Transcript Многопороговые алгоритмы, реализованны

Non-Binary
Multithreshold Decoders
with Almost Optimum
Performance
(For ISCTA’07)
Space Research Institute RAS United
Radioelectronic Technologies
--------
V.V.Zolotarev, S.V.Averin
They think, that only
Reed-Solomon
codes may be used
for non-binary flows
• 1. RS
decoders
require
~n2 operations
• 2. More effective RS decoders
can work with complexity near
~n3 operations
• But q-ary MTD has linear complexity!!!
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The Block Multithreshold Decoder
for Code with R=1/2 and d=5
It is and q-ary simbolic MTD also
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SOFTWARE
IMPLEMENTATION OF
Q-MULTITHRESHOLD
DECODER
1.The complexity of
software MTD decoder
– 4÷8 lines of code C++!
2. It can decode up to 25÷50
Mbit/s