangan yang berbeza (K=3 dan K=4) dan kadar kod (1/2 dan 1/3) di kod konvolutional pada HARQ jenis I telah dipersembahkan. Beberapa kebolehupaya kesilapan pembetulan disediakan pada setiap penghantaran semula paket dan maklumat yang boleh dibaiki semula dengan sendiri dari setiap penghantaran atau penghantaran semula jikalau kesilapan adalah berada di antara julat kebolehupaya pembetulan kesilapan. Simulasi HARQ adalah terhad kepada tiga penghantaran semula bagi setiap satu SNR dalam beberapa kali perulangan. Kata kunci: Istilah–Hibrid ARQ; ARQ; pengkodan konvolusional; kawalan kesilapan A Hybrid Automatic Repeat reQuest (HARQ), error control scheme based on a convolutional code for packet transmission over wireless channels was proposed. The analysis of the throughput and bit–error rate (BER) performance, according to the different constraint lengths (K=3 and K=4) and code rate (1/2 and 1/3) of convolutional codes on HARQ type I simulation scheme are presented. Certain error correction capability is provided in each (re)transmitted packet, and the information can be recovered from each transmission or retransmission alone if the errors are within the error correction capability. Simulation of HARQ is limited up to three retransmissions for each SNR in several iterations. Key words: Terms–Hybrid ARQ; ARQ; convolutional coding; error control

A General Framework of Algorithm-Based Fault Tolerance Technique for Computing Systems

2014 ◽  
pp. 1-21 ◽  
Author(s):  
Hodjatollah Hamidi
Keyword(s):  
Fault Tolerance ◽  
Error Correction ◽  
General Framework ◽  
Fault Tolerant ◽  
Convolutional Code ◽  
Numerical Algorithms ◽  
Convolutional Codes ◽  
Computing Systems ◽  
Specific Level ◽  
Computing Paradigm

The Algorithm-Based Fault Tolerance (ABFT) approach transforms a system that does not tolerate a specific type of faults, called the fault-intolerant system, to a system that provides a specific level of fault tolerance, namely recovery. The ABFT philosophy leads directly to a model from which error correction can be developed. By employing an ABFT scheme with effective convolutional code, the design allows high throughput as well as high fault coverage. The ABFT techniques that detect errors rely on the comparison of parity values computed in two ways. The parallel processing of input parity values produce output parity values comparable with parity values regenerated from the original processed outputs and can apply convolutional codes for the redundancy. This method is a new approach to concurrent error correction in fault-tolerant computing systems. This chapter proposes a novel computing paradigm to provide fault tolerance for numerical algorithms. The authors also present, implement, and evaluate early detection in ABFT.

scholarly journals Bluetooth Low Energy Error Correction Based on Convolutional Coding

2021 ◽  
Vol 2093 (1) ◽  
pp. 012033
Author(s):  
Yue Cao ◽  
Zaixin Liu ◽  
Longyu Wu
Keyword(s):  
Internet Of Things ◽  
Information Transmission ◽  
Error Correction ◽  
Signal To Noise Ratio ◽  
Convolutional Codes ◽  
Correction Method ◽  
Low Energy ◽  
High Signal ◽  
Bluetooth Low Energy ◽  
Convolutional Coding

Abstract Contemporarily, the Internet of Things (IoT) is recently a newly emerging technology for connecting small devices into a platform; the IoT has been an increasingly demanded front-edge technology in terms of connecting different devices using information transmission and storage technology. To adapt to the small capacities of device batteries, Bluetooth Low Energy is adopted as the protocol of communication. However, the existing standards do not have a suitable and specific error correction method. As there is no ideal information transmission channel, there must be errors that occurred during message transmission. The performance and capacity of error correction become decisive factors in evaluating how efficient the IoT communication system performs. This article uses convolutional coding—a better-performing coding scheme than block coding—to correct errors in information transmission and reception on Internet of Things devices. It is better competent to control and correct bit errors in information transmission. To achieve this goal, convolutional coding algorithms devised by Dr Justin Coon at the University of Oxford have been referred to. By simulation using MATLAB, it has been found that the error rate is enhanced significantly for high Signal-to-Noise Ratio (SNR) in convolutional codes compared to uncoded messages.

scholarly journals Area and Energy Efficient QCA Based Compact Serial Concatenated Convolutional Code Encoder

2022 ◽  
Vol 2161 (1) ◽  
pp. 012025
Author(s):  
B.S. Premananda ◽  
T.N. Dhanush ◽  
Vaishnavi S. Parashar
Keyword(s):  
Energy Dissipation ◽  
Error Correction ◽  
Forward Error Correction ◽  
Convolutional Code ◽  
Internal Clock ◽  
Random Errors ◽  
Clock Generation ◽  
Convolutional Coding ◽  
External Clock ◽  
Forward Error

Abstract Quantum-dot Cellular Automata (QCA) is a transistor-less technology known for its low power consumption and higher clock rate. Serial Concatenated Convolutional Coding (SCCC) encoder is a class of forward error correction. This paper picturizes the implementation of the outer encoder as a (7, 4, 1) Bose Chaudhary Hocquenghem encoder that serves the purpose of burst error correction, a pseudo-random inter-leaver used for permuting of systematic code words and finally the inner encoder which is used for the correction of random errors in QCA. Two different architectures of the SCCC encoder have been proposed and discussed in this study. In the proposed two architectures, the first based on external clock signals whereas the second based on internal clock generation. The sub-blocks outer encoder, pseudo-random inter-leaver and inner encoder of the SCCC encoder are optimized, implemented and simulated using QCADesigner and then integrated to design a compact SCCC encoder. The energy dissipation is computed using QCADesigner-E. The proposed SCCC encoder reduced the total area by 46% and energy dissipation by 50% when compared to the reference SCCC encoder. The proposed encoders are more efficient in terms of cell count, energy dissipation and area occupancy respectively.

Research on Network Coding Based on Convolutional Codes

2013 ◽  
Vol 694-697 ◽  
pp. 2270-2273
Author(s):  
Hai Ping Liu ◽  
Shi Bin Su
Keyword(s):  
Outage Probability ◽  
Network Coding ◽  
Convolutional Code ◽  
Convolutional Codes ◽  
Probability Analysis ◽  
System Model ◽  
Code Scheme ◽  
Cooperation Network

For the system with two sources, three relays and one destination, cooperation network convolutional code scheme is presented to solve the relay sharing problem. The scheme searches out convolutional code corresponding to system model, and then decides relay coding structure. Outage Probability analysis and BER simulation show that 3-order diversity is achieved.

THE ANALYTICAL MODEL OF NOISE IMMUNITY CALCULATION OF COMMUNICATION SYSTEMS WITH MULTI-POSITION TYPES OF MODULATION AND CONVOLUTIONAL CODING

2020 ◽  
Author(s):  
Э.Б. ЛИПКОВИЧ ◽  
А.А. СЕРЧЕНЯ
Keyword(s):  
Computer Simulations ◽  
Communication Systems ◽  
Error Probability ◽  
Noise Immunity ◽  
Convolutional Code ◽  
Analytical Models ◽  
Signal To Noise ◽  
Probability Of Error ◽  
Information Efficiency ◽  
Convolutional Coding

Получены математические модели расчета отношений сигнал/шум и несущая/шум, требуемые для обеспечения заданной вероятности ошибки на выходе декодера с «мягким» решением, без необходимости вычисления коэффициентов спектра сверточного кода и выполнения процедур компьютерного моделирования характеристик помехоустойчивости. Приведены расчетные выражения для определения исправляющей способности декодера, энергетического выигрыша от кодирования и информационной эффективности систем связи в зависимости от параметров многопозиционных видов модуляции, сверточного кодирования и вероятности ошибки в информационном бите. По полученным аналитическим моделям построены зависимости и дана оценка результатов исследований. Mathematical models are obtained for calculating signal-to-noise and carrier-to-noise ratios required to provide a given error probability at the decoder output with a “soft” solution and without calculating the convolutional code spectrum coefficients and performing computer simulations of noise immunity characteristics. Calculation expressions are given to determine the correcting ability of the decoder, the energy gain from coding, and the information efficiency of communication systems depending on the parameters of multi-position types of modulation, convolutional coding, and the probability of error in the information bit. Dependencies are constructed according to the obtained analytical models and the research results are evaluated.

scholarly journals On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2962
Author(s):  
Ángel Luis Muñoz Muñoz Castañeda ◽  
Noemí DeCastro-García ◽  
Miguel V. Carriegos
Keyword(s):  
Coding Theory ◽  
Convolutional Codes ◽  
Codes Over Rings ◽  
Input State ◽  
First Order ◽  
Convolutional Coding ◽  
Artinian Rings ◽  
Base Ring ◽  
Order Representation ◽  
Classical Construction

In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.

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