Optimum Decoding Characteristics Achievement on the Basis of Multithreshold Algorithms (for...

Optimum Decoding Optimum Decoding Characteristics Characteristics

Achievement on the Basis Achievement on the Basis of Multithreshold of Multithreshold

AlgorithmsAlgorithms(for ISCTA’07)(for ISCTA’07)

Space Research Institute RAS Space Research Institute RAS United Radioelectronic TechnologiesUnited Radioelectronic Technologies

- - - - - - - -- - - - - - - -

V.V.Zolotarev, S.V.Averin, I.V.Chulkov

35 years MTD35 years MTD 22

Application of noiseproof coding is

necessary, because:

• 1. The large code gain can be received!1. The large code gain can be received!

• Thus:

• 2. Distance of communication increases.2. Distance of communication increases.

• 3. Data transmission reliability and speed 3. Data transmission reliability and speed increases.increases.

• 4. The sizes of aerials considerably decrease.4. The sizes of aerials considerably decrease.

• 6. Work of a communication system is 6. Work of a communication system is provided at essential higher noise levels.provided at essential higher noise levels.


The lower estimations for error probabilities The lower estimations for error probabilities ofof

an optimum decoding block an optimum decoding block codes with R=1/2 in codes with R=1/2 in BSC.BSC.

Even codes of length n=1000 are inefficient Even codes of length n=1000 are inefficient at probability of an error Ро~0.08 in the channel.at probability of an error Ро~0.08 in the channel. But the theory states, that it is possible to work

successfully if P0<0.11 when C>R

n=24

C=RC=R

0,110,11


Threshold repeated short convolutional code decoding R=1/2 d=5

But it was a weak result!

ThresholThresholdd

elementelement

InformationInformation

SyndromeSyndrome

OutOut OutOut


Repeated Application Repeated Application Efficiency of the Threshold Efficiency of the Threshold

AlgorithmAlgorithm

10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

Число ошибок в блоке

Дол

я ис

прав

ляем

ых

блок

ов

1

2

1) попытка 12) попытка 2

VeryVery

goodgood!!

Why is it Why is it much more much more than d/2?than d/2?

d=11 R=1/2 d=11 R=1/2 n=1000 n=1000

N errors in code blockN errors in code block

Part of Part of

good good

decodedecodedd

blocksblocks

11

22


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

The Convolutional Multithreshold Decoder for a

Code with R=1/2, d=5 and 3 iterations

It is - It is - discovery!discovery!


The Block Multithreshold Decoder for Code with R=1/2 and d=5


SOFTWARE IMPLEMENTATION SOFTWARE IMPLEMENTATION OF MULTITHRESHOLD DECODEROF MULTITHRESHOLD DECODER

1. The complexity of software implementation: NMTD1=(I+1)(d+2) additive equivalent operations on an information bit, where I is number of iterations and d is a minimal code distance.2. MTD is applicable for codes with d<20 and needs about 10-20 decoding iterations.3. It’s possible to decrease number of operations to NMTD2~4d+3I operations. It is much less than turbo codes decoder

complexity! -In ~100 times more quickly, than for turbo codes!


Chipset MTD DecoderChipset MTD Decoder at PLISat PLIS XilinxXilinx


NEW DECODER IN ALTERA PLIS FOR SPEED 600Mb/s AND MORE IN THE SPACE

CHANNEL

Декодер МПД на ПЛИС ALTERA, 640 Мб/с Pb(e)~10-7

Created – Создано - in 2007


HARDWARE IMPLEMENTATION OF HARDWARE IMPLEMENTATION OF MULTITHRESHOLD DECODERMULTITHRESHOLD DECODER

1. MTD consists of shift registers. They are the fastest elements in PLIS or BIS. The part of other elements in MTD is less than 1%.

2. MTD consists of 6 - 40 parallel shift registers and one-step threshold elements. That’s why the complexity of MTD implemented on PLIS is in 100 and more times faster than other decoder

3. Characteristics of MTD PLIS codec : - speed is about 320 - 960 Mbps and more, - coding gain is about 6,5 - 9,5 dB. So, decoding speed is as for single 2 bit adder!


