1. Error Detection and Correction (Pengesanan dan Pembetulan ralat)

2. DKT 224 DATA COMMUNICATION & NETWORK
Causes of error
1.Distance of data transmission
delay,attenuation
2.Enviroment change of
temperature,rain,fog
3.Medium of transmission
4.Devices modem,mux,repeater, etc
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3. DKT 224 DATA COMMUNICATION & NETWORK
Types of Error
an error occurs when a bit is altered between transmission and reception
single bit errors
only one bit altered
caused by white noise
burst errors
contiguous sequence of B bits in which first last and any number of intermediate bits in error
caused by impulse noise or by fading in wireless
effect greater at higher data rates
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Figure Single-bit error
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Figure Burst error of length 8
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Errors Detection
To detect or correct errors, we need to send extra (redundant) bits with data.
Redundant – extra bits added at each transmission data.
Errors detection techniques
A) Asynchronous - i) Codewords checking - Vertical
Redundancy Checking (VRC).
ii) Block sum check – Checksum
B) Synchronous - i) Longitudinal Redundancy
Checking (LRC).
ii) Cyclic Redundancy
Checking (CRC).
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7. Vertical Redundancy Checking (VRC).
Extra bits are added to each codeword before transmits.
Purpose- to identify nos of bits 1 in codeword is either even or odd.
Even or odd parity is depend on the system set up, either in even parity or odd parity checking.
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8. Vertical Redundancy Checking (VRC) cont..
Even parity checking
If nos of bits 1 in codewords is odd, bits level is set at 1.
If nos of bits 1 in codewords is even, bits level is set at 0.
Odd parity checking
If nos of bits 1 in codewords is odd, bits level is set at 0.
If nos of bits 1 in codewords is even, bits level is set at 1.
Pros & cons
Simple mechanism for detecting error in single bit error BUT failed in burst errors.
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Figure Datawords and codewords in block coding
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Block Sum Check
When blocks of character are being transmitted, there is an increased probability that a character (the block) will contain a bit error.The probability of a block containing an error is known as block error rate
All data are collected and grouped together in block for transmission.(Block coding)
Refer to figure 10.5
Datawords are divided into m segments with same size (n bits).
Sum-up all segments using binary arithmetics
Checksum is using one’s complement of resulted sum.
The checksum value is attached to original codeword before transmit.
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Example:
Data to be sent: size of checksum = 8 bits
Generate Checksum 1)
segment segment2
2) add both segments
segment
segment
sum using binary arithmetic
checksum using one’s complement
Attach checksum to original data, therefore the transmitted data will be
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Checksum checking
1.Received data unit are divided into m segment with 8 bits each
segment segment segment3
2. add all segments using binary arithmetic
segment
segment
segment
sum using binary arithmetic
checksum complimentary =0. This shows that received data unit is
free from errors
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Error detection: Synchronisation Transmission - Cylic Redundancy Check (CRC)
Cylic Redundancy Check (CRC)- very efficient and widely use in data communication.
The division operation is equivalent to performing the Exclusive-OR operation bit by bit in parallel as each bit in the frame is processed.
Data block to be sent will be divided by CRC generator/divisor
CRC process
1. To obtain the CRC code, additional n bits 0 are added to data block, where n<1bit from generator bits. M(x) =frame contents,i.e data block + additional bits.
2. M(x)/G(x), where G(x)= CRC generator, the Remainder (R(x)) is then the frame check sequence (FCS) which is appended at the tail of the information digits.
3. The resultant CRC bits will replace all additional bits 0 in step1.If the quotient bits < n bits, add bits 0 on the most left bit until n bits. This data unit will be sent to receiver.
4. Similarly, on receipt,the received bits stream including the FCS digits is again divided by the same generator polynomial.
if R(x)=0,therefore no errors are present or some bits are corrupted, but the encoder
failed to detect them.
if R(x) = 0,therefore an error is present.
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EXAMPLES
1. A series of 8 bit message blocks (frames) is to be transmitted across a data link using a CRC for error detection. A generation polynomial of is to be used. Use an example to illustrate the following :
(a) The FCS generation process
(b) The FCS checking process
2. Data to be transmitted is and using a CRC generator of
1101. With the information given , show the generation process
and checking process of CRC.
