Outline Building Blocks Shannon’s Theorem Encoding

Spring 2001 CS 585 1

OutlineBuilding BlocksShannon’s TheoremEncoding

11. Physical Layer


Building Blocks

• Node– Network Adaptor (memory is the speed bottleneck)

– Router (input ports, switch fabric, output ports)

• Links– C = f λ

– Cables

– Leased Lines: T1(DS1), T3(DS3), OC-1(STS-1),OC-3(STS-3),OC-48(STS-48,2.48Gbps)

– Last mile links: modem, xDSL, ISDN, cable modem


Shannon’s Theorem

• C = B log (1+S/N)– C: channel capacity, in bps

– B: bandwidth, in hertz

– S: average signal power

– N: average noise power

• dB = 10 * log (S/N)

– dB: signal-noise ratio expressed in decibels

2

10


Shannon’s Theorem

• Example:– B : 300 Hz to 3300 Hz

– N/S = 30 dB

– C = 3000 log (1001) = 30 Kbps2


Encoding

• Signals propagate over a physical medium– modulate electromagnetic waves

– e.g., vary voltage

• Schemes– NRZ

– NRZI

– Manchester

– 4B/5B


OutlineFramingError DetectionSliding Window AlgorithmToken rings (FDDI)Wireless

12. Data Link Layer


Data Link Layer

• Data Link Layer– Framing– Error Detection– Sliding Window (reliable transmission, flow control)

• Medium Access Control (MAC) Sub-Layer– Token ring (FDDI)– Wireless

• Logical Link Control (LLC) : IEEE802.2


Framing

• Break sequence of bits into a frame• Typically implemented by network adaptor

Frames

BitsAdaptor Adaptor Node BNode A


Approaches• Sentinel-based

– delineate frame with special pattern: 01111110

– e.g., HDLC, SDLC, PPP

– problem: special pattern appears in the payload

– solution: bit stuffing

• sender: insert 0 after five consecutive 1s

• receiver: delete 0 that follows five consecutive 1s

Header Body

8 16 16 8

CRCBeginningsequence

Endingsequence

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Approaches (cont)

• Counter-based– include payload length in header– e.g., DDCMP

– problem: count field corrupted– solution: catch when CRC fails

SY

N

Header Body

8 8 4214 168

SY

N

Cla

ss CRCCount

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Approaches (cont)

• Clock-based– each frame is 125us long– e.g., SONET: Synchronous Optical Network– STS-n (STS-1 = 51.84 Mbps)

Overhead Payload

90 columns

9 rows

STS-1Hdr STS-1Hdr STS-1Hdr

STS-3cHdr

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Error Detection

• Parity• Two-dimensional parity• Internet Checksum• CRC

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Cyclic Redundancy Check (CRC)

• Add k bits of redundant data to an n-bit message– want k << n

– e.g., k = 32 and n = 12,000 (1500 bytes)

• Represent n-bit message as n-1 degree polynomial– e.g., MSG=10011010 as M(x) = x7 + x4 + x3 + x1

• Let k be the degree of some divisor polynomial– e.g., C(x) = x3 + x2 + 1

• Modulo 2 operation (XOR)

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CRC (cont)

• Transmit polynomial P(x) that is evenly divisible by C(x) – shift left k bits, i.e., M(x)xk

– subtract remainder of M(x)xk / C(x) from M(x)xk

• Receiver polynomial P(x) + E(x)– E(x) = 0 implies no errors

• Divide (P(x) + E(x)) by C(x); remainder zero if:– E(x) was zero (no error), or

– E(x) is exactly divisible by C(x)

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Selecting C(x)

• All single-bit errors, as long as the xk and x0 terms have non-zero coefficients.

• All double-bit errors, as long as C(x) contains a factor with at least three terms

• Any odd number of errors, as long as C(x) contains the factor (x + 1)

• Any ‘burst’ error (i.e., sequence of consecutive error bits) for which the length of the burst is less than k bits.

• Most burst errors of larger than k bits can also be detected

• See Table 2.6 on page 102 for common C(x)

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Sliding Window

• Stop and wait• Selective repeat• Go back N

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Acknowledgements & TimeoutsSender Receiver

Frame

ACK

Tim

eout

Tim

e

Sender Receiver

Frame

ACK

Tim

eout

Frame

ACKTim

eout

Sender Receiver

Frame

ACKTim

eout

Frame

ACKTim

eout

Sender Receiver

Frame

Tim

eout

Frame

ACKTim

eout

(a) (c)

(b) (d)

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Stop-and-Wait

• Two sequence numbers (0 and 1)• Problem: keeping the pipe full• Example

– 1.5Mbps link x 45ms RTT = 67.5Kb (8KB)– 1KB frames imples 1/8th link utilization

Sender Receiver

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Sliding Window• Allow multiple outstanding (un-ACKed) frames• Upper bound on un-ACKed frames, called window

Sender Receiver

Tim

e

……

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SW: Sender• Assign sequence number to each frame (SeqNum)• Maintain three state variables:

– send window size (SWS)– last acknowledgment received (LAR)– last frame sent (LFS)

• Maintain invariant: LFS - LAR <= SWS

• Advance LAR when ACK arrives • Buffer up to SWS frames

SWS

LAR LFS

… …

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SW: Receiver• Maintain three state variables

– receive window size (RWS)– largest frame acceptable (LFA)– last frame received (LFR)

• Maintain invariant: LFA - LFR <= RWS

• Frame SeqNum arrives:– if LFR < SeqNum < = LFA accept– if SeqNum < = LFR or SeqNum > LFA discarded

• Send cumulative ACKs

RWS

LFR LFA

… …

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Sequence Number Space• SeqNum field is finite; sequence numbers wrap around• Sequence number space must be larger then number of

outstanding frames• SWS <= MaxSeqNum-1 is not sufficient

– suppose 3-bit SeqNum field (0..7)– SWS=RWS=7– sender transmit frames 0..6– arrive successfully, but ACKs lost– sender retransmits 0..6– receiver expecting 7, 0..5, but receives second incarnation of 0..5

• SWS < (MaxSeqNum+1)/2 is correct rule• Intuitively, SeqNum “slides” between two halves of sequence

number space

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Selective Repeat

• At the receiver, it will send an ack for each frame received, even if the frame is out of order.

• The sender sets a timeout value for each frame sent out, and will resend the frame upon timeout. The timeout flag is cleared when an ack for the frame is received.

• Only those frames (or acks for them) are lost are retransmitted.

• The receiver may need a large buffer to hold out of order frames.

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Go Back N

• At the receiver, it will send an ack for each frame received, only if the frame is out of order. Out of order frames are discarded. It also sends a NAK when it finds a frame is lost.

• The timer mechanism is the same.

• The acks are cumulative in the sense that an ack indicates that the receiver has got all the frames up to the frame acked.

• The sender will resend all the frames starting from the frame for which a NAK is received.

• The receiver does not need a large buffer to hold out of order frames.

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Outline Building Blocks Shannon’s Theorem Encoding