Humming Code

1
Humming Code

• COSC 4436 E Computer Networks

2
Error Detection and Correction

• Telephone system has three parts switches,
  interoffice trunks and local loops.
• Switches and interoffice trunks are almost
  entirely digital.
• Local loops are still analog twisted pair.
  Expensive to replace

3
Error Detection and Correction

• Errors are rare on the digital medial
• Errors are still common on the local loops
• Wireless communications are becoming more common
  and the error rates here are orders of magnitude
  in comparison to fiber and copper media.

4
Error Detection and Correction

• Transmission errors are going to be with us for
  very long time
• We have to learn how to deal with them
• Errors come in bursts or single-bit

5
Two basic strategies for dealing with errors

• One way is to include enough redundant
  information with each block of data enabling the
  receiver to deduce what the transmitted data was.
  (Error-correcting codes)
• The other way is to include only enough
  information enabling the receiver to deduce that
  an error has occurred and request retransmission.
  (Error-detecting codes)

6
Two basic strategies for dealing with errors

• On channels with higher reliability, such as
  fiber, it is cheaper to use error-detecting
  codes. The receiver will just simple ask for the
  retransmission.
• On channels, such as wireless that make many
  errors, it is better to add enough redundancy to
  each block forcing the receive to figure out the
  original block of data.

7
Humming code history

• Hamming worked at Bell Labs in the 1940s on the
  Bell Model V computer.
• Input was fed in on punch cards punch cards,
  which would invariably have read errors.
• During weekdays, special code would find errors
  and flash lights so the operators could correct
  the problem.

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Humming code history

• During after-hours periods and on weekends, when
  there were no operators, the machine simply moved
  on to the next job.
• Hamming worked on weekends, and grew increasingly
  frustrated.
• Over the next few years he worked on the problem
  of error-correction
• In 1950 he published what is now known as Hamming
  Code, which remains in use in some applications
  today.

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Types of Humming code

• Hamming codes with additional parity (SECDED)
• Hamming(7,4) code
• Hamming(8,4) code
• Hamming(11,7) code. We are going to talk about
  this code.

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Humming Code

• 7-bit data word "0110101".
• d to signify data bits and p to signify parity
  bits.
• The data bits are inserted into their appropriate
  position.
• Parity bits calculated in each case using even
  parity.

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Humming Code
12
Humming Code
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Humming Code

• The new data word (with parity bits) is now
  "10001100101".
• We now assume the final bit gets corrupted and
  turned from 1 to 0.
• Our new data word is "10001100100"
• We analyze how the Hamming codes were created we
  flag each parity bit as 1 when the even parity
  check fails.

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Humming Code
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Humming Code

• The final step is to evaluate the value of the
  parity bits.
• The integer value of the parity bits is 11,
  signifying that the 11th bit in the data word
  (including parity bits) is wrong and needs to be
  flipped

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Humming Code

• Flipping the 11th bit changes 10001100100 back
  into 10001100101.
• Removing the Hamming codes gives the original
  data word of 0110101.
• Questions .