1. Scientific session DNIT of the RAS New optimization coding theory and its applied achievements 24.04.2008. V.V.Zolotarev, SRI RAS

2. V.V.Zolotarev. The coding theory2 The main fundamental scientific problem of transition from analog Communications(connections) and computer science To digital Maintenance of a high level of reliability of formation, processing, transfer and storage of figures. Maintenance of a high level of reliability of formation, processing, transfer and storage of figures. Means of the decision of this problem - methods of the theory of noiseproof coding Means of the decision of this problem - methods of the theory of noiseproof coding Theoretical basis of unequivocal exact restoration of an analog signal is the theorem of readout of academician V.A.Kotelnikov. At transition of our technological civilization to transmission and storage of the information to a discrete form the main requirement to such systems, becomes their conformity to Shannon theorem. In this case it is possible to restore always in the receiver the digital message deformed in a channel, with as much as necessary small error probability if the length of the code block will grow. This theorem has begun the modern theory of coding.

3. Coding - This introduction of redundancy K - the information + R - superfluous symbols R=k/n <1 - code speed n=k+r - length of the block + Coding - This is introduction of redundancy k – the informationr - superfluous symbols n=k+r - length of the block R=k/n <1 - code rate

4. V.V.Zolotarev. The coding theory4 WIT H C <1!

5. V.V.Zolotarev. The coding theory5 The basic restriction of the Information Theory for coding Always condition Always condition R <C must satisfy! must satisfy! In this case there are systems of coding which can provide transfer of the digital information with as much as small probability of a mistake if the length of the block of the data will be great enough (K.Shannon, the theorem of coding existence) In this case there are systems of coding which can provide transfer of the digital information with as much as small probability of a mistake if the length of the block of the data will be great enough (K.Shannon, the theorem of coding existence)

6. V.V.Zolotarev. The coding theory6 What is necessary for codes in communication networks? What is necessary for codes in communication networks? It is - a code gain, CG!, - a measure of signal energy effectiveness increase. It is - a code gain, CG!, - a measure of signal energy effectiveness increase. Now every one additional dB in CG gives in communication networks economic benefit in many millions dollars! Now every one additional dB in CG gives in communication networks economic benefit in many millions dollars! Resource ЭВК can be realized at ERS for decrease of aerials sizes, and also for increase in speed, reliability and distance of communication. It is extremely important for satellite communication systems such as VSAT, and also projects micro- and nano- satellites or other high-speed communication systems. It is achieved only by correct fast mathematical processing of a digital stream! Resource ЭВК can be realized at ERS for decrease of aerials sizes, and also for increase in speed, reliability and distance of communication. It is extremely important for satellite communication systems such as VSAT, and also projects micro- and nano- satellites or other high-speed communication systems. It is achieved only by correct fast mathematical processing of a digital stream!

7. The low estimations of error probabilities decoding for block codes with R=1/2 Even codes of length n=1000 are inefficient at error probability in the channel Ro> 0.08. And the theory asserts it is possible to work successfully at Ро 0.08. And the theory asserts it is possible to work successfully at Ро <0.11 !!! And it occurs at 2 500 variants of decisions! Number of atoms in the Universe is more little! 234

8. V.V.Zolotarev. The coding theory8 Complexity of decoders for different codes with length n enen VA !!! MTD Discr. algebra

9. V.V.Zolotarev. The coding theory9 The block multithreshold decoder for a code with R=1/2, d=5 and I iterations MTD,complexity-N~d*I*n

10. V.V.Zolotarev. The coding theory10 The reasons of high efficiency new MTD a method 1. Procedure is applied special very easy for realization iterative оптимизационная. 1. Procedure is applied special very easy for realization iterative оптимизационная. 2. Special codes with a minimum level of grouping of mistakes - too a method of optimization are constructed. 2. Special codes with a minimum level of grouping of mistakes - too a method of optimization are constructed. 3. Process of many hundreds parameters special optimization in the decoder was realized. 3. Process of many hundreds parameters special optimization in the decoder was realized. Problems 1 and 2 - “are very difficult" Problems 1 and 2 - “are very difficult" The problem 3 - has not appeared at all The problem 3 - has not appeared at all

11. Minimum of calculations at decoding - in MTD! (Number of operations per bit, soft realization) Usually: N 1 ~ d*I, - product and in MTD: only N 2 ~d+I, - the sum of key parameters d and I. It is in ~100 times easier and faster than, for example, at use of a turbo codes! It was realized in special TV-system.