Characteristics MTD, VA and a Turbo Codes in Gaussian Channels at R=1/2

1,E-07

1,E-06

1,E-05

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

0 0,5 1 1,5 2 2,5 3 3,5 4

RATIO Eb/N0, dB

Bit

erro

r rat

e P

b(e)

_

MTD-X

MTDmd2VA+RS

MTD+CC2

MTD-L

MTD+CC3

MTD-NEC

TURBO

VA К=7

С=1/2


Which decoder must be used? - Most simple and - Most simple and effectiveeffective !!! !!!

Improvements in decoder effectivenessCG - the history of increments

0

1

2

3

4

5

6

7

8

9

10

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Years

CG

,dB

ЭВК

TDVA CC: VA:RS

MTD

Turbo

cc: turbo, MTD, LDPC??


Welcome for everybody! Visitors of our site

www.mtdbest.iki.rssi.ru in November, 2006.

~5 Gbytes asked data from us for more than 8000 site visitors of 60 countries in 2006.

------------------------------------------------------------------------------------------------------------------------

RussiRussiaa

????????

240 data 240 data unitsunits

USUSAA


Гости двуязычного специализированного сайта

ИКИ РАН www.mtdbest.iki.rssi.ru в декабре 2006г.

Свыше 8000 посетителей нашего веб-сайта из 46 стран переписали более 2 Гбайт данных об алгоритмах МПД в 2006 г.

Свыше 8000 посетителей нашего веб-сайта из 60 стран переписали более 5 Гбайт данных об алгоритмах МПД в 2006 г.

USA

Россия

Более 240 блоков данных!

Статистика за 2006 год, декабрь

????????


Reference bookReference book«Помехоустойчивое «Помехоустойчивое

кодирование.кодирование. Методы и алгоритмы» Методы и алгоритмы»

под редакцией под редакцией Ю.Б.ЗубареваЮ.Б.Зубарева

Авторы: В.В.Золотарёв, Г.В.ОвечкинАвторы: В.В.Золотарёв, Г.В.Овечкин

Издательство Издательство «Горячая линия - Телеком», 2004г. «Горячая линия - Телеком», 2004г.


В.В.ЗолотарёвВ.В.Золотарёв Теория и Теория и алгоритмы алгоритмы

многопорогового многопорогового декодированиядекодирования

Под редакцией Под редакцией члена-корреспондента РАН члена-корреспондента РАН

Ю.Б.ЗубареваЮ.Б.Зубарева Издательства Издательства

«Радио и связь», «Радио и связь», «Горячая линия - «Горячая линия -

Телеком» Телеком» 20062006 г.г.


ConclusionsConclusions1. We have invented effective iterative MTD algorithms 35 years ago. 2. Complexity of program versions MTD - for today an absolute minimum of calculations. A difference from a turbo codes on number of operations at comparable efficiency of ~100 times! 3. Hardware MTD can be faster than a turbo decoders up to 1000 times! 4. Decisions MTD quickly aspire to decisions of the optimum decoder (OD) even for large noise level 5. MTD – is the absolute leader by criteria "speed" and "complexity-efficiency". 6. MTD – is one of the leading algorithms! WE SUGGEST TO WORK TOGETHER!


17.07.200717.07.2007

In Russia: e-mail: In Russia: e-mail: [email protected]@yandex.ru Work ph.: +7 495 333 45 45, Work ph.: +7 495 333 45 45, +7 +7 4 495 95 573 51 32573 51 32mоb.: mоb.: +7 916 518 86 28, +7 916 518 86 28, V.V.Zolotarev, S.V.Averin, I.V.Chulkov

www.mtdbest.iki.rssi.ru

SRI RAS, URT

mailto:[email protected]


17.07.2007 17.07.2007 г.г.

Space Research Institute RASSpace Research Institute RASт.+7-(495)-333-45-45 E-mail: [email protected]моб.: +7-916-518-86-28

www.mtdbest.iki.rssi.ru

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