ADC_13_Error_Corc.ppt

ANALOG & DIGITAL COMMUNICATION
By Engr. Hyder Bux Mangrio
Institute of Information & Communication Technologies
Mehran University of Engineering and Technology, Jamshoro.
10TL-BATCH
Today's Lecture:
46-52
ERROR DETECTION,CORRECTION & CONTROL
1/13/2023 1
hyder.bux@muet.edu.pk

Error Correction & Detection
 A major design criterion for all
telecommunication system is to achieve
error free transmission.
 Error, unfortunately do occur
 Two basic techniques employed
 One is to detect the error and request for
re-transmission of the corrupted message
 Second is to correct the error at the
receiving end without having to re-transmit
the message.
 Redundancy decreases system
1/13/2023 hyder.bux@muet.edu.pk 2

Parity
 Parity is the simplest & oldest method of error
detection.
 It is not very effective in data transmission.
 A single bit called parity bit is added to a group
of bits representing a letter, number or symbol.
 The parity bit is computed by the transmitting
device based on the number of 1 bit set in the
character.
 Parity can be either odd or even.

ODD-EVEN Parity
 If the odd parity is selected, the parity
is set to a 1 or 0 to make the total
number of 1 bits in character including
parity bit itself equal to an odd value.
 If the even parity is selected, the parity
is set to a 1 or 0 to make the total
number of 1 bits in character including
parity bit itself equal to an even value.

ODD-EVEN Parity
 The selection of even or odd parity is
generally arbitrary.
 The transmitting or receiving stations,
however, must be set to same mode.

Problem
 Check the even parity code for a “H” in
ASCII code. When two bits are
corrupted (6th and 7th ).

ODD-EVEN Parity
 Parity is primarily used for detecting
errors in a serial data character.
 Vertical Redundancy checking(VRC)
is used to correct single bit error in
received data stream.
 Longitudinal redundancy
checking(LRC) character is
transmitted with message signal to
determine error position with respect
to VRC.

VRC-LRC
 VRC-LRC is used to create a
crossmatrix type of configuration
where the VRC bit denotes the
row(character) and the LRC
column(bit position) of message’s
error bit.

9
Parity Examples - Using Even
Parity
Parity
1 0 0 1 1 1 0 0
0 0 1 1 1 0 0 1
1 1 1 0 1 1 1 0
Data
VRC
1 0 0 1 1 1 0 0
0 0 1 1 1 0 0 1
1 1 1 0 1 1 1 0
1 1 1 0 1 1 1 0
0 0 1 1 1 0 0 1
0 0 1 0 1 0 1 1
0 0 1 1 1 0 0 1
1 0 0 0 1 1 1 0 LRC
Data
Even Parity of 1’s LRC/VRC

Problem
 Determine the states of the LRC bits
for the asynchronous ASCII message
“Help!” using even VRC parity.

ASCII code

Cyclic Redundancy checking
 A power full method than the LRC and
VRC for detection in block is cyclic
redundancy checking CRC.
 CRC is most commonly used for error
detection in block transmission.
 Efficiency of error detection is 99.9%.
 CRC involves a division of the
transmitted message block by a
constant called the generator
polynomial. 1/13/2023 hyder.bux@muet.edu.pk 12

CRC
 The quotient is discarded and the
remainder is transmitted as BCC.
 The receiving station performs same
computation on received message
block.
 The computed remainder, or BCC is
compared to the remainder received
from the transmitter.
 If the two(received and transmitted)
match means no error otherwise there

CRC
 If the two do not match, either a
request a send for retransmission or
errors are corrected through the use of
special coding techniques.
 Cyclic codes contain a specific
number bits, governed by the size of
character within message block.
 Three of the mostly commonly used
cylic code are CRC-12, CRC-16 and
CRC-CCITT.

