For channels with a large noise level: MTD -

For channels with a large noise level:

MTD -

IKI RAS

Dr. Sc. V. V. Zolotarev

2V.V.Zolotarev. The quick decoders

The main limitation in information theory for coding

The condition must be always satisfied:

R < C !Here: R - code rate, C - channel capacity.

In this case digital transmission is possible with an arbitrary small probability of an error.

V.V.Zolotarev. The quick decoders

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Whenever possible - it is else easier!!!

An example of the encoder for a convolutional code with a code rate R=1/2.


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!


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Main problems Main problems of coding technicsof coding technics

1. Decoding - more simple!.2. Reliability - better!. 3. To take into account real communications’ requirements4. How must they achieve it? With iterative multithreshold decoders (MTD)!!!


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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 - a result of iterative methods application Usually "price" of the OD solution

((as for Viterbi algorithm) as for Viterbi algorithm) - - total searchtotal search,, But for MTD the complexity is linear !!!But for MTD the complexity is linear !!!


This is convolutional MTD with R=1/2, d=5 and 3 iterations

Рис. 1. Многопороговый декодер сверточного СОК с R=1/2, d=5 и nA=14

0 1 2 3 4 5 6

0 1 2 3 4 5 6

6 5 4 3 2 1

T1

v

u

0

0 1 2 3 4 5 6

0 1 2 3 4 5 6

6 5 4 3 2 1

T2

0

0 1 2 3 4 5 6

0 1 2 3 4 5 6

6 5 4 3 2 1

T3

0


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Hard realization complexity (VLSI)

1. MTD contains almost only memory or shift registers. They are most quick elements in all PLIS or VLSI. Other scheme elements - are less than 1% . 2. MTD has 3 - 40 such registers and threshold switches (TS) are with instant function calculation reaction. So this decoders appear to be for some code parameters in ~ 1000 times more quick than turbo and others decoders!


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Minimum computations in MTD (number of operations per bit, software realization)

Typical complexity: N1=C0*d*I,

but in MTD: only N2=C1*d+C2*I,- Sum d and I, no multiplications(!!!) Ci - little integers, d – code distance, I-iterations.- It is in ~ 100 times (!!!) more simple than for turbo codes also!


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The explanation of MTD efficiency

1. The special very simple iterative procedure was created. 2. The new 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!


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What is needed for communications?

Prof. Berlecamp (USA) said in 1980 in IEEE survey:

“ It is a code gain”, - the measure of signal power growth effect due

to coding of transmitting data with profit ~$1 million for 1 dB of code gain.

Now it is else much more desirable {see our survey in main Russian communication magazine «Electrosvaz» No.9, 2003; its translation is placed at our web-site www.mtdbest.iki.rssi.ru too} Every 1 dB of code gain gives for communication nets profit up to hundreds millions of dollars now!


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Code Gain - power increase effect!


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The scientific and technological revolutions in coding

The effectiveness of old and new decoding algorithms for R=1/2

1,E-07

1,E-06

1,E-05

1,E-04

1,E-03

1,E-02

1,E-01

0 1 2 3 4 5 6 7 8 9 10

Eb/N0

BE

R,

bit

err

o r

ate

without coding

Viterbi

MTD usual

MTD-C

1-st revolution

2-nd revolution


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Welcome for everybody! Visitors of our site

www.mtdbest.iki.rssi.ru in March, 2004.

~1 Gbytes asked data from us for more than 5000 site visitors of 38 countries in 2004.


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Conclusions1. We discovered iterative MTD methods 32 years ago.

2. Complexity of software MTD is absolutely minimal.

Difference is ~100 times with turbo codes!

3.Hardware MTD is ~1000 times more quick than turbo!

4. MTD decisions very quickly converge to optimal decoder (OD) results!

5. MTD is absolute leader among all decoders on criterion “complexity-effectiveness”. 6. So we are absolute leaders forever in decoding! We go ahead of the whole world!


10.010.066.2004.2004

In Russia: e-mail: In Russia: e-mail: [email protected] Work tel. +7 095 333 23 56, Work tel. +7 095 333 23 56, +7 +7 095 095 261 261 554 444 44mоb.: +7 916 518 86 28, mоb.: +7 916 518 86 28, V.V.ZolotarevV.V.Zolotarev

www.mtdbest.iki.rssi.ru

For channels with a large noise level: MTD -

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