Chapter 6 - William Stallings, Data and Computer Communications

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Data and Computer
Communications
Chapter 6 – Digital Data
Communications Techniques
Asynchronous and
Synchronous Transmission
 timing
problems require a mechanism to
synchronize the transmitter and receiver


receiver samples stream at bit intervals
if clocks not aligned, drifting will sample at
wrong time after sufficient bits are sent
 two


techniques to synchronize
asynchronous transmission
synchronous transmission
Asynchronous Transmission
Asynchronous - Behavior
 simple
 cheap
 overhead
of 2 or 3 bits per char (~20%)
 good for data with large gaps (keyboard)
Synchronous Transmission

block of data transmitted, sent as a frame
 clocks must be synchronized



need to indicate start and end of block


can use separate clock line
or embed clock signal in data
use preamble and post-amble
more efficient (lower overhead) than
asynchronous
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 are in error
caused by impulse noise or by fading in wireless
effect is greater at higher data rates
Error Detection
 will
have errors
 detect using error-detecting code
 added by transmitter
 recalculated and checked by receiver
 still chance of undetected error
 parity


parity bit set so frame has even number of
ones (even parity) or odd number of ones
(odd parity)
even number of bit errors goes undetected
Error Detection Process
Error Detection
 Pb=
Probability a bit is received in error,
Bit Error Rate (BER)
 P1= Probability a frame is received with no
error
 P2= Probability a frame is received with
undetected error
 F = number of bits / frame
 Then, P1= (1- Pb)F , P2= (1- P1)
Error Detection
# ISDN has 64 Kbps channel, 1 frame with
undetected error per day is expected, (1
frame = 1000 bits), Calculate the number
of Frames / day and P2.
actual Pb= 10-6, can we achieve the
above P2?
 If
Cyclic Redundancy Check
 one
of most common and powerful checks
 for block of k bits, transmitter generates an
n-k bit frame check sequence (FCS)
 Transmits n bits which is exactly divisible
by some number
 receiver divides frame by that number


if no remainder, assume no error
for math, see Stallings chapter 6
Cyclic Redundancy Check
 Basis:
Modulo-2 arithmetic (X-or for + or -)
 Message, M = 1010001101
 Pattern, P = 110101 (MSB & LSB = ‘1’)
 FCS = ? (5 bits) (01110)
 Multiply the Message by 25, then divide by
the Pattern. Remainder is added with the
Message and transmitted.
 P is one bit longer than FCS.
Cyclic Redundancy Check
Selection of polynomial P:
- Should not be divisible by X
- Should be divisible by X+1
Benefits:
- Detects all burst errors that affect odd
number of bits
- Detects all burst errors of length less than
or equal to degree of the polynomial
Cyclic Redundancy Check
-
Detects, with high probability, all burst
errors of length greater than the degree of
the polynomial
Cyclic Redundancy Check
# CRC-12 (X12+ X11+X3+X+1)
Degree: 12
Detects all burst errors that affects odd
number of bits, Detects all burst errors of
length less than or equal to 12, Detects
(99.97 percent of) all burst errors of length
more than or equal to 12.
Cyclic Redundancy Check
 Digital
Logic Implementation:
 Message, M = 1010001101 = X9+
X7+X3+X2+1, Pattern, P = 110101 = Poly.?
 Register length = FCS
 Presence of a gate corresponds to a term
in polynomial P, excluding 1 (X0) and Xn-k
Error Correction

correction of detected errors usually requires
correct data block to be retransmitted
 not appropriate for wireless applications



bit error rate is high causing lots of retransmissions
when propagation delay long (satellite) compared with
frame transmission time, resulting in retransmission of
frame in error plus many subsequent frames
instead need to correct errors on basis of bits
received
 error correction provides this
Error Correction Process
Error Correction
 2-dimensional
Parity:
 “Data is arranged in 2-dimensional array and
parity bit is added for each row and column”

PV
0 1 1 00
“Detects and Corrects all single
10100
bit errors”
1 1 1 01
“Detects all odd number of
01111
bit errors and some even
0 1 0 1 0 PH number of bit errors”
How Error Correction Works
 adds
redundancy to transmitted message
 can deduce original despite some errors
 e.g. 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
 for
math, see Stallings chapter 6
 Much reduced effective data rate
Block Code Principles
 Hamming
distance = difference in # of bits,
 p = 011011, q = 110001, d (p,q) = ?
 Data
Code
 00
00000
 01
00111
 10
11001
 11
11110
 # Find the distance between all the valid
codes (in pairs) on this slide.
Block Code Principles
 Received
00100, valid? Can it be corrected?
 Find distances and the minimum.
 ‘Select the valid code at the minimum
distance’
 Received 00100, correct word?
 More than one minimum distance!!!
 01010 (Invalid) => valid 00000 and 11110
 ‘Equidistance of 2’ => can detect, not correct
Hamming ECC
 ‘use
of extra parity bits to allow the
position identification of a single error’
 1. Mark all bit positions that are powers of
2 as parity bits. (positions 1, 2, 4, 8, 16,
etc.)
 2. All other bit positions are for the data to
be encoded. (positions 3, 5, 6, 7, 9, 10, 11,
12, 13, 14, 15, etc.)
Hamming ECC
 3.
Each parity bit calculates the parity for
some of the bits in the code word. The
position of the parity bit determines the
sequence of bits that it checks.
 Position 1: checks bits (1,3,5,7,9,11,...) –
Alternate
Position 2: checks bits
(2,3,6,7,10,11,14,15,...) – Alternate 2-bits
 Position 4: checks bits
(4,5,6,7,12,13,14,15,20,21,22,23,...) Alternate 4-bits
Hamming ECC
 Position
8: checks bits (8-15,24-31,4047,...) – Alternate 8-bits
4. Set the parity bit to create even parity.
A
byte of data: 10011010
 Place the data word, leaving spaces for
the parity bits: _ _ 1 _ 0 0 1 _ 1 0 1 0
Calculate the parity bits.
Hamming ECC
 Position
1 checks bits 1,3,5,7,9,11:
? _ 1 _ 0 0 1 _ 1 0 1 0. set position 1 to a
0: 0 _ 1 _ 0 0 1 _ 1 0 1 0
 Position 2 checks bits 2,3,6,7,10,11:
0 ? 1 _ 0 0 1 _ 1 0 1 0. set position 2 to a
1: 0 1 1 _ 0 0 1 _ 1 0 1 0
 Position 4 checks bits 4,5,6,7,12:
0 1 1 ? 0 0 1 _ 1 0 1 0. set position 4 to a
1: 0 1 1 1 0 0 1 _ 1 0 1 0
Hamming ECC
 Position
8 checks bits 8,9,10,11,12:
0 1 1 1 0 0 1 ? 1 0 1 0. set position 8 to a
0: 0 1 1 1 0 0 1 0 1 0 1 0
 Final code word: 011100101010.
 Finding and fixing a corrupted bit:
 Suppose that the word was received as
011100101110 instead.
 The method is to verify each check bit.
Hamming ECC
 Parity
bits 2 and 8 are incorrect. It is 2 + 8
= 10, that bit position 10 is the location of
the bad bit and needs to be inverted.
 # Test if these Hamming-code words are
correct. If one is incorrect, indicate the
correct code word. Also, indicate what the
original data was.
 010101100011
 111110001100
 000010001010
Problem
# For each data unit of following sizes, find
the minimum number of redundancy bits
needed to correct single bit error (using
Hamming code). Specify their positions.
a) 12
b) 16
c) 24
d) 64
Find also the utilization of the code space.
Burst Error Correction
 Hamming
Code can be used:
 - Arrange N data elements (with ECC) in
two dimension
 - Transmit all the first bits from N elements
 - Transmit all the second bits from N
elements
 - And so on …
 Organize them as N elements at receiver.
Burst Error Correction
 Any
burst error of length <= N is seen as a
single bit error in a data element and can
be corrected.
 X2 X1 X0
X2 Y2 Z2
X2 X1 X0
 Y2 Y1 Y0
X1 Y1 Z1
Y2 Y1 Y0
 Z2 Z1 Z0
X0 Y0 Z0
Z2 Z1 Z0
 Original
Transmit
Received and
Organized
Line Configuration - Topology
 physical
arrangement of stations on
medium

point to point - two stations
• such as between two routers / computers

multi point - multiple stations
• traditionally mainframe computer and terminals
• now typically a local area network (LAN)
Line Configuration - Topology
Line Configuration - Duplex

classify data exchange as half or full duplex
 half duplex (two-way alternate)



only one station may transmit at a time
requires one data path
full duplex (two-way simultaneous)


simultaneous transmission and reception between
two stations
requires two data paths
• separate media or frequencies used for each direction
Summary
 asynchronous
verses synchronous
transmission
 error detection and correction
 line configurations

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