12. Hardware realization MTD at VLSI 1.MTD will consist almost completely of store elements or shift registers. These are the fastest elements in VLSI. The share of other elements in MTD is less than 1 %. 2.MTD may be absolutely parallel one step algorithm. For this reason MTD for some values of parameters approximately in 1000 times faster, than for example, a turbo decoders. A delay - as for the elementary 2- input key - absolute minimum. 3.Realization: throughput: up to 1,6Gb/s, and CG = 7 - 9,5 dB

13. V.V.Zolotarev. The coding theory13 Chipset of the MTD decoder at Xilinx for channels with speeds up to 150 Mb / s

14. V.V.Zolotarev. The coding theory14 Multithreshold decoder (MTD) for satellite and space channels, raises efficiency of their use in 3-10 times, including for EDS. Simple MODEL MTD at Altera for channels up to 640 Mbit / s. The method can work at information speeds up to 1,6 Gbit / s MTD - for the Space!

15. V.V.Zolotarev. The coding theory15 New scientific and technological revolution – data transmission with the minimal power WITHWITH, дБ

16. V.V.Zolotarev. The coding theory16 The symbolical multithreshold decoder for a code with R=1/2, d=5 and I iterations QMTD-symbolic? -

17. V.V.Zolotarev. The coding theory17 Welcome! Visitors of web-site SRI RAS www.mtdbest.iki.rssi.ru in March, 2008. More than 18000 visitors of our web-site from 56 countries have copied more than 7 Gbytes data about MTD algorithms during last year. ??? USANetw ork

18. V.V.Zolotarev. The coding theory18 Chipset MTD decoder at ALTERA basis

19. V.V.Zolotarev. The coding theory19Conclusions 1. We have opened iterative MTD algorithms 35 years ago. 2. Complexity of the soft versions MTD is an absolute known minimum of calculations. A difference with other codes is ~100 times! The rare case in the theory! We outstrip all countries ~ 7 ÷ 10 years. 3. Hard MTD are faster than a other codes ~1000 times! 4. Decisions MTD are almost always optimum even at the big noise level. 5. MTD - the absolute leader by criteria "complexity - efficiency". It is created in Russia! 6. Non-binary codes for MTD - the most unique discovery in the coding theory during last 30 years. They are unknown abroad! The Russian scientific school - again in the group of world leaders in the theory!

20. V.V.Zolotarev. The coding theory20 24.04.2008. SRI of the Russian Academy of Sciences in Moscow w.ph.: (495) 333 45 45, www.mtdbest.iki.rssi.ru, e-mail: zolotasd@yandex.ru mobil: +7 916 518 86 28 V.V.Zolotarev

21. V.V.Zolotarev. The coding theory21 Further there are help slides - appendices to the report

22. V.V.Zolotarev. The coding theory22 Whenever possible - to code easier!!! An example of the coder for свёрточного a code with code speed R=1/2

23. V.V.Zolotarev. The coding theory23

24. V.V.Zolotarev. The coding theory24 Complexity of various algorithms of decoding Codes and algorithms Algorithm Viterbi Algebraic codes Turbo codes Low dencity parity codes Majority codes- - only in Russia - MTD which almost always converges to optimum (total search!) the decision, but with linear complexity Complexity 2 n n 2 C1*nC2*n C3*n С3 <C2 <C1

25. V.V.Zolotarev. The coding theory25 Fig. 1. The multithreshold decoder сверточного JUICE with R=1/2, d=5 and nA=14 Convolutionale multithreshold decoder for a code with R=1/2, d=5 and 3 iterations

26. The reasons of high efficiency new МПД a method 1. Procedure is applied special very easy for realization iterative оптимизационная. 1. Procedure is applied special very easy for realization iterative оптимизационная. 2. Special codes with a minimum level of grouping of mistakes - a method of optimization are constructed. 2. Special codes with a minimum level of grouping of mistakes - a method of optimization are constructed. 3. Special optimization of many hundreds parameters of the decoder is carried out. 3. Special optimization of many hundreds parameters of the decoder is carried out. Problems(Tasks) 1 and 2 - "very difficult" Problems(Tasks) 1 and 2 - "very difficult" The problem(task) 3 - was not put at all The problem(task) 3 - was not put at all

27. V.V.Zolotarev. The coding theory27 Multithreshold decoding (MTD) –MTD repeatedly changes symbols of the accepted message and can achieve at linear complexity of realization the decision of the optimum decoder (OD). –It is a result of the iterative approach application to the error correction. It was revealed at USSR at 22 years earlier, than in the West. –Usually "price" of optimum decoding – (as for Viterbi algorithm, VA) - full search, and complexity MTD - only linear function of a code length!!! –

28. What is necessary from codes for communication networks? What is necessary from codes for communication networks? Prof. Berlecamp (USA) had said in 1980 in the review : Prof. Berlecamp (USA) had said in 1980 in the review : " It - a code gain! ", - a measure of effect of increase in energy of the signal, estimated as ~ $1 million per 1 dB CG. " It - a code gain! ", - a measure of effect of increase in energy of the signal, estimated as ~ $1 million per 1 dB CG. Now it is even more important as it is shown on ours website SRI RAS www.mtdbest.iki.rssi.ru Now it is even more important as it is shown on ours website SRI RAS www.mtdbest.iki.rssi.ruwww.mtdbest.iki.rssi.ru Now every additional one dB CG gives in the big networks economic benefit in hundred millions dollars! Now every additional one dB CG gives in the big networks economic benefit in hundred millions dollars! Resource CG can be realized for decrease in the sizes of aerials, and also for increase in speed, reliability and distance of communication. It is extremely important for satellite systems of communication such as VSAT, and also projects micro- and nano- satellites or other high-speed systems of communication. Resource CG can be realized for decrease in the sizes of aerials, and also for increase in speed, reliability and distance of communication. It is extremely important for satellite systems of communication such as VSAT, and also projects micro- and nano- satellites or other high-speed systems of communication.

29. V.V.Zolotarev. The coding theory29 The main fundamental scientific problem of transition from analog Communications(connections) and computer science To digital Maintenance of a high level of reliability of formation, processing, transfer and storage of figures. Maintenance of a high level of reliability of formation, processing, transfer and storage of figures. Means of the decision of this problem - methods of the theory of noiseproof coding Means of the decision of this problem - methods of the theory of noiseproof coding The main fundamental scientific problem of transition from analog Communications and computer science to the digital one Maintenance on completely new theoretical principles of a high level of reliability of transmission and storage of data. Maintenance on completely new theoretical principles of a high level of reliability of transmission and storage of data. The most successful decisions of this problem are offered with the theory of noiseproof coding The most successful decisions of this problem are offered with the theory of noiseproof coding

30. The main problems of coding technology 1. To decode - it is easier!. 1. To decode - it is easier!. 2. Reliability - is higher! 2. Reliability - is higher! 3. Maximum to take into account Conditions of coding in real systems of communication 3. Maximum to take into account Conditions of coding in real systems of communication 4. How it may be reached? Multithreshold Decoders!!! 4. How it may be reached? Multithreshold Decoders!!! Why? They are extremely simple and very affective! Why? They are extremely simple and very affective!

31. V.V.Zolotarev. The coding theory31 Limiting opportunities of codes Capacity of the channel C R1

32. V.V.Zolotarev. The coding theory32

33. V.V.Zolotarev. The coding theory33 Limiting code cain (CG) in the case of the condition R <C