eec-484/584 computer networks lecture 8 wenbing zhao [email protected] (part of the slides are based...

EEC-484/584EEC-484/584Computer NetworksComputer Networks

Lecture 8Lecture 8

Wenbing ZhaoWenbing Zhao

[email protected]@ieee.org(Part of the slides are based on materials supplied by (Part of the slides are based on materials supplied by

Dr. Louise Moser at UCSB and Prentice-Hall)Dr. Louise Moser at UCSB and Prentice-Hall)

Spring Semester 2006Spring Semester 2006 EEC-484/584: Computer NetworksEEC-484/584: Computer Networks Wenbing ZhaoWenbing Zhao

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OutlineOutline

• Error detection and correction

• Elementary Data Link Protocols

• Example protocols (not required for quiz)


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Error-Correcting CodesError-Correcting Codes

• n-bit codeword – an n-bit unit containing data and check bits – m bits of data, r bits redundant/check bits

(n = m+r)

• How to measure the differences between two codewords (num of different bits)– Using exclusive OR and counting number of

1 bits in the result


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• Hamming distance – number of bit positions in which two codewords differ

• If two codewords are a Hamming distance d apart, it will require d single-bit errors to convert one into the other


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• Complete code– Complete list of all legal codewords:

2m possible data messages– Recall that there are m bits of data

• Hamming distance of the complete code– Find two codewords whose Hamming

distance is minimum


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Error-Detection CodesError-Detection Codes

• A distance d+1 code can detect up to d errors, why?– If there are d+1 errors, one valid codeword

might be turned into another valid codeword– ≤ d errors will change a valid codeword into

an illegal codeword can be detected!


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• To correct d errors, need a distance 2d+1 code– Legal codewords are so far part that even

with d changes, original codeword is still closer than any other codeword, so it can be uniquely determined


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Error-Correcting Codes: ExampleError-Correcting Codes: Example

• Consider a code with only four valid codewords– 0000000000, 0000011111, 1111100000, 1111111111

• This code has a distance 5 can correct double errors– If 0000000111 arrives, receiver knows the original

must have been 0000011111– However, if triple error changes 0000000000 to

0000000111, the error will not be corrected properly


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Parity BitParity Bit• Parity bit – a single bit is appended to the data• Parity bit is chosen so that number of 1 bits in

the codeword is even or odd• Example: Given 1011010

– With even parity 10110100

– With odd parity 10110101

• A code with a single parity bit has a distance 2– Since any single-bit error produces a codeword with

wrong parity can be used to detect single bit errors


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Error-Detecting Codes: CRCError-Detecting Codes: CRC

• Polynomial code, also known as CRC (Cyclic Redundant Code)

• Treat bit string as polynomial with 0 and 1 coefficients

• m-bit frame: M(x) = bm-1xm-1 + … + b0

• E.g.: 11011010 => M(x) = x7 + x6 + x4 + x3 + x1

• Use modulo 2 arithmetic– No carries or borrows: XOR


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Cyclic Redundant CodeCyclic Redundant Code• Sender and receiver agree on generator

polynomial G(x) (High & low order bits must be 1)• For a frame with m bits corresponding to M(x),

m > deg G(x) = r• Append checksum to end of frame so polynomial

T(x) corresponding to checksummed frame is divisible by G(x)

• When receiver gets checksummed frame, divides T(x) by G(x)

• If remainder R(x) != 0, then transmission error


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Algorithm to Compute CRC ChecksumAlgorithm to Compute CRC Checksum

• Let m = deg M(x), r = deg G(x)• Append r 0 bits to lower-order end of frame: xrM(x)• Divide bit string corresponding to xrM(x) by bit string

corresponding to G(x)• Subtract remainder R(x) from bit string corresponding

to xrM(x), result is checksummed frame. Let T(x) be its polynomial– xrM(x) = Q(x)G(x) + R(x)– xrM(x) – R(x) = Q(x)G(x) = T(x)


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Compute CRC Compute CRC ChecksumChecksum

XOR


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International Standard PolynomialsInternational Standard Polynomials

• CRC-12 G(x) = x12 + x11 + x3 + x2 + x1 + 1– Used for 6-bit characters

• CRC-16 G(x) = x16 + x15 + x2 + 1CRC-CCITT G(x) = x16 + x12 + x5 + 1– Used for 8-bit characters

• CRC-32 G(x) = x32 + x26 + x23 + x22 + x16 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x1 + 1– Used in IEEE 802– Detects all bursts of length 32 or less and all bursts

affecting an odd number of bits


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ExerciseExercise

• Given 1011011, calculate the parity bit to be appended to the bit string– If even parity is used– If odd parity is used– If the highest order bit is inverted to 0, show

how the error can be detected


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ExerciseExercise

• To provide more reliability than a single parity bit can give, an error-detecting coding scheme uses one parity bit for checking all the odd-numbered bits and a second parity bit for all the even-numbered bits. What is the Hamming distance of this code?


