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Example64-kbps ISDN channel’s bit error rate is less

than 10-6. User requires that at least, all but 1 frame are successfully transmitted on the average day. Frame is 1000 bits. In a day, 5.529 x 106 frames transmitted. Required frame error rate of 1/ 5.529 x 106, or

P2 = 0.18 x 10-6.

But Pb = 10-6, so P1 = (1-Pb)F = 0.999 and P2 = 1 - P1 = 10-3, which is >>> required P2

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Cyclic Redundancy CheckCRC is one of the most effective and

common error detecting schemes.Let M be m-bit message, G (r+1)-bit

pattern. Transmitter appends r 0’s to M, 2r*M. Divide 2r*M by G and add the remainder from

2r*M forming T (m+r bits), which is transmitted.

Receiver computes T/G; if remainder, then error.

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Cyclic Redundancy Check

CRC is one of the most effective and common error detecting schemes.

Represent frames as polynomials M= 1010001101 -> x9+x7+x3+x2+x0

Both source and destination use a generator polynomial G – r bits/r+1 degree polynomial

Idea: Transmit extended frame [M|V], such that the polynomial representation is exactly divisible by G. Thus, if G does not exactly divide the received frame, there is an error.

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CRC

How to find V such that G exactly divides [M|V]? Divide xrM by G. Set V = the remainder. [M|V] = xrM + V [M|V] = (xrM + V)/G = xrM/G + V/G = S

+ V/G + V/G = S + 2V/G. But in binary 2 is the same as zero. So [M|V] / G = S.

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CRC Example

Frame M 1010001101 = x9+x7+x3+x2+x0.

Pattern G 110101.Dividing (frame*25) by pattern results

in 01110.Thus T 101000110101110.Receiver can detect errors unless

received message Tr is divisible by G.

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CRC Performance and Generators Instead of [M|V] we receiver [M|V] + E (E is the error). Burst errors – CRC detects bursts of length r or less.

a string of errors, with E = 0 …0 1 X X X X 1 0 … E(x) = xi(xk-1 + … + 1) where the burst length is k. If G is degree k or greater and G has a 0th degree term, then G

will not divide E.

dividemight

1

122

x

xxx

xG

xE i

dividenever will

12

12

xx

xx

xG

xE ie.g.

Will CRC detect single bit errors?Suppose that you use 4 bits (as in Ethernet), and BER is 106 what is the frame error probability?

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CRC Performance and Generators

Burst Errors Continued If the burst has length r+1, then the

errors will not be detected if the burst is the same as G. If an error of length r+1 occurs and all combinations of errors are equally likely, then the burst will match G with prob. ½r-1. (So prob is BERr+1 x ½r-1)

In general, for longer bursts, the prob. is ½r

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CRC

Lastly, if G contains x+1 as a factor, and E has an odd number of bit, then G will not divide E.

In IEEE 802x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7

+ x5 + x4 + x2 + x + 1

CRC can be implemented in hardware with registers.

Problem: errors can occur in some pattern, so the probabilities are not quite right.

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Error Correcting Codes

Hamming distance between bit strings: The number of bits where the string

differ XOR them and count the 1’s 1 0 1 0 0

1 0 0 1 00 0 1 1 0 = 2 – the distance is two.

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Error Correcting codes

Take an n bit string and encode it as n+k bits in such a way that each encoded n bit string is at least d distance from any other encoded n bit string. Then you can detect errors of length d.

Do the same thing, but make it so the distance between any encoded n bit string is 2d+1 bits. Then the an error of d bits or less can be corrected by assigning the string to its closest legal value.

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Error Correcting Code

Legal strings – these are the encoded versions of n bit strings.

Illegal strings – no n bit string is encode to these

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Error Correcting Code

Suppose that this code is 0 1 0 1 0 But this code 0 1 1 0 1 0 is received

Then you know an error occurred, and you figure that what was meant to be sent is the code 0 1 0 1 0 (the nearest legal neighbor).

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Error Correcting Code

Suppose that this code is 0 1 0 1 0 But this code 0 1 1 0 1 1 is received

Then you know an error occurred. But you are sure which code was actually sent.

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Error Correcting Codes

Linear block and Hamming codes are like the ones just described. They can be encoded very fast. Error detection is very fast. Error correction requires a look-up table.

There are many many more types of error correcting codes. Reed-Solomon are good for burst errors and are used in CDs and cable modems.

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Error Control Mechanisms to detect and correct transmission

errors. Consider 2 types of errors:

Lost frame: frame is sent but never arrives. Often the first few bytes of frame provide synchronization. If

there is an error receiving these bytes, synchronization fails and the frame is not received.

Damaged frame: frame arrives but in error. If the hardware checks the CRC (typical case), it will not pass the

frame to the driver unless the CRC is correct.

Error control: combination of error detection, feedback (ACK or NACK) from receiver, and retransmission by source.

Coupled with flow control feedback.

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ARQ

ARQ: automatic repeat request.Works by creating a reliable data link

from an unreliable one.3 versions:

Stop-and-wait ARQ. Go-back-N ARQ. Selective-reject ARQ.

