Error Detection Algorithms, Error Detection Algorithms, Compression, Multiplexing,Compression, Multiplexing,

(ch. 13)(ch. 13)

ENGR 475 – TelecommunicationsENGR 475 – TelecommunicationsSeptember 12, 2006September 12, 2006Harding UniversityHarding University

Jonathan WhiteJonathan White

Error DetectionError Detection

Hopefully built into the physical layer Hopefully built into the physical layer encodingencoding For example, Differential Manchester physical For example, Differential Manchester physical

encoding can detect errors in 1 bitencoding can detect errors in 1 bit Error Detection is also employed in other Error Detection is also employed in other

layers further up the protocol stack.layers further up the protocol stack. We are going to be looking at We are going to be looking at

transport/network layer error detection.transport/network layer error detection. Your application will also hopefully do error Your application will also hopefully do error

detection. detection.

Error DetectionError Detection

3 main low-level methods:3 main low-level methods: Parity Bit (even or odd)Parity Bit (even or odd)

• VRC, often used in trusted mediumsVRC, often used in trusted mediums• Detects approximately 65% of errorsDetects approximately 65% of errors

Longitudinal redundancy checkLongitudinal redundancy check• LRC, rarely usedLRC, rarely used• Detects 85% of errorsDetects 85% of errors

Cyclic redundancy checkCyclic redundancy check• CRC, very awesome, will use all your math skillsCRC, very awesome, will use all your math skills• Detects upwards of 99.99995% of all errorsDetects upwards of 99.99995% of all errors

Parity BitsParity Bits

Add a single parity bit to the end of each byte Add a single parity bit to the end of each byte sent.sent.

Can be even or odd parity.Can be even or odd parity. For odd parity, the number of 1’s must add to an For odd parity, the number of 1’s must add to an

odd number, including the parity.odd number, including the parity. For even parity, the number of 1’s must add to For even parity, the number of 1’s must add to

an even number, including the parity.an even number, including the parity. Used inside of computers.Used inside of computers. What’s the overhead for parity bits?What’s the overhead for parity bits? What type of errors aren’t found?What type of errors aren’t found?

LRCLRC

Adds horizontal and vertical checking.Adds horizontal and vertical checking. Works on an n-1 X n grid.Works on an n-1 X n grid.

In our example, 8 vertical 7 bit words.In our example, 8 vertical 7 bit words. Better at detecting errors, but only slightly.Better at detecting errors, but only slightly. What’s the overhead in our example?What’s the overhead in our example? Can you make an error that’s not Can you make an error that’s not

detected?detected?

CRCCRC

Type of hash functionType of hash function Works on a block of dataWorks on a block of data Adds extra bits to the end of the data using Adds extra bits to the end of the data using

binary division by relatively prime divisors.binary division by relatively prime divisors. Similar to previousSimilar to previous

The receiver then computes the same hash The receiver then computes the same hash function on the data.function on the data. If the CRCs match, then the data is trusted to be what If the CRCs match, then the data is trusted to be what

was sentwas sent• Note: Some messages can get the same hash value, but Note: Some messages can get the same hash value, but

this is a very low percentage.this is a very low percentage.

CRC good pointsCRC good points

CRCs are one wayCRCs are one way Can be very many bits longCan be very many bits long Can be very fastCan be very fast Examples of common hash functions:Examples of common hash functions:

MD5MD5 SHA1SHA1 RIPEMDRIPEMD

Used on almost every digital communication linkUsed on almost every digital communication link http://en.wikipedia.org/wiki/http://en.wikipedia.org/wiki/

Cyclic_Redundancy_CheckCyclic_Redundancy_Check

CRC ExampleCRC Example

RFIDRFID

CompressionCompression

Lossless vs LossyLossless vs Lossy Where would each work?Where would each work?

• Video (VGA SVGA), voice, movies, source code, Video (VGA SVGA), voice, movies, source code, mathematical formulasmathematical formulas

Digital voice is compressed only rarely.Digital voice is compressed only rarely. Takes a lot of effort to compress and voice is Takes a lot of effort to compress and voice is

very time sensitive.very time sensitive. WinZip and File Structures class.WinZip and File Structures class.

MultiplexingMultiplexing

Definition:Definition: The process of combining two or more The process of combining two or more

communication paths into one path.communication paths into one path.

Why use multiplexing:Why use multiplexing: Saves communication paths, which saves money.Saves communication paths, which saves money.

3 main types:3 main types: Time divisionTime division Frequency divisionFrequency division Space Division (not really multiplexing)Space Division (not really multiplexing)

Time Division MultiplexingTime Division Multiplexing Only digitalOnly digital The multiplexing unit slots time.The multiplexing unit slots time. Each of the sends is assigned one slot to send Each of the sends is assigned one slot to send

in.in. If the multiplexing unit can slot time fast enough, If the multiplexing unit can slot time fast enough,

the senders will each get a guaranteed certain the senders will each get a guaranteed certain rate of speed.rate of speed. The limit is on the bandwidth of the downward pipe.The limit is on the bandwidth of the downward pipe. That’s why we use fiber.That’s why we use fiber.

Slotting time is a big job. This is actually a slow Slotting time is a big job. This is actually a slow process.process.

Statistical multiplexing.Statistical multiplexing.

TDMTDM

Invented in WW2.Invented in WW2. Used in T1s by the 1960s.Used in T1s by the 1960s.

Used in:Used in: T1 architecture of telephonesT1 architecture of telephones WAV formatWAV format GSM cell phone network (TDMA).GSM cell phone network (TDMA).

Negatives:Negatives: Too slowToo slow

Frequency Division MultiplexingFrequency Division Multiplexing

An analog technology.An analog technology. Combines several signals by onto 1 Combines several signals by onto 1

medium be sending signals in defined medium be sending signals in defined frequency ranges.frequency ranges.

The receiver can then “tune” into that The receiver can then “tune” into that frequency.frequency.

Very easy to do.Very easy to do. However, it takes up more bandwidth than However, it takes up more bandwidth than

TDM.TDM.

FDMFDM

Used in cable TV, FM/AM radio, portable Used in cable TV, FM/AM radio, portable telephones.telephones.

http://en.wikipedia.org/wiki/http://en.wikipedia.org/wiki/Frequency_division_multiplexingFrequency_division_multiplexing

Space Division MultiplexingSpace Division Multiplexing

Not really multiplexingNot really multiplexing Each signal has its own wire that is just Each signal has its own wire that is just

bundled together.bundled together. This is what the telephone company does This is what the telephone company does

at a junction box.at a junction box.