Advanced Computer Networks

Chapter 2: Direct Link Networks

Direct Link (Point-to-Point) Networks

• Simplest network possible, consisting of two hosts and one link

• Look into different function at the link level– Encoding– Framing– Error detection/correction– Reliable delivery– Media access control

Host A physical Link

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Host B

2.1.1 Nodes

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Figure 2.1: Example workstation architecture

Figure 2.1: Example workstation architecture

Figure 2.3: Memory bandwidth on a modern PC-class machine

2.1.2 Links• Cables• Leased Lines• Last-Mile Links• Wireless Links

4Figure 2.4: Electromagnetic Spectrum

Physical Medium• Signals travel through the medium and represent

bits.• Shannon’s Capacity Theorem

C = B log2(1+S/N)

• Defines the upper bound on the link capacity C in Hz.

• Can be used to evaluate the “error-free” bandwidth of a line

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Shannon’s Theorem: Example• Voice-grade phone line: B =3,300 -300 Hz = 3 KHz• Typical SNR = 30 dB, where

dB = 10 x log10(S/N)

• For 30 dB S/N =1,000C = 3,000 x log2(1+1,000) ≈ 30 Kbps

• Higher bandwidth B (in Hz), higher capacity• Higher S/N, higher capacity• Can we have unlimited capacity?

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Shannon’s Theorem: Example 2• Can the signal be weaker than the noise?• Assume capacity of 50 KHz (approx 50Kbps) over

1MHz• The required SNR would then be

C = B log2(1+S/N)

S/N = 2C/B - 1 = 0.035 or -14.5 dB • Think of spread spectrum communications• Transmit a weak signal over a large bandwidth

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2.2 Encoding• Map binary bits into signals

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Figure 2.8 Signals (electrical, electromagnetic) travel between signaling components; bit flow between adaptors

2.2 Encoding (Contd.)• Example: Low signal represents a 0, high signal

represents a 1• Non Return-to-Zero (NRZ)

• Problem: Long periods of silence (zero) or high signals are possible– Baseline wander (receiver loses track of reference sig)– Clock recovery (receiver loses clock synchronization)

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Encoding: More Schemes• NRZ Inverted (NRZI): Switch from current state to

represent a 1• Manchester: XOR the bit stream with the clock

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4B/5B Encoding Scheme• Encode 4-bit symbols into 5-bit Codes• 24 symbols must be mapped to 24 code-words out

of the possible 25. Table 2.4, Page 83. • Each codeword has no more than one starting

zero, and no more than two trailing zeros• No more than 3-consequtive zeros• Then use NRZI to solve the consecutive 1s

problem• 80% efficiency (1 bit is overhead)

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2.3 Framing• The process of grouping bits into frames

(messages or packets)• Typically implemented by the network adaptor

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Byte-Oriented Framing• In such protocols, frame is collection of bytes• Need to indicate the beginning and end of a frame

• Example: Point-to-Point (PPP) protocol, used by IP

– Start of Text: Flag: 01111110– Address and Control field usually carry default values– Protocol: IP or IPX Start of header– Payload: 1,500 bytes– Checksum: 2 or 4 bytes

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Overhead: 8/1508 =0.5%

Byte-counting Framing• Include the # of bytes in the frame as a field in the

header• Digital Data Communications Protocol (DDCMP)

• Count: Specifies # of bytes in the body• CRC ensures that count field is not corrupted

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Bit-oriented Framing• High-Level Data Link Control (HDLC)

• Beginning/end of frame, flag: 01111110• Instead of inserting bytes do bit stuffing to avoid

detection of flag in data.• Sender adds a 0 after five consecutive 1s• Receiver removes zero after five 1s

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Example of Bit-stuffing• Sender

– 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0

• Receiver– 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0

• Length of frame– Variable, depends on the data – We can calculate and optimize the overhead of bit stuffing

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0 0 0 0

x x x x

2.3.3 Clock-Based Framing (SONET)• SONET: Synchronous Optical Network• Ninety rows of nine bytes each• First three bytes of each rare overhead• Data XORed with known sequence to ensure

synchronization

17Figure 2.16: A SONET Synchronous Transport Signal (STS)-1: Frame (51.84 Mbps)

2.4 Error Detection • Types of errors

– Isolated errors: Bit errors that do not affect other bits – Burst errors: A cluster of bits in which a number of

errors occur

• Burst errors increase with data rate– 1μs of impulse noise or fading effect will affect

• At most 2 bits when data rate is 1Mbps• At most 101 bits when data rate is 100Mbps

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Dealing with Errors• Receiver must be aware that an error occurred in

a frame– Need to have an error detection mechanism

• Receiver must receive the correct frame• Two possible strategies

– Add information redundancy to correct errors (error correcting codes)

– Ask sender to re-send frame (retransmission strategies).