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Stop-and-Wait ARQSingle outstanding frame at any time.Simple but inefficient.Use of timers to trigger retransmission of data

or ACKs.2 types of errors:

Damaged or lost frame. Damaged or lost ACK.

Sequence numbers alternate between 0 and 1. Inefficient for connections with large bandwidth

delay product.

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Stop-and-Wait ARQ: ExampleSender ReceiverFrame 0

ACK1

Frame 1ACK 0

Frame 0

Timeout

Frame 0

ACK 1

Timeout

Frame 0

ACK 1 B discards duplicate.

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Bandwidth Delay Product

Which has high/low bandwidth, delay, bandwidth delay product?

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Go-Back-N ARQVariation of sliding window for error

control.Allows a window’s worth of frames to be in

transit at any time.RR: ack’s receipt of frame.REJ: negative acknowledgment indicating

the frame in error.Destination discards frame in error plus

subsequent frames.

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Go-Back-N – single loss frameS

0 R

rr?

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Go-Back-N – many loss frames

S R0

rr?

Time out

Either retransmit frame 8Or send a small packet requesting an RR frame (P bit)

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In this case, a single loss ACK is ok.

S R0

rr1

rr6

S R0

rr1

rr6

In this case, a single loss ACK is not that bad.

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Go-Back-N ARQ Issues

For k-bit sequence number, maximum window size is (2k-1). If window size is too large, ACKs may be

ambiguous: not clear if ACK is a duplicate ACK (errors occurred).

Example: 3-bit sequence number and 8 -frame window.Source transmits f0, gets back rr1, then

sends f1--f0, and gets back another rr1. ???

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Selective-Reject ARQ

Only frames transmitted are the ones that are NACK’ed (SREJ) or that timeout.

More efficient than Go-Back-N regarding amount of retransmissions.

But, receiver must buffer out-of-order frames.

More restriction on maximum window size; for k-bit sequence #’s, 2k-1 window.

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Fragmentation

A packet is broken up into smaller pieces. Each fragment is sent as a frame. Link layer has an upper bound on the size of frame. E.g.,

ethernet frames must be smaller than 1500 bytes. ATM must be smaller than 53 bytes, cable modem use 204 bytes.

P1 = (1-Pb)^F. So the smaller the F, the smaller P1. But the smaller the F, the lower the throughput. The

frame has overhead, e.g., the destination address, source address, etc. So a frame of 64 byte Ethernet frame will only contain 38 bytes of data.

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Example Data Link Layer Protocol

High-Level Data Link Control (HDLC) Widely-used (ISO standard). Single frame format. Synchronous transmission.

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HDLC: Frame Format

Flag: frame delimiters (01111110). Address field for multipoint links. 16-bit or 32-bit CRC. Refer to book (pages 214-221) for more

details.

8bits

8ext.

8 or16

variable 16 or32

8

flag address control data FCS flag

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Other DLL Protocols 2

LLC: Logical Link Control. Part of the 802 protocol family for LANs. Link control functions divided between

the MAC layer and the LLC layer. LLC layer operates on top of MAC layer.

Dst.MACaddr

Src.MACaddr

FCSDst.LLCaddr

Src.LLCaddr

LLCctl. DataMAC

control

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Other DLL Protocols 3

SLIP: Serial Line IP Dial-up protocol. No error control. Not standardized.

PPP: Point-to-Point Protocol Internet standard for dial-up

connections. Provides framing similar to HDLC.

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Multiplexing

Sharing a link/channel among multiple source-destination pairs.

Example: high-capacity long-distance trunks (fiber, microwave links) carry multiple connections at the same time.

MU

X

...

DE

MU

X ...

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Multiplexing Techniques

3 basic types: Frequency-Division Multiplexing (FDM). Time-Division Multiplexing (TDM). Statistical Time-Division Multiplexing

(STDM).

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FDM 1

High bandwidth medium when compared to signals to be transmitted.

Widely used (e.g., TV, radio).Various signals carried simultaneously

where each one modulated onto different carrier frequency, or channel.

Channels separated by guard bands (unused) to prevent interference.

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FDM 2

Time

Frequency

1 2 N

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TDM 1

TDM or synchronous TDM.High data rate medium when

compared to signals to be transmitted.

Time

Frequency

12

N

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TDM 2

Time divided into time slots.Frame consists of cycle of time slots.In each frame, 1 or more slots

assigned to a data source.

1 2 N... 1 2 ... N

frame Time

U1 U2 ... UN

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TDM 3

No control info at this level.Flow and error control?

To be provided on a per-channel basis. Use DLL protocol such as HDLC.

Examples: SONET (Synchronous Optical Network) for optical fiber.

+’s: simple, fair.-’s: inefficient.

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Statistical TDM 1Or asynchronous TDM.Dynamically allocates time slots on

demand.N input lines in statistical multiplexer, but

only k slots on TDM frame, where k < n.Multiplexer scans input lines collecting

data until frame is filled.Demultiplexer receives frame and

distributes data accordingly.

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STDM 2

Data rate on mux’ed line < sum of data rates from all input lines.

Can support more devices than TDM using same link.

Problem: peak periods. Solution: multiplexers have some buffering

capacity to hold excess data. Tradeoff data rate and buffer size (response

time).