CRC
 Blocks containing characters that are
6-bit in length typically use CRC-12.
 Blocks formatted with 8-bit characters
typically use CRC-16 or CRC-CCITT
CRC-12 generator polynomial
G(x)= X12+X11+X3+X2+X+1
CRC-16 generator polynomial
G(x)= X16+X15+X2+1
CRC-CCITT generator polynomial
G(x)= X16+X12+X5+1

Computing the BCC of the
message block using CRC
Generator polynomial Quotient discarded
 Constant Message block
 Constant
 Next character
 Constant
 Next character
 Constant
 Remainder BCC

Computing the Block check
character
 The generating polynomial G(x) and
message polynomial M(x) used for
computing the BCC include degree
terms that represent position in a
group of bits that are binary 1 and
missing terms are represented by a 0.
 The highest degree in the polynomial
is one less than the number in the
binary code.

Steps
 If we let n equal to the total number of bits
in a transmitted block and k equal the
number of data bits, then n-k equals the
number of bits in BCC.
 Message block M(x) is multiplied by Xn-k to
achieve correct number bits of BCC.
 Resulting product is then divided by the
generator polynomial G(X)
 The quotient is discarded and the
remainder B(x) or BCC is transmitted at the
end of the message block

Steps
 The entire transmitted message block
can be represented by CRC
T(x)= Xn-k[M(x)]+B(x)

Problem
 The transmitted message block
contains total number of 14. Nine of
the 14 are data bits. And generator
polynomial, G(x)=X5+X2+X+1and
message polynomial,
M(x)=X8+X6+X3+X2+1. Compute the
value of BCC and T(x)

Problem.
 a 16-bit message using CRC-16 is
used. The total number of bits in
transmitted message block, n is 32.
the generator polynomial for CRC-16
is G(x)= X16+X15+X2+1 and message
polynomial is
M(x)=X15+X13+X11+X10+X7+X5+X4+1.
Compute the value BCC and T(x).

CHECKSUM
 Error detection through the use of
checksum.
 Checksum is a basically summation
quantity
 Like CRC and LRC, the checksum serves
as BCC.
 Checksum is transmitted at end of
message block. Commonly used in large
file transfer between mass device.

Types of checksum
 Single precision
 Double precision
 Honey Well
 Residue

Single Precision Checksum
 Performing a binary addition of each
n-bit data word in the message block.
 Any carry or overflow during the
addition process is ignored
 The resultant checksum is also n-bit
length.

Double Precision Checksum
 Extend the computed checksum to 2n
bits in length.

Honey Well Checksum
 An alternative form of the double precision
checksum.
 Its length is also 2n
 Honey well checksum is based on interleaving
consecutive data words to form double
precision checksum
 The advantage of the honey well is that
SAI and stuck at o bit errors occurring is
the same bit positions of all word can be
detected during the error detection
process. 1/13/2023 hyder.bux@muet.edu.pk 28

Residue Checksum
 Carryout of the MSB position of the
checksum word is “wrapped around”
and added to the LSB.

Error Correction
 Automatic Repeat reQuest
ARQ is to request the retransmission
of the data block received in error
 Forward Error Correction
 FEC is used in simplex transmission
or applications where it is impractical
or impossible to request a
retransmission of the corrupted
message block.

HAMMING CODE
 Hamming code employs the use of
redundant bits that are inserted into
the message stream for error
correction.
 Hamming bits are used to identify the
position of error. This position known
as the syndrome

Developing of Hamming code
 Hamming code for single-bit FEC
 10 bits will be used. The hamming bits
depends on the number of data bits.
2m ≥ n+1
Where n is number data bits + hamming
bits and m is number of hamming bits.
 Hamming bits can be placed
anywhere in the transmitted message.

 Compute the number of the Hamming
bits m required for a message of n
bits.
 Insert the Hamming bits H into orginal
message stream.
 Express each bit position containing a
1 as the m-bit binary number and
exclusive-OR each of the these
numbers together.
starting from the left bit positions. This
will be the hamming code.
 Place the value of the hamming bits

 The Hamming bits are extracted from
the received message stream and
exclusive-ORed with the binary
representation of the bit positions
containing a 1. this will detect the bit
position in error, or the syndrome.

Problem
 Given the 12 bit message
101110101011, determine the
following:
a. Number a Hamming bits, m required
b. Total number of the transmitted bits,
n
c. Hamming code
d. Syndrome if the bit position 10 is
corrupted.

ADC_13_Error_Corc.ppt

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