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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 !

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For channels with a large noise level mtd

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 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


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 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 of coding technics
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 mtd
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


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

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

V.V.Zolotarev. The quick decoders


Hard realization complexity vlsi
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 number of operations per bit software realization
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 of mtd efficiency
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 for communications
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
Code Gain - power increase effect! сверточного СОК с

V.V.Zolotarev. The quick decoders


The scientific and technological revolutions in coding
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
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


10 0 6 2004

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


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