scholarly journals Codes on Key Errors

2014 ◽  
Vol 14 (2) ◽  
pp. 31-37 ◽  
Author(s):  
P. K. Das
Keyword(s):  
Coding Theory ◽  
Linear Codes ◽  
Simultaneous Detection ◽  
Communication Channels ◽  
Upper Bounds ◽  
Parity Check ◽  
Lower And Upper Bounds ◽  
Different Types

Abstract Coding theory has started with the intention of detection and correction of errors which have occurred during communication. Different types of errors are produced by different types of communication channels and accordingly codes are developed to deal with them. In 2013 Sharma and Gaur introduced a new kind of an error which will be termed “key error”. This paper obtains the lower and upper bounds on the number of parity-check digits required for linear codes capable for detecting such errors. Illustration of such a code is provided. Codes capable of simultaneous detection and correction of such errors have also been considered.

scholarly journals Codes correcting and simultaneously detecting solid burst errors

2013 ◽  
Vol 2 (1) ◽  
pp. 143-150
Author(s):  
P.K. Das
Keyword(s):  
Coding Theory ◽  
Linear Codes ◽  
Communication Channels ◽  
Upper Bounds ◽  
Parity Check ◽  
Lower And Upper Bounds ◽  
Parity Check Matrix ◽  
Burst Error ◽  
Check Matrix ◽  
Error Detecting

Detecting and correcting errors is one of the main tasks in coding theory. The bounds are important in terms of error-detecting and -correcting capabilities of the codes. Solid Burst error is common in several communication channels. This paper obtains lower and upper bounds on the number of parity-check digits required for linear codes capable of correcting any solid burst error of length b or less and simultaneously detecting any solid burst error of length s(>b) or less. Illustration of such a code is also provided.Keywords: Parity check matrix, Syndromes, Solid burst errors, Standard arrayDOI: 10.18495/comengapp.21.143150  

REPEATED BURST ERROR CORRECTING LINEAR CODES

2008 ◽  
Vol 01 (03) ◽  
pp. 303-335 ◽  
Author(s):  
B. K. Dass ◽  
Rashmi Verma
Keyword(s):  
Data Transmission ◽  
Coding Theory ◽  
Linear Codes ◽  
Practical Importance ◽  
Practical Interest ◽  
Lower And Upper Bounds ◽  
Burst Error ◽  
The Subject ◽  
Error Detecting ◽  
Parallel Growth

Many kinds of errors in coding theory have been dealt with for which codes have been constructed to combat such errors. Though there is a long history concerning the growth of the subject and many of the codes developed have found applications in numerous areas of practical interest, one of the areas of practical importance in which a parallel growth of the subject took place is that of burst error detecting and correcting codes. The nature of burst errors differ from channel to channel depending upon the behaviour of channels or the kind of errors which occur during the process of data transmission. In very busy communication channels, errors repeat themselves more frequently. In view of this, it is desirable to consider repeated burst errors. The paper presents lower and upper bounds on the number of parity-check digits required for a linear code correcting errors in the form of repeated bursts. An upper bound for a code that detects m-repeated bursts has also been derived. Illustrations of several codes that correct 2-repeated bursts of different lengths have also been given.

scholarly journals Blockwise and Low Density Key Error Correcting Codes

2020 ◽  
Vol 5 (6) ◽  
pp. 1234-1248
Author(s):  
Pankaj Kumar Das ◽  
Subodh Kumar
Keyword(s):  
Linear Code ◽  
Communication System ◽  
Linear Codes ◽  
Upper Bounds ◽  
Error Correcting Codes ◽  
Low Density ◽  
Code Length ◽  
Lower And Upper Bounds ◽  
Noisy Channels ◽  
Know How

To protect the information from disturbances created by noisy channels, redundant symbols (called check symbols) with the information symbols are added. These extra symbols play important role for the efficiency of the communication system. It is always important to know how much these check symbols are required for a code designed for a specific purpose. In this communication, we give lower and upper bounds on check symbols needed to a linear code correcting key errors of length upto p which are confined to a single sub-block. We provide two examples of such linear codes. We, further, obtain those bounds for the case when key error occurs in the whole code length, but the number of disturbing components within key error is upto a certain number. Two examples in this case also are provided.

scholarly journals Bounds on linear codes capable of detecting, locating and correcting of repeated burst errors prevailing in multiple sub-blocks

2020 ◽  
Vol 39 (6) ◽  
pp. 1577-1596
Author(s):  
Pankaj Kumar Das ◽  
Subodh Kumar
Keyword(s):  
Linear Codes ◽  
Upper Bounds ◽  
Lower And Upper Bounds

Linear codes are presented that can detect, locate and correct all repeated burst errors of length b or less which occur in multiple sub-blocks. We obtain lower and upper bounds on the number of check digits for the existence of these codes. Three examples, one for each type of code, are provided.

scholarly journals Non Classical Structures and Linear Codes

2021 ◽  
Author(s):  
Surdive Atamewoue Tsafack
Keyword(s):  
Finite Field ◽  
Fuzzy Sets ◽  
Coding Theory ◽  
Linear Codes ◽  
Parity Check ◽  
Parity Check Matrix ◽  
Check Matrix ◽  
Generating Matrix

This chapter present some new perspectives in the field of coding theory. In fact notions of fuzzy sets and hyperstructures which are consider here as non classical structures are use in the construction of linear codes as it is doing for fields and rings. We study the properties of these classes of codes using well known notions like the orthogonal of a code, generating matrix, parity check matrix and polynomials. In some cases particularly for linear codes construct on a Krasner hyperfield we compare them with those construct on finite field called here classical structures, and we obtain that linear codes construct on a Krasner hyperfield have more codes words with the same parameters.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

Sign in / Sign up

Export Citation Format

Share Document