Error Detection _amp;Correction by dffhrtcv3

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									Error Correction
    ECE 734
    Chapter 6
                Error Correction

• detected errors usually require data blocks to be
  retransmitted
• not sufficient for some applications
   – When bit error rate is high causing lots of
     retransmissions.
   – When propagation delay long (satellite) compared
     with frame transmission time.
   – Real time audio, video, etc.
• instead need to correct errors on basis of bits
  received
• error correction provides this
Error Correction Process
       How Error Correction Works

• adds redundancy to transmitted message
• can deduce original despite some errors
• eg. block error correction code
  – map k bit input onto an n bit codeword
  – each distinctly different
  – if get error assume codeword sent was closest to that
    received
• reduces net data rate, but decreases probability
  of uncorrected bit errors
       How Error Correction Works
• block error correction code
  – map each k bit data input onto an n bit codeword
  – 2k different n bit codewords needed, out of set of 2n
    possibilities
  – Hamming distance is number of bits different between
    two codewords.
  – If minimum number of bits different between two
    codewords is 3 (5,7), can correct 1 (2,3) bit errors
    based on mimimum Hamming distance match to ideal
    codes.
• reduces net data rate, but decreases probability
  of uncorrected bit errors
                 Convolutional Codes
• Convolutional codes are error correcting codes that can be
  computed incrementally as serial data is clocked out.
   – In contrast, block codes require conde an entire data block at
      one time.
• A convolutional encoder maps the data symbols s[n] into physical
  symbols x[n], such that x[n] is dependent not only on the current
  s[n], but also on recent past symbols s[n-1], s[n-2],…
• This introduces time dependence into the transmitted symbol stream
  x[n]; for random data any s[n] sequence could occur, but as the
  result of the time dependence some x[n] sequences can never occur
  regardless of the original data
• At the receiver, a single value of the received physical symbol x’[n]
  can not be used to determine a single value of the data symbol s’[n]
• Each received data symbol s’[n] is dependent not only on the current
  x’[n], but also on recent past received physical symbols x’[n-1], x’[n-
  2],…
• This makes decoding more complicated, but can be used to reduce
  noise sensitivity

								
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