• In practice both are employed19

Error Detection Methods• Single parity checks

– Append a single parity bit at end of frame. Parity is 1 if # of ones is odd, and zero otherwise

– Example: 0 1 1 0 1 0 1 0 1 1 0 0 ← parity– Single parity check can detect any odd # of errors– Cannot tell where the error took place or how many

occurred– Not useful for burst errors

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Two-dimensional Parity• Arrange bits of a frame into a two dimensional array

• Can detect all 1-, 2-, and 3-bit errors, and most 4-bit errors but not all

• Can also correct 1-bit errors, if it is known that a one-bit error occurred

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1 0 0 1 0 1 0 1

0 1 1 1 0 1 0 0

1 1 1 0 0 0 1 0

1 0 0 0 1 1 1 0

0 0 1 1 0 0 1 1

1 0 1 1 1 1 1 0

Checksum • Treat data as 16-bit words• Add all words complement one and then append

the sum at the end of data• Complement one arithmetic

– Negative numbers are inverted positive ones – Carry from MSB is added to the result– Example : (-5) + (-3) = (-0101)+(-0011) = (1010) +(1100)

= 0110 + 1 = 0111 = ones complement of 8

• What type of errors can remain undedected?

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Cyclic Redundancy Check (CRC)• Add k redundant bits on a n-bit message

– Design goal k<<n so that overhead is low– Example: 32-bit CRC adequate for 12,000 bits (1,500)

bytes

• Represent (n+1)-bit messages as n degree polynomials

• Example: 10011010 maps to x7 + x4 + x3 + x1

• The bits of the message to be transmitted become the coefficients of the polynomial

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Polynomial Arithmetic• Facts:

– Any polynomial B(x) is divisible by a polynomial C(x) if deg(B) ≥ deg(C). C(x) is called the divisor

– If C(x) and B(x) are of the same degree, the remainder is obtained by subtracting C(x) from B(x)

– Modulo 2 arithmetic, subtraction is an XOR operation between coefficients

• Example B(x) = x3 + 1, C(x) = x3 + x2 + 1 • Remainder: R(x) = x2

• B(x) = 1001, C(x) =1101, R(x) = 0100 (XOR of B(x), C(x))

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CRC Calculation• Goal: For message M(x), and divisor C(x),

construct polynomial P(x) that is divisible by C(x)• C(x) known to both sender and receiver• Process

– Step 1: multiply M(x) by xk (add k zeros at the end of message) and obtain T(x)

– Step 2: Divide T(x) by C(x)– Step 3: Subtract the remainder R(x) from T(x). – Step 4: Obtain P(x) = M(x)|R(x) divisible by C(x)

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Example: CRC Calculation• M = 10011010, C(x) = x3 + x2 +1

• T(x) = 10011010 | 0000• R(x) = 101• P(x) = 10011010 | 101

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Selection of C(x)• Bit errors can be seen as a polynomial E(x) added to P(x)• Error remains undetected if E(x) not divisible by C(x)• Single-bit errors: E(x) = xi, xk, x0 coefficients are nonzero,

all single-bit errors detected• Double-bit errors: C(x) has a factor with at least 3 terms• Odd number errors: C(x) contains the factor (x+1)• Any burst error of less than k bits and most burst errors

of larger than k bits

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Commonly Used CRCsCRC C(x)

CRC-8 x8 + x2 + x + 1

CRC-10 x10 + x9 + x5 + x4 + x + 1

CRC-12 x12 + x11 + x3 + x2 + 1

CRC-16 x16 + x15 + x2 + 1

CRC-CCITT x16 + x12 + x5 + 1

CRC-32 x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x +1

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Fundamentals of Coding• Coding: Map an k-bit word to an n-bit word.

– Notation: This code is usually referred to as (n,k)-code

• Weight of a word: The number of ones in the word.– Ex.: W(100011101)= 5

• Hamming distance between x, y: d(x,y) = W(xy)– Ex. x = 10011101, y = 11100110, d = 6

• # words at a hamming distance d: • # words at a distance up to d: • Minimum distance: the minimum Hamming distance out

of all distances in a code

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d

n

d

i i

n

0

Detecting and Correcting Errors• An (n, k)-code can detect (n-k) / can detect up to

n-k-1 errors and correct up to n-k/2 errors• Example

– Hamming (7,4)-code, can detect any single or two bit errors, and correct any single bit error

• Well known codes– Hamming codes– Reed-Solomon codes: used in DSL, WiMax, CD, DVD,

Blue-Ray Discs

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