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Data transmission through channels with a large noise level:

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 # ?. The main limitation in information theory for coding. The condition should be always satisfied: R < C !

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Data transmission through channels with a large noise level:

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  1. 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 # ?

  2. The main limitation in information theory for coding • The condition should be always satisfied: • R < 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. • . V.V.Zolotarev The effective decoders

  3. Whenever possible - it is else easier!!! An example of the encoder for a convolutional code with a code rate R=1/2. V.V.Zolotarev The effective decoders

  4. The lower estimations of error probabilities of optimum block code decoding with R=1/2 in BSC. Even the codes with length n=1000 are ineffective at channel error probability Po > 0.07. But the theory affirms, that it is possible to work successfully at Po < 0.11, in accordance to main condition C > 1/2. And it is true for total searching methods! V.V.Zolotarev The effective decoders

  5. 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!!! V.V.Zolotarev The effective decoders

  6. 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) V.V.Zolotarev The effective decoders

  7. The principles of iterative decoding Does MTD achieves true decisions always? Yes, they do it almost always! ? True massage Noise! Start! V.V.Zolotarev The effective decoders

  8. 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 !!! V.V.Zolotarev The effective decoders

  9. Рис. 1. Многопороговый декодер сверточного СОК с R=1/2, d=5 и nA=14 This is convolutional MTD with R=1/2, d=5 and 3 iterations V.V.Zolotarev The effective decoders

  10. 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 и 2 - «very heavy» • task 3 - it was not even claimed! V.V.Zolotarev The effective decoders

  11. Minimum computing load in MTD (number of operations per bit) N=C1*d+C2*I here Ci- little integers, d – code distance, I- iteration number. • It is in ~ 100 times (!!!) more simple than for turbo codes V.V.Zolotarev The effective decoders

  12. 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} V.V.Zolotarev The effective decoders

  13. The scientific and technological revolutions in coding V.V.Zolotarev The effective decoders

  14. The visitors of our site in January, 2004. Welcome for everybody! Top 18 of 18 Total Countries # Hits Files KBytes Country 1 1351 55.78% 935 88.63% 102015 60.97% Russian Federation 2 853 35.22% 610 57.82% 46268 27.65% Unresolved/Unknown 3 110 4.54% 55 5.21% 6870 4.11% US Commercial 4 45 1.86% 31 2.94% 4486 2.68% Network 5 14 0.58% 14 1.33% 1525 0.91% Estonia 6 10 0.41% 10 0.95% 465 0.28% France 7 10 0.41% 10 0.95% 1185 0.71% Ukraine 8 5 0.21% 4 0.38% 1251 0.75% Israel 9 4 0.17% 4 0.38% 301 0.18% Hungary 10 4 0.17% 4 0.38% 342 0.20% Romania 11 3 0.12% 3 0.28% 555 0.33% Germany 12 3 0.12% 3 0.28% 488 0.29% Lithuania 13 2 0.08% 2 0.19% 312 0.19% Austria 14 2 0.08% 2 0.19% 440 0.26% Belgium 15 2 0.08% 2 0.19% 216 0.13% Canada 16 2 0.08% 2 0.19% 327 0.20% Thailand 17 1 0.04% 1 0.09% 182 0.11% Kazakhstan 18 1 0.04% 1 0.09% 86 0.05% Mauritius V.V.Zolotarev The effective decoders

  15. NIIRadio Thank you! 21.02.2004 Moscow Space Research Institute E-mail: zolotasd@yandex.ru Work tel. +7 095 333 2356, +7 095 261 54 44 моb.: +7 916 518 86 28 www.mtdbest.iki.rssi.ru V.V.Zolotarev The effective decoders

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