Transcript CS3502-data link layer - Naval Postgraduate School

CS3502:
Data and Computer Networks
DATA LINK LAYER - 1
data link layer : objectives
 thorough
understanding of DL layer --
 where/how
 service
it fits into network/other layers
it provides (to higher layers)
 services
it uses (from lower layer)
 synchronous/asynchronous
 error
transmission
detection and correction
 describe
flow control protocols: sliding window
 specify/verify
 elementary
basic DL protocols
performance analysis of DL protocols
data link layer

phys. layer subject to errors; not reliable; and
only moves information as bits, which alone
are not meaningful. DL layer adds these, and
combines bits into frames, or messages.

purpose of DL: transform unreliable physical
bit stream into reliable data communications
link...

PHY + DL = DATA COMMUNICATIONS
 MAC
layer (media access control) - takes place
of DL layer in LANs (together with LLC)
data link layer : functions
 framing
 frames
and frame synchronization
marked by sync/async technique
 error
control
 flow
control
 addressing
 control
information, data on same link (unlike
EIA232)
 link
management (3 phases)
data link layer : framing
 bits
must be grouped into frames or messages
 frames
marked by synchronous transmission:
frame starts, ends with a special flag pattern
 Meathods
 Character
 Start
Count
+ End Characters
 Flags
 Physical
 Finite
Layer Code Violation
state machine for Bit stuff flag 011110
data link layer : framing
 allows
bits to be grouped into fields, subgroups;
two main types are data and control bits.
 several
 error
types of control bits; some for
detection and/or correction
 addressing
 flow
control
 other
control type information
data link layer : error control
3
basic techniques in this course (more complex
techniques exist)
 parity

very simple and easy error detection
 CRC

checking
- cyclic redundancy check
more complex, but very effective and efficient
 Hamming

code
limited error correction; based on complex combinations of
parity checks
data link layer : parity checking
 to
a group of data bits add a single extra bit,
known as the parity bit. This bit is chosen to
make the total number of 1s in the group even (or
odd). Called even (odd) parity checking.
 example:
data bits 0011001; add parity bit 1 -->00110011.
 exercise:
construct a FSM to
(1) output correct parity bit
(2) read a string and decide parity
data link layer : parity checking
 what
is the problem with simple parity checking
as described? (show how to fool it)
X X X P
 LRC - double parity checks improve this
X X X X P
X X X X P
X X X X P
P P P P P
 show how to fool this error check
 improves error probability by factor of 102 - 104
data link layer : error probabilities
let PB = Prob [single bit error];
then (1 - PB ) = Prob [no error]
for group of Nb bits, define
P1 : Prob[no errors]
P2 : Prob[undetected error]
P3 : Prob[detected error]
By definition,
P1 + P 2 + P 3 = 1
data link layer : error probabilities
 examples
in a 10 bit word, what is P[only bit 3 wrong]?
P[exactly 1 error]? P[exactly 3 errors]?
P[at most 3 errors]? P[3 errors or more]?
P[3 bit burst error, with other 7 bits correct]?
data link layer : error probabilities
Case 1: no error detection
Then what are these 3 probabilities for Case 1?
P1 = Pr [no error] =
P2 = Pr [undetected error] =
P3 = Pr [detected error] =
example
data link layer : error probabilities
Case 2: error detection using parity bit
 for
even parity, even # errors goes undetected; so P2 is
Pr(even # of errors)
P1 = (1 - PB)Nb
Nb/2
P2 =  NbC2a Pb 2a (1-Pb)Nb-2a
a=1
P3 = 1- P2 - P1
hint: what is Pr(1 error)? Pr(2 errors)? ... k errors?
data link layer : error probabilities
 frame
probabilities, parity checking
 given a frame, sent as a sequence of
words/bytes, each with a parity check. What are
Pf1, Pf2, and Pf3?
Pf1 = probability of no error in the whole frame
Pf2 = probability of an undetected error and no
detected error anywhere else in the frame
Pf3 = probability of an detected error
data link layer : error probabilities
 Nb =
no.bits/word; Nc = no.words/frame.
Pf1 =
P1Nc
where: P1 is the probability of no error in a word
Nc
Pf2 =  NcCi P2 i [ (1-Pb)Nb]Nc -i
i=1
where: P2 is the probability of undetected error in a word
Pb is the probability there is an error in a bit
Pf3 = 1 - Pf1 - Pf2
error checking : CRC
 stronger
error check needed
 idea:
insert a group of bits in the frame, which
serve as as more powerful check.
 added
bits (frame check sequence, FCS) cause
the resulting frame to be exactly divisible by a
predetermined number.
 modulo-2
no carries
arithmetic used; binary addition with
 examples
error checking : CRC
let M denote data message, k bits long
to M, add F, the FCS, which is n bits long
resulting transmitted frame is T,
T = 2 n M + F = M| F
is evenly divisible by some pattern P, a sequence of
(n + 1) bits.
Q: how is F calculated from M and P?
error checking : CRC
F
is n bits, pattern P is (n + 1) bits
 1st, last bits of P must be 1
 FCS F computed from M, P:
F = remainder R, when dividing
2n M / P = Q + R
note: this “division” is modulo-2, no carries
example : let M = 110011; k = 6; n = 3; p = 1001. Find
F and T. (answer next page)
error checking : CRC
 quotient
Q = 110101; remainder R = 101; so T =
110011101.
 check:
divide T by P, R should be 0.
 example
: M = 1010001101; P = 110101. Find F, T.
Then check it.
error checking : CRC
 CRC
summary
 all
single and double bit errors
 all odd numbers of errors
 all burst errors smaller than n
 most larger burst errors
 If error detected, frame is retransmitted; does NOT
correct error.
 both
CRC and parity checking widely used; CRC
used in many network protocols, in addition to
data link layer, including most LANs.
 CRC can be implemented efficiently in
hardware... computation done bit by bit
error checking : CRC
 shift
implementation
register, XOR gates
 1 XOR gate for each “1” in pattern P, minus 1.
 (n-1) 1-bit shift registers
 example : show logic circuit for P - 110101.
error checking : Hamming code
 correct
a single bit error
 detect multiple errors
 extended parity checking; ie, redundant parity
bits
Idea:
parity bits appear in positions corresponding to the
nodes of a binary tree; data bits appear in
positions corresponding to the leafs. If a bit is in
error, the other bits “point” to it by their related
positions in the tree.
error checking : Hamming code
 each
parity bit appears in a position
corresponding to a power of 2: k = 0,1,2,4,8,16,...
 bits checked by parity bit in position n are:
1. itself
2. continue for next n bits (including itself)
3. off (don’t check) next n bits
4. on (check) the next n bits
and continue to end of message.
Example: for the data 1101101, show Hamming
coded mesage.
error checking : Hamming code
 How
is single error bit detected?
example: suppose 111100010101 is received.
1st parity bit, position 1:
2nd parity bit, position 2:
3rd parity bit, position 4:
4th parity bit, position 8:
0 parity bit, position 0:
result:
error checking : Hamming code
 example:
suppose 0111011 received; is it correct?
Q: for a n-bit message, approximately how many
bits are needed?
Summary, error correction:



more complex codes correct multiple errors
require more redundancy, overhead. Also more time... so
not widely used in communications.
do have a place in longer distance communications -- eg,
deep space, etc. In fact could be critical to long distance
(time) communications