1. Applied Algorithmics - week8
Networking
Networking began its infancy in the mid -1960’s by the US Department of Defence (DoD). The original intention of networking was being developed to withstand a nuclear war. Telephone networks were to vulnerable and would terminate all conversations should a nuclear war occur.
ARPA (Advanced Research Projects Agency) was created in response with the launching of Russian Sputnik in ARPA decided that a DoD network should be packet switched networked consisting of a subnet and host computers. Experimental network research was awarded to UCLA, UCSB, SRI and Univ. of Utah in These areas were chosen because they all had a large number of ARPA contracts.
10/02/2018
Applied Algorithmics - week8

2. Applied Algorithmics - week8
Networking
These 4 universities also had different and completely incompatible host computers. ARPANET protocols were not suitable for running over multiple networks, so TCP/IP model and protocols were invented in ARPA awarded several other contracts and specifically University of California at Berkeley to integrate the protocols with the Berkeley UNIX operating system.
Berkeley developed a convenient program interface to the network and wrote many applications, utility, and management programs to make networking easier. In it early infancy, the OSI protocols were crushed and the TCP/IP protocols were already in widespread use. The OSI Model had seven layers because at the time, IBM had a propriety seven-layer protocol called SNA (Systems Network Architecture).
10/02/2018
Applied Algorithmics - week8

3. OSI-ISO 7-layer reference model
The OSI model divides the functions of a protocol into a series of layers. Each layer has the property that it only uses the functions of the layer below, and only exports functionality to the layer above.
A system that implements protocol behavior consisting of a series of these layers is known as a protocol stack or simply a stack. Protocol stacks can be implemented either in hardware or software, or a mixture of both.
Typically, only the lower layers are implemented in hardware, with the higher layers being implemented in software.
10/02/2018
Applied Algorithmics - week8

4. OSI-ISO 7-layer reference model
This OSI model is roughly adhered to in the computing and networking industry. Its main feature is in the interface between layers which dictates the specifications on how one layer interacts with another.
This means that a layer written by one manufacturer can operate with a layer from another (assuming that the specification is interpreted correctly). These specifications are typically known as Requests for Comments or (RFCs) in the TCP/IP community. They are ISO standards in the OSI community.
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Applied Algorithmics - week8

5. OSI-ISO 7-layer reference model
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Applied Algorithmics - week8

6. OSI-ISO 7-layer reference model - data encapsulation
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Applied Algorithmics - week8

7. OSI-ISO 7-layer reference model
Messages
Messages
Segments
Transport
layer
Transport
layer
Network
service
Network
service
Network
layer
Network
layer
Network
layer
Network
layer
End system a
Data link
layer
Data link
layer
Data link
layer
Data link
layer
End system b
Physical
layer
Physical
layer
Physical
layer
Physical
layer
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Applied Algorithmics - week8

8. Transmission errors in networks
Transmission errors are caused by:
thermal noise
impulse noise
signal distortion during transmission
crosstalk
voice amplitude signal compression
quantization noise
jitter
receiver and transmitter out of synchronization
10/02/2018
Applied Algorithmics - week8

9. Applied Algorithmics - week8
Error detection
Error detection is achieved via adding small but enough number of extra bits to deduce that there is an error but not enough bits to correct the error
If only error detection is employed in a network transmission the retransmission process is triggered to recover the frame (data link layer) or the packet (network layer).
At the data link layer, this is referred to as ARQ (Automatic Repeat reQuest).
10/02/2018
Applied Algorithmics - week8

10. Error detection and correction
Error correction requires some number of additional (redundant) bits to deduce what the correct bits must have been.
Example:
Hamming Codes
Superimposed codes (related to selectors)
FEC = Forward Error Correction found in MPEG-4
and others
10/02/2018
Applied Algorithmics - week8

11. Error detection and correction
Hamming codes:
Codewords in Hamming (error detecting and error correcting) codes consist of m data bits and r redundant bits.
Hamming distance between two strings represents the number of bit positions on which two bit patterns differ (mismatches).
relative Hamming distance refers to the ratio between the Hamming distance and the length of compared sequences
Hamming distance of the code is determined by the two codewords whose Hamming distance is the smallest.
error detection involves determining if codewords in the received message match closely enough legal codewords.
10/02/2018
Applied Algorithmics - week8

12. Error detection and correction
A code with poor distance properties
(b)
A code with good distance properties x o x o
code distance
x = codewords o = non-codewords
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Applied Algorithmics - week8

13. Error detection and correction
To detect properly d single bit errors, one needs to apply a d+1 code distance.
To correct properly d single bit errors, one needs to apply a 2d+1 code distance.
In general, the price for redundant bits is too expensive (!!) to do error correction for all network messages
Thus safety and integrity of network communication is based on error detecting codes and extra transmissions in case any errors were detected
10/02/2018
Applied Algorithmics - week8

