Error detection and correction

Error Detection and Correction

Presented By:

Maria Akther
Dept.: Computer Science
Daffodil International University

Data can be corrupted during transmission.
some applications require that errors be detected
and corrected.

1.Single-Bit Error
2.Burst Error

In a single-bit error only 1 bit in the data unit has
changed.
Example:

The effect of a single-bit error on a data unit in shown fig.The
impact of the change, imagine that each group of 8bit is an
ASCII character with a 0 bit added to the left. In fig.00000010
was sent ,meaning start of text,but 00001010 was received,
meaning line feed.

A burst error means that 2 or more bits in the data unit have
changed.
Example:

The effect of a burst error on a data unit.In this
case,0100010001000011 was sent,but 0101110101100011 was
received.the length of the burst is measured from the first
corrupted bit to the last corrupted bits

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.

Detection
In error detection, we are looking only if any error has
occurred. A single bit error is the same for us as a
burst error.

Correction
In correction, we need to know the exact number of
bits that are corrupted and their location in the
message. The number of the errors and size of
message are important.

 Forward error correction
 Retransmission

 Block coding
 Convolution coding

In block coding, we divide our message into blocks,
each of k bits, called datawords. We add r redundant
bits to each block to make the length n = k + r. The
resulting n-bit blocks are called codewords.

Two conditions are met to detect an error by the
receiver-
2.The receiver has a list of valid codewords.

3.The original codeword has changed to an invalid
one.

The sender encodes the dataword 01 as 011 and
sends it to the receiver.
 The receiver receives 011.
 The receiver receives 111.

Assume the sender creates dataword 01 as
01011.The codeword is corrupted during
transmission and 01001 is received.

• The Hamming distance between two words
is the number of differences between
corresponding bits.

• Hamming distance between two words x and
y can be shown as d(x, y)

1. The Hamming distance d(000, 011) is 2

2. The Hamming distance d(10101, 11110) is 3

Error detection and correction

Error detection and correction

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