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ExerciseExercise

• A bit stream 10011101 is transmitted using the standard CRC method described in the text. The generator polynomial is x3 + 1. Show the actual bit string transmitted. Suppose the third bit from the left is inverted during transmission. Show that this error is detected at the receiver's end.


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Elementary Data Link ProtocolsElementary Data Link Protocols

• An Unrestricted Simplex Protocol

• A Simplex Stop-and-Wait Protocol

• A Simplex Protocol for a Noisy Channel


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Initial AssumptionsInitial Assumptions

• Physical, data link, network layers are independent processes

• Sender has infinite amount of data ready to send, supplied by network layer

• “wire-like” service: DLL provides reliable, source ordered delivery service to NL

• Packet from NL is treated as pure data• When sender accepts packet from NL, it

encapsulates in a frame with a header and trailer


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Initial AssumptionsInitial Assumptions

• Receiver waits for arrived of frame, which generates an interrupt

• When frame arrives at receiver, hardware computes checksum– If error then DLL informed event = chksum_err– Else DLL informed event = frame_arrival

• DLL acquires frame from physical layer, checks control info in header

• If ok then passes packet to NL


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Protocol DefinitionsProtocol Definitions

Continued


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Unrestricted Simplex ProtocolUnrestricted Simplex Protocol

• Additional assumptions– Processing time insignificant– Infinite buffer space– Communication channel never loses or

damages frames

• Uses no sequence numbers or acks– Only event type frame_arrival


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Simplex Stop-and-Wait ProtocolSimplex Stop-and-Wait Protocol

• Drop assumption– Receiver processing time insignificant, or,

equivalently, infinite input buffer at receiver• Main problem

– To prevent sender from overwhelming the receiver

• If receiver takes t time units to execute from physical layer to network layer, sender must not transmit more than one frame per time t


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Simplex Stop-and-Wait ProtocolSimplex Stop-and-Wait Protocol• One solution – too conservative

– Restrict sender so transmits so slowly that even if frame undergoes max delay no buffer overflows

• Better solution– Receiver provides feedback to sender and gives

sender permission to send next frame

• Sender sends frame, stop and wait for ack• Alternates between sender and receiver

– Half-duplex


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• Drop assumption– Frames not damaged or lost

• Assumption– If frame is damaged, receiver will detect it when it

computes the checksum

• Possible solution– Receiver sends acknowledgement if receives

uncorrupted frame, discards frame if damaged– Sender sends frame again if doesn’t receive

acknowledgement before timeout

Simplex Protocol for Noisy ChannelSimplex Protocol for Noisy Channel


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• Problem: duplicate messages– Receiver receives uncorrupted frame, sends

acknowledgement – Sender times out before receiving acknowledgement,

sends frame again– Receiver receives second copy uncorrupted – has

duplicate copies

• Solution– Use sequence numbers: 1 bit suffices


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• How to determine timeout value– Timeout must be long enough so sender does

not send duplicate when ack is on its way– Timeout must allow

• Frame to get to receiver• Receiver to process frame• Ack to get to sender


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• Acks need to be matched against frames– Sender remembers next_frame_to_send– Receiver remembers frame_expected

• Positive Acknowledgement with Retransmission (PAR), or, Automatic Repeat reQuest (ARQ)– Sender waits for a positive acknowledgement before

advancing to the next data item


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Continued


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Simplex Protocol for Noisy ChannelSimplex Protocol for Noisy Channelsend3() (cont’d)


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Continued


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Simplex Protocol for Noisy ChannelSimplex Protocol for Noisy Channelsend3() (cont’d)


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Example Data Link ProtocolsExample Data Link Protocols

• High-Level Data Link Control

• PPP

• Included for completeness, not required for quiz


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High-Level Data Link ControlHigh-Level Data Link Control

• Bit oriented, using bit-stuffing

• Address • Control – used for sequence numbers, acks, and other

purposes• Data – may contain any info. May be arbitrarily long• Checksum – cyclic redundancy code• Flag – 01111110• Types of frames: information, supervisory, unnumbered


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HDLC Information FrameHDLC Information Frame

• Uses a sliding window with a 3-bit sequence number– Seq – sequence number– Next – piggybacked ack– P/F – Poll/Final


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Point-to-Point ProtocolPoint-to-Point Protocol

• A framing method (using byte stuffing)• LCP (link control protocol) – for bringing

lines up, testing them, negotiating options and bringing them down again

• NCP (network control protocol) – to negotiate network-layer options in a way that is independent of the network layer protocol to be used


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PPPPPP

• Frame format – resembles HDLC frame format• Major difference – byte stuffing, character oriented• Does not provide reliable transmission using

sequence numbers and acks as the default• Connection oriented service might not guarantee

reliability!

eec-484/584 computer networks lecture 8 wenbing zhao [email protected] (part of the slides are based...

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