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Polynomial Codes
Polynomial arithmetic instead of check sums
Implemented using shift-register circuits
Also called cyclic redundancy check (CRC) codes
Most data communications standards use polynomial codes for error detection
Polynomial codes also Polynomials instead of vectors for codewords basis for powerful error-correction methods
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16. Binary Polynomial Arithmetic
Binary vectors map to polynomials
(ik-1 , ik-2 ,…, i2 , i1 , i0)  ik-1xk-1 + ik-2xk-2 + … + i2x2 + i1x + i0
Addition:
(x7 + x6 + 1) + (x6 + x5) = x7 + x6 + x6 + x5 + 1
= x7 +(1+1)x6 + x5 + 1
= x7 +x since 1+1=0 mod2
Multiplication:
(x + 1) (x2 + x + 1) = x(x2 + x + 1) + 1(x2 + x + 1)
= x3 + x2 + x) + (x2 + x + 1)
= x3 + 1
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17. Binary Polynomial Division
Division with Decimal Numbers
35 ) 1222 3
105 17 2 4
140
divisor
quotient
remainder
dividend
1222 = 34 x
dividend = quotient x divisor +remainder 32
x3 + x + 1 ) x6 + x5
x x4 + x3
x5 + x4 + x3
x x3 + x2
x x2
x x2 + x x
= q(x) quotient
= r(x) remainder
divisor
dividend
+ x
+ x2 x3
Polynomial Division
Note: Degree of r(x) is less than degree of divisor
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18. Polynomial Coding Code has binary generating polynomial of degree n–k
g(x) = xn-k + gn-k-1xn-k-1 + … + g2x2 + g1x + 1
k information bits define polynomial of degree k – 1
i(x) = ik-1xk-1 + ik-2xk-2 + … + i2x2 + i1x + i0
Find remainder polynomial of at most degree n – k – 1
g(x) ) xn-k i(x)
q(x)
r(x)
xn-ki(x) = q(x)g(x) + r(x)
Define the codeword polynomial of degree n – 1
b(x) = xn-ki(x) + r(x)
n bits
k bits
n-k bits
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19. Polynomial example: k = 4, n–k = 3
Generator polynomial: g(x)= x3 + x + 1
Information: (1,1,0,0) i(x) = x3 + x2
Encoding: x3i(x) = x6 + x5
x3 + x + 1 ) x6 + x5
x3 + x2 + x
x x4 + x3
x5 + x4 + x3
x x3 + x2
x x2
x x2 + x x
1011 )
1110
1011
1010
010
Transmitted codeword:
b(x) = x6 + x5 + x
b = (1,1,0,0,0,1,0)
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20. The Pattern in Polynomial Coding
All codewords satisfy the following pattern:
b(x) = xn-ki(x) + r(x) = q(x)g(x) + r(x) + r(x) = q(x)g(x)
All codewords are a multiple of g(x)!
Receiver should divide received n-tuple by g(x) and check if remainder is zero
If remainder is nonzero, then received n-tuple is not a codeword
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21. Standard Generator Polynomials
CRC = cyclic redundancy check
CRC-8:
CRC-16:
CCITT-16:
CCITT-32:
= x8 + x2 + x + 1
ATM
Bisync
= x16 + x15 + x2 + 1
= (x + 1)(x15 + x + 1)
HDLC, XMODEM, V.41
= x16 + x12 + x5 + 1
IEEE 802, DoD, V.42
= x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1
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Error Correction
There are two main methods of error correction:
i) Correction by retransmission.
ii) Forward Error Correction.
- Error can be detected and correct it at the receiver (the receiver must be intelligent).
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23. Error Correction Process
Figure 6.7 shows in general how this is done. On the transmission end, each k-bit block of data is mapped into an n-bit block (n > k) called a codeword, using an FEC (forward error correction) encoder. The codeword is then transmitted. During transmission, the signal is subject to impairments, which may produce bit errors in the signal. At the receiver, the incoming signal is demodulated to produce a bit string that is similar to the original codeword but may contain errors. This block is passed through an FEC decoder, with one of four possible outcomes:
1. If there are no bit errors, the input to the FEC decoder is identical to the original codeword, and the decoder produces the original data block as output.
2. For certain error patterns, it is possible for the decoder to detect and correct those errors, the FEC decoder is able to map this block into the original data block.
3. For certain error patterns, the decoder can detect but not correct the errors, the decoder simply reports an uncorrectable error.
For certain, typically rare, error patterns, the decoder does not detect that any errors have occurred and maps the incoming data block into a block different from the original.
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24. How Error Correction Works
adds redundancy to transmitted message
can deduce original despite some errors
eg. block error correction code
map k bit input onto an n bit codeword
each distinctly different
if get error assume codeword sent was closest to that received
means have reduced effective data rate
In essence, error correction works by adding redundancy to the transmitted message. The redundancy makes it possible for the receiver to deduce what the original message was, even in the face of a certain level of error rate. In this section we look at a widely used form of error-correcting code known as a block error-correcting code. If wish to transmit blocks of data of length k bits, so map each k-bit sequence into a unique n-bit codeword, which differ significantly from each other. Typically, each valid codeword reproduces the original k data bits and adds to them (n – k) check bits to form the n-bit codeword. Then if an invalid codeword is received, assume the valid codeword is the one that is closest to it, and use the input bit sequence associated with it.
