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 For example, Differential Manchester physical encoding can detect errors in 1 bit 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. Your application will also hopefully do error detection.

Error Detection  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 check Longitudinal redundancy check LRC, rarely usedLRC, rarely used Detects 85% of errorsDetects 85% of errors Cyclic redundancy check Cyclic redundancy check CRC, very awesome, will use all your math skillsCRC, very awesome, will use all your math skills Detects upwards of % of all errorsDetects upwards of % of all errors

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?

LRC  Adds horizontal and vertical checking.  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.  What’s the overhead in our example?  Can you make an error that’s not detected?

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

CRC good points  CRCs are one way  Can be very many bits long  Can be very fast  Examples of common hash functions: MD5 MD5 SHA1 SHA1 RIPEMD RIPEMD  Used on almost every digital communication link  Check

CRC Example  RFID

Compression  Lossless vs Lossy Where would each work? Where would each work? Video (VGA SVGA), voice, movies, source code, mathematical formulasVideo (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. Takes a lot of effort to compress and voice is very time sensitive.  WinZip and File Structures class.

Multiplexing  Definition: The process of combining two or more communication paths into one path. The process of combining two or more communication paths into one path.  Why use multiplexing: Saves communication paths, which saves money. Saves communication paths, which saves money.  3 main types: Time division Time division Frequency division Frequency division Space Division (not really multiplexing) Space Division (not really 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. 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 process.  Statistical multiplexing.

TDM  Invented in WW2. Used in T1s by the 1960s. Used in T1s by the 1960s.  Used in: T1 architecture of telephones T1 architecture of telephones WAV format WAV format GSM cell phone network (TDMA). GSM cell phone network (TDMA).  Negatives: Too slow Too slow

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.

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