Data transmission through channels with a large noise level:

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Data transmission through channels with a large
noise level
The effective decoders

• D. Sc. V. V. Zolotarev

0 1 0 0 0?1110? 01? 0 1 ?
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The main limitation in information theory
for coding

• The condition should be always satisfied
• R lt C !
• In this case there are coders, which one can
  ensure a digital transmission with an arbitrary
  small probability of an error, if the block
  length will be great enough.
• .

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Whenever possible - it is else easier!!!
An example of the encoder for a convolutional
code with a code rate R1/2.
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The lower estimations of error probabilities of
optimum block code decoding with R1/2 in
BSC. Even the codes with length n1000 are
ineffective at channel error probability Po gt
0.07. But the theory affirms, that it is
possible to work successfully at Po lt 0.11,
in accordance to main condition C gt 1/2. And
it is true for total searching methods!
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Main problems of coding technics

• 1. Decoding - more simple!.
• 2. Reliability - better!.
• 3. To take into account real communications
  requirements
• 4. How must they achieve it?
• With iterative methods!!!

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Principle of the numerical iterative equation
solution f(x)0 . It was transferred into
coding engineering within 6 years since 1972. On
the West this approach have revealed only
in 1993 (turbo codes)
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The principles of iterative decoding
Does MTD achieves true decisions always?
Yes, they do it almost always!
?
True massage
Noise!
Start!
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Multithreshold decoding (MTD)

• If MTD for a long time changes characters of
  the received data, it can achieve the solution of
  the optimum decoder (OD) with linear decoder
  complexity
• It is - an outcome
• of iterative methods application
• Usually "price" of the OD solution
• (as for Viterbi algorithm) - total search,
• But for MTD the complexity is linear !!!

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This is convolutional MTD with R1/2,
d5 and 3 iterations
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The substantiation of a new method efficiency

• 1. The special simple iterative procedure was
  created.
• 2. The special codes with minimal grouping of
  errors were constructed.
• 3. The optimization of many hundreds parameters
  of the decoder is carried out.
• Problems 1 ? 2 - very heavy
• task 3 - it was not even claimed!

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Minimum computing load in MTD (number of
operations per bit)
NC1dC2I here Ci - little
integers, d code distance, I- iteration number.

• It is in 100 times (!!!)
  more simple than for turbo
  codes

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What is neaded for communications?

• Channel energy decrease -
• - prof. Berlecamp said in 1980 in IEEE
• It is a code gain also
• Now it is else much more desirable.
• see our survey in Russian magazine
  Electrosvaz its translation is placed at
  our site too

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The scientific and technological revolutions in
coding
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The visitors of our site in January, 2004.
Welcome for everybody!
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21.02.2004
NIIRadio
Thank you!
Moscow
Space Research Institute
E-mail zolotasd_at_yandex.ru Work tel. 7
095 333 2356, 7 095 261 54 44 ??b. 7 916 518
86 28
www.mtdbest.iki.rssi.ru