The ratio of redundant bits to data bits, (n – k)/k, is called the redundancy of the code, and the ratio of data bits to total bits, k/n, is called the code rate. The code rate is a measure of how much additional bandwidth is required to carry data at the same data rate as without the code. For example, a code rate of 1/2 requires double the transmission capacity of an uncoded system to maintain the same data rate.
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Block Code Principles
The Hamming distance between two words
is the number of differences between
corresponding bits.
The minimum Hamming distance is the smallest Hamming distance between all possible pairs in a set of words.
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Example
Let us find the Hamming distance between two pairs of words.
1. The Hamming distance d(000, 011) is 2 because
2. The Hamming distance d(10101, 11110) is 3 because
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Example
Find the minimum Hamming distance of the coding scheme in Table 10.1.
Solution
We first find all Hamming distances.
The dmin in this case is 2.
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28. To guarantee the detection of up to s errors in all cases, the minimum
Note
To guarantee the detection of up to s errors in all cases, the minimum
Hamming distance in a block code must be dmin = s + 1.
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Error Control
Digital transmission systems introduce errors
Applications require certain reliability level
Data applications require error-free transfer
Voice & video applications tolerate some errors
Error control used when transmission system does not meet application requirement
Error control ensures a data stream is transmitted to a certain level of accuracy despite errors
Two basic approaches:
Error detection & retransmission (ARQ)
Forward error correction (FEC)
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Error Control (Cont..)
ARQ :
Stop and wait
Go back N
Selective repeat
Forward error correction (FEC)
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Stop and wait ARQ
One frame at time. After sending, sender waits for ACK signal and doesn't send any further frames until it is received.
If the received frame is damaged or lost, the receiver discards it and does not send an ACK. If a certain time, known as the timeout, passes without ACK, the sender sends the frame again.
Problem 1 - is where the ACK sent by the receiver is damaged or lost. In this case, the sender doesn't receive the ACK, times out, and sends the frame again. Now the receiver has two copies of the same frame, and doesn't know if the second one is a duplicate frame or the next frame of the sequence carrying identical data.
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32. Stop and wait ARQ (cont..)
Problem 2 - is when the sender's timeout runs out before the frame reaches the receiver. In this case the sender resends the same packet. Eventually the receiver gets two copies of the same frame, and sends an ACK for each one. The sender, waiting for a single ACK, receives two ACKs, which may cause problems if it assumes that the second ACK is for the next frame in the sequence.
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33. Stop and wait ARQ (cont..)
To avoid these problems, the most common solution is to define a 1 bit sequence number which is attached to the header of the frame. This sequence number alternates (from 0 to 1) in subsequent frames. When the receiver sends an ACK, it attaches the sequence number of the next packet it expects. This way, the receiver can detect duplicated frames by checking if the frame sequence numbers alternate. If two subsequent frames have the same sequence number, they are duplicates, and the second frame is discarded. Similarly, if two subsequent ACKs have the same sequence number, they are acknowledging the same frame.
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Go back N ARQ
Protocol, in which the sending process continues to send a number of frames specified by a window size without receiving an ACK packet from the receiver.
The receiver process keeps track of the sequence number of the next frame it expects to receive, and sends that number with every ACK it sends.
If a frame from the sender does not reach the receiver, the receiver will stop acknowledging received frames.
Once the sender has sent all of the frames in its window, it will detect that all of the frames since the first lost frame are outstanding, and will go back to sequence number of the last ACK it received from the receiver process and fill its window starting with that frame and continue the process over again.
Demo :
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Selective Repeat ARQ
Protocol, in which the sending process continues to send a number of frames specified by a window size even after a frame loss. Unlike Go-Back-N ARQ, the receiving process will continue to accept and acknowledge frames sent after an initial error.
The receiver process keeps track of the sequence number of the earliest frame it has not received, and sends that number with every ACK it sends. If a frame from the sender does not reach the receiver, the sender continues to send subsequent frames until it has emptied its window.
The receiver continues to fill its receiving window with the subsequent frames, replying each time with an ACK containing the sequence number of the earliest missing frame. Once the sender has sent all the frames in its window, it re-sends the frame number given by the ACKs, and then continues where it left off.
Demo :
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