scholarly journals Construction for obtaining trellis run length limited error control codes from convolutional codes

2017 ◽  
Vol 68 (5) ◽  
pp. 401-404
Author(s):  
Peter Farkaš ◽  
Frank Schindler
Keyword(s):  
Error Control ◽  
Convolutional Codes ◽  
Block Codes ◽  
Parity Check ◽  
Error Control Codes ◽  
Run Length ◽  
Linear Block Codes ◽  
Low Density Parity Check ◽  
New Construction ◽  
The One

Abstract Recently a new construction of run length limited block error control codes based on control matrices of linear block codes was proposed. In this paper a similar construction for obtaining trellis run length limited error control codes from convolutional codes is described. The main advantage of it, beyond its simplicity is that it does not require any additional redundancy except the one which is already contained in the original convolutional error control code. One example is presented how to get such a code from a convolutional low density parity check code.

scholarly journals Run length limited error control codes construction based on one control matrix property

2017 ◽  
Vol 68 (4) ◽  
pp. 322-324
Author(s):  
Peter Farkaš ◽  
Frank Schindler
Keyword(s):  
Error Control ◽  
Specific Property ◽  
Block Codes ◽  
Low Density ◽  
Parity Check ◽  
Simple Method ◽  
Error Control Codes ◽  
Run Length ◽  
Low Density Parity Check ◽  
Matrix Property

AbstractIn this manuscript a simple method is presented for constructing run length limited error control codes from linear binary block codes. The run length limited properties are obtained via addition of a carefully chosen fixed binary vector - a modifier to all codewords without introducing any additional redundancy. Modifier selection is based on a specific property, which can be found in some of the linear binary block codes control matrices. Similar known methods are based on properties of generator matrices. However some codes are specified via control matrices, for example low density parity check codes. The method proposed in this letter could be applied to some of them directly. This is illustrated in this manuscript using example in which a run length limited low density parity check code is obtained from Gallager code.

scholarly journals Construction of Error Control Run Length Limited Codes Exploiting Some Parity Matrix Properties

2015 ◽  
Vol 66 (3) ◽  
pp. 182-184 ◽  
Author(s):  
Katarína Farkašová ◽  
Peter Farkaš ◽  
Martin Rakús ◽  
Eugen Rušický ◽  
Adāo Silva ◽  
...  
Keyword(s):  
Error Control ◽  
Electronic Devices ◽  
Block Code ◽  
Error Control Codes ◽  
New Approach ◽  
Run Length ◽  
Consumer Electronic ◽  
Check Matrix ◽  
Matrix Properties ◽  
New Construction

Abstract Error control codes (ECC) as well as translation codes (TC) are used today in many different systems such as computer storages, communications systems and consumer electronic devices. ECC introduce redundancy into the encoded digital sequence in order to decrease the number of errors at output of its decoder [1]. TC introduce redundancy, in order to translate any digital sequence at the input of TC encoder to such output sequence, which fulfills constrains deduced from practical requirements. It is possible to construct codes, which have both of these properties, so called Transcontrol codes or their subclass error control run length limited (ECRLL) codes. In this manuscript a new approach to construction of EC-RLL codes is presented. The new construction is based on some parity check matrix properties of a linear binary block code from which the new EC-RLL code is obtained.

scholarly journals On run-length limited error control codes constructed from binary product codes

2018 ◽  
Vol 69 (3) ◽  
pp. 245-249
Author(s):  
Peter Farkaš ◽  
Tomáš Janvars ◽  
Katarína Farkašová ◽  
Eugen Ružický
Keyword(s):  
Error Control ◽  
Error Control Codes ◽  
Run Length ◽  
One Dimensional ◽  
Product Codes ◽  
Binary Component ◽  
Control Code ◽  
Error Control Code ◽  
The One

Abstract In this paper it is presented that run-length limited error control codes could be constructed from any two or more- dimensional binary product codes as long as at least one of the one-dimensional binary component codes is or can be converted to a run-length limited error control code. The advantages of this construction are as follows: It does not require any additional redundancy except that which is already contained in the original error control code and that the encoding and decoding procedure used for the underlying error control code do not to be changed

scholarly journals Deep Neural Networks Classification via Binary Error-Detecting Output Codes

2021 ◽  
Vol 11 (8) ◽  
pp. 3563
Author(s):  
Martin Klimo ◽  
Peter Lukáč ◽  
Peter Tarábek
Keyword(s):  
Neural Networks ◽  
Categorical Data ◽  
Coding Theory ◽  
Hamming Distance ◽  
Activation Function ◽  
Block Codes ◽  
Ease Of Use ◽  
Linear Block Codes ◽  
Binary Coding ◽  
The One

One-hot encoding is the prevalent method used in neural networks to represent multi-class categorical data. Its success stems from its ease of use and interpretability as a probability distribution when accompanied by a softmax activation function. However, one-hot encoding leads to very high dimensional vector representations when the categorical data’s cardinality is high. The Hamming distance in one-hot encoding is equal to two from the coding theory perspective, which does not allow detection or error-correcting capabilities. Binary coding provides more possibilities for encoding categorical data into the output codes, which mitigates the limitations of the one-hot encoding mentioned above. We propose a novel method based on Zadeh fuzzy logic to train binary output codes holistically. We study linear block codes for their possibility of separating class information from the checksum part of the codeword, showing their ability not only to detect recognition errors by calculating non-zero syndrome, but also to evaluate the truth-value of the decision. Experimental results show that the proposed approach achieves similar results as one-hot encoding with a softmax function in terms of accuracy, reliability, and out-of-distribution performance. It suggests a good foundation for future applications, mainly classification tasks with a high number of classes.

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