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Error Detection Algorithms, Compression, Multiplexing, (ch. 13). ENGR 475 – Telecommunications September 12, 2006 Harding University Jonathan White. Error Detection. Hopefully built into the physical layer encoding

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Error detection algorithms compression multiplexing ch 13

Error Detection Algorithms, Compression, Multiplexing,(ch. 13)

ENGR 475 – Telecommunications

September 12, 2006

Harding University

Jonathan White

Error detection
Error Detection

  • Hopefully built into the physical layer encoding

    • For example, Differential Manchester physical encoding can detect errors in 1 bit

  • Error Detection is also employed in other layers further up the protocol stack.

  • We are going to be looking at transport/network layer error detection.

    • Your application will also hopefully do error detection.

Error detection1
Error Detection

  • 3 main low-level methods:

    • Parity Bit (even or odd)

      • VRC, often used in trusted mediums

      • Detects approximately 65% of errors

    • Longitudinal redundancy check

      • LRC, rarely used

      • Detects 85% of errors

    • Cyclic redundancy check

      • CRC, very awesome, will use all your math skills

      • Detects upwards of 99.99995% of all errors

Parity bits
Parity Bits

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

  • Can be even or odd parity.

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

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

  • Used inside of computers.

  • What’s the overhead for parity bits?

  • What type of errors aren’t found?


  • Adds horizontal and vertical checking.

  • Works on an n-1 X n grid.

    • In our example, 8 vertical 7 bit words.

  • Better at detecting errors, but only slightly.

  • What’s the overhead in our example?

  • Can you make an error that’s not detected?


  • Type of hash function

  • Works on a block of data

  • Adds extra bits to the end of the data using binary division by relatively prime divisors.

    • Similar to previous

  • The receiver then computes the same hash function on the data.

    • If the CRCs match, then the data is trusted to be what was sent

      • Note: Some messages can get the same hash value, but this is a very low percentage.

Crc good points
CRC good points

  • CRCs are one way

  • Can be very many bits long

  • Can be very fast

  • Examples of common hash functions:

    • MD5

    • SHA1

    • RIPEMD

  • Used on almost every digital communication link



  • Lossless vs Lossy

    • Where would each work?

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

  • Digital voice is compressed only rarely.

    • Takes a lot of effort to compress and voice is very time sensitive.

  • WinZip and File Structures class.


  • Definition:

    • The process of combining two or more communication paths into one path.

  • Why use multiplexing:

    • Saves communication paths, which saves money.

  • 3 main types:

    • Time division

    • Frequency division

    • Space Division (not really multiplexing)

Time division multiplexing
Time Division Multiplexing

  • Only digital

  • The multiplexing unit slots time.

  • Each of the sends is assigned one slot to send in.

  • If the multiplexing unit can slot time fast enough, the senders will each get a guaranteed certain rate of speed.

    • The limit is on the bandwidth of the downward pipe.

    • That’s why we use fiber.

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

  • Statistical multiplexing.


  • Invented in WW2.

    • Used in T1s by the 1960s.

  • Used in:

    • T1 architecture of telephones

    • WAV format

    • GSM cell phone network (TDMA).

  • Negatives:

    • Too slow

Frequency division multiplexing
Frequency Division Multiplexing

  • An analog technology.

  • Combines several signals by onto 1 medium be sending signals in defined frequency ranges.

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

  • Very easy to do.

  • However, it takes up more bandwidth than TDM.


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


Space division multiplexing
Space Division Multiplexing

  • Not really multiplexing

  • Each signal has its own wire that is just bundled together.

  • This is what the telephone company does at a junction box.