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# For channels with a large noise level: MTD - - PowerPoint PPT Presentation

For channels with a large noise level: MTD -. Quick Decoders. IKI RAS Dr. Sc. V. V. Zolotarev. 0 1 0 0 0?1110? 01? 0 1 # ?. The main limitation in information theory for coding. The condition must be always satisfied : R < C !

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### For channels with a large noise level:MTD -

Quick Decoders

IKI RAS

Dr. Sc. V. V. Zolotarev

0 1 0 0 0?1110? 01? 0 1 # ?

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

An example of the encoder

for a convolutional code

with a code rate R=1/2.

V.V.Zolotarev. The quick decoders

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 quick decoders

Main problems 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. 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 multithreshold decoders (MTD)!!!

V.V.Zolotarev. The quick decoders

Multithreshold decoding 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. (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) - total search,

But for MTD the complexity is linear !!!

V.V.Zolotarev. The quick decoders

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 quick decoders

Hard realization complexity (VLSI) сверточного СОК с

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 parametersin ~ 1000 times more quickthan turbo and others decoders!

V.V.Zolotarev. The quick decoders

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

Typical complexity: N1=C0*d*I,

but in MTD: onlyN2=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!

V.V.Zolotarev. The quick decoders

The explanation сверточного СОК с 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!

V.V.Zolotarev. The quick decoders

What is needed сверточного СОК с 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!

V.V.Zolotarev. The quick decoders

Code Gain - power increase effect! сверточного СОК с

V.V.Zolotarev. The quick decoders

The scientific and technological revolutions in coding сверточного СОК с

V.V.Zolotarev. The quick decoders

Welcome for everybody! сверточного СОК с Visitors of oursite 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.

V.V.Zolotarev. The quick decoders

Conclusions сверточного СОК с

1. 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!

V.V.Zolotarev. The quick decoders

Thank you! сверточного СОК с

Moscow

10.06.2004

Russia

Space Research Institute RAS

In Russia: e-mail: [email protected]

Work tel. +7 095 333 23 56, +7 095 261 54 44

mоb.: +7 916 518 86 28, V.V.Zolotarev

www.mtdbest.iki.rssi.ru

V.V.Zolotarev. The quick decoders