14. Error-Detection System using Check Bits
Received information bits
Information bits
Recalculate check bits
Channel
Calculate check bits
Compare
Received check bits
Information accepted if check bits match
Check
bits
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Applied Algorithmics - week8

15. Cyclic Redundancy Checking (CRC)
cyclic redundancy check (CRC) is a popular technique
for detecting data transmission errors. Transmitted
messages are divided into predetermined lengths
that are divided by a fixed divisor. According to
the calculation, the remainder number is appended
onto and sent with the message. When the message
is received, the computer recalculates the remainder
and compares it to the transmitted remainder.
If the numbers do not match, an error is detected.
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Applied Algorithmics - week8

16. Error detection -- via parity of subsets of bits
Note
Check bits occupy
power of 2 slots ….
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Applied Algorithmics - week8

17. Detection via parity of subsets of bits
Consider 4 bit words.
Add 3 parity bits.
D3D2D1D0
P2P1P0 1 1
? ? ?
Each parity bit computed on a subset of bits
P2= D3 xor D2 xor D1 = 0 xor 1 xor 1 = 0
P1 = D3 xor D2 xor D0 = 0 xor 1 xor 0 = 1
P0= D3 xor D1 xor D0 = 0 xor 1 xor 0 = 1
Use this word bit arrangement
D3D2D1P2D0P1P0 1 1 1 1
Check bits occupy power of 2 slots!
10/02/2018
Applied Algorithmics - week8

18. Detection via parity of subsets of bits - no error occurred
D3D2D1P2D0P1P0
First, we send:
No error occurred. But how do we know that? 1 1 1 1
Later, someone gets:
D3D2D1P2D0P1P0 1 1 1 1
And computes:
B2= P2 xor D3 xor D2 xor D1 = 0 xor 0 xor 1 xor 1 = 0
If all
B2,B1,B0 = 0
B1= P1 xor D3 xor D2 xor D0 = 1 xor 0 xor 1 xor 0 = 0
there are no errors!
B0= P0 xor D3 xor D1 xor D0 = 1 xor 0 xor 1 xor 0 = 0
These equations come from how we computed:
P2= D3 xor D2 xor D1 = 0 xor 1 xor 1 = 0
P1 = D3 xor D2 xor D0 = 0 xor 1 xor 0 = 1
P0= D3 xor D1 xor D0 = 0 xor 1 xor 0 = 1
10/02/2018
Applied Algorithmics - week8

19. Detection via parity of subsets of bits - single bit is twisted
D3D2D1P2D0P1P0
What if a cosmic ray hit D1? How would we know that?
First, we send: 1 1 1 1
D3D2D1P2D0P1P0
Later, someone gets: 1 1 1
And computes:
B2= P2 xor D3 xor D2 xor D1 = 0 xor 0 xor 1 xor 0 = 1
B2B1B₀ = 101 = 5
B1= P1 xor D3 xor D2 xor D0 = 1 xor 0 xor 1 xor 0 = 0
And what does 101= 5 mean?
B0= P0 xor D3 xor D1 xor D0 = 1 xor 0 xor 0 xor 0 = 1 7 6 5 4 3 2 1
The position of the flipped bit!
To repair, just flip it back
We number the least significant bit with 1, not 0!
0 is reserved for “no errors”.
D3D2D1P2D0P1P0 1 1 1
10/02/2018
Applied Algorithmics - week8

20. Detection via parity of subsets of bits - magic trick revealed
For any 4 bit word
we add 3 parity bits
D3D2D1D0
P2P1P0 1 1
? ? ?
Observation: The parity bits need to encode “no error” scenario, plus a number for each bit (both data and parity bits)
For p parity bits and d data bits: d + p + 1 ≤ 2p
10/02/2018
Applied Algorithmics - week8

21. Detection via parity of subsets of bits - magic trick revealed
For any 4 bit word
we add 3 parity bits
D3D2D1D0
P2P1P0
Question: Why do we arrange bits?
Start by numbering, 1 to 7. 7 6 5 4 3 2 1
D3 D D0 P0
With this order, an odd parity means an error in 1,3,5, or 7.
So, P0 is the right parity bit to use:
D3D D0P1P₀
D3D2D1P2₁P₀
etc ... each bit narrows down the suspect bits, until it is certain.
D3D2D1P2D0P1P0
An odd parity means a mistake must be in 2, 3, 6, or 7 -- the four numbers possible if P1 = 1!
10/02/2018
Applied Algorithmics - week8

22. Detection via parity of subsets of bits - magic trick revealed
For any 4 bit word
we add 3 parity bits
D3D2D1D0
P2P1P0
P2 = D3 xor D2 xor D1
P1 = D3 xor D2 xor D0
P₀ = D3 xor D1 xor D0
D₃D₂D₁P₂D₀P₁P₀
7 bits can code 128 numbers, but only 16 of these numbers are legal. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
It takes 3 bit flips to move from one legal
number to another (for all 16 numbers)
If only one bit flips, we can always figure out the “closest” legal number, and correct the number.
10/02/2018
Applied Algorithmics - week8