REPORT ON

Error Detection & Correction

of

Burst Error

Assigned by,

Ashraful Hoque Lecturer

CSE Department Southeast University

Submitted by,

Tanzila Islam

Section : 01 30th Batch of CSE

Date of Submission: 25,April 2015

Hamming Code, Burst Error Correcting of Burst Error

A study on Burst Error

April, 2015

Ashraful Hoque Lecturer, Department of CSE, Southeast University. Dear Sir,

Here is the Term Paper on Error correction & detection of Burst Error that you

asked us to submit on April, 2015.

In this report the concept of Hamming Code, Burst Error, and how to detect &

correct it are discussed first. Then described those using figure.

It was my pleasure to complete this report. I have prepared this report with my

utmost earnestness and sincere effort. Please let me know, if you have any query

concerning the report.

Thank you.

Sincerely yours,

Tanzila Islam

ID#2012000000022

30th Batch, Sec-01

Dept. of CSE

Southeast University

Abstract

The codes we have considered so far have been designed to correct random errors. In general, a t-error correcting code corrects all error patterns of weight t or less in a codeword of block length n. It may be, however, that certain channels introduce errors localized in short intervals rather than at random. For example, in storage mediums, errors resulting from physical irregularities or structural alteration, perhaps flaws in the original medium or damage due to wear and tear, are not independent, but rather tend to be spatially concentrated. Similarly, interference over short time intervals in serially transmitted radio signals causes errors to occur in bursts. There exist codes for correcting such burst errors. Many of these codes are cyclic. We briefly consider burst-error correcting codes in this section.

Hamming code:

Hamming code is a set of error-correction code s that can be used to detect and

correct bit errors that can occur when computer data is moved or stored. Reliable

communication is assured if the hamming distance between the transmitter and

receiver is less than or equal to one. Error coding is a method of detecting and

correcting these errors to ensure information is transferred intact from its source to

its destination. Error coding is used for fault tolerant computing in computer

memory, magnetic and optical data storage media, satellite and deep space

communications, network communications, cellular telephone networks, and almost

any other form of digital data communication.

Types of Errors: Whenever bits flow from one point to another, they are subject to unpredictable changes because of interference. This interference can change the shape of the signal. In a single-bit error, a 0 is changed to a 1 or a 1 to a 0. The term single-bit error means that only 1 bit of a given data unit (such as a byte, character, or packet) is changed from 1 to 0 or from 0 to 1. The term burst error means that 2 or more bits in the data unit have changed from 1 to 0 or from 0 to 1.

Burst error:

The term burst error means that two or more bits in the data unit have changed

from 0 to 1 or vice-versa. Even if we know what type of errors can occur, we can’t

simple recognize them. We can do this simply by comparing this copy received with

another copy of intended transmission. In this mechanism the source data block is

send twice. The receiver compares them with the help of a comparator and if those

two blocks differ, a request for re-transmission is made. To achieve forward error

correction, three sets of the same data block are sent and majority decision selects

the correct block. These methods are very inefficient and increase the traffic two or

three times. Fortunately there are more efficient error detection and correction

codes. There are two basic strategies for dealing with errors. One way is to include

enough redundant information (extra bits are introduced into the data stream at the

transmitter on a regular and logical basis) along with each block of data sent to

enable the receiver to deduce what the transmitted character must have been. The

term burst errors suggest that those errors are cor-related, i.e. if one bit is

erroneous; it is quite likely that the adjacent bits have also been corrupted. When

one refers to the term burst error of size m, what is meant is that the distance in bits

from the first to the last error in the frame is at most m – 1 while the intermediate

bits may or may not be corrupted.

Redundancy: The central concept in detecting or correcting errors is redundancy. To be able to detect or correct errors, we need to send some extra bits with our data. These redundant bits are added by the sender and removed by the receiver. Their presence allows the receiver to detect or correct corrupted bits. The concept of including extra information in the transmission for error detection is a good one. But instead of repeating the entire data stream, a shorter group of bits may be appended to the end of each unit. This technique is called redundancy because the extra bits are redundant to the information: they are discarded as soon as the accuracy of the transmission has been determined. Figure 8 shows the process of using redundant bits to check the accuracy of a data unit. Once the data stream has been generated, it passes through a device that analyses it and adds on an appropriately coded redundancy check. The data unit, now enlarged by several hits, travels over the link to the receiver. The receiver puts the entire stream through a checking function. If the received hit stream passes the checking criteria, the data portion of the data unit. Correcting Burst Errors: Consider a linear code C. If all burst errors of length t or less occur in distinct cosets of a standard array for C, then each can be uniquely identified by its syndrome, and all such errors are then correctable. Furthermore, if C is a linear code capable of correcting all burst errors of length t or less, then all such errors must occur in distinct cosets. To see this, suppose C can correct two such distinct errors e1 and e2 which lie in some coset Ci of C. Then e1- e2 = c is a non-zero codeword. Now suppose e1 is a received vector. How should it be decoded? The codeword 0 could have been altered to e1 by the error e1, or the codeword c could have been altered to e1 by the error e2. We get a contradiction, since the code cannot correct this burst error of length t or less. Thus, we conclude that these errors must lie in distinct cosets. Theorem: A linear code C can correct all burst errors of length t or less if and only if all such errors occur in distinct cosets of C.

Consider a binary representation of length l such that l > 1. Now, if non-zero bits of the representation are cyclically confined to l consecutive positions with nonzero first and last positions, we say that this is burst of length l.

A code is said to be l-burst-error-correcting code if it has ability to correct burst errors up to length I.

Example: 00110010000 is a burst of length 5, while 010000000000001000 is a burst of length 6.

A burst of length l that is obtained by any cyclic shift of a burst of length l is called Wraparound burst of length I. Following are typical parameters that a burst can have 1. Location of burst - Least significant digit of burst is called as location of that burst. 2. Pattern of burst - A burst pattern of a burst of length l is defined as the polynomial b(x) of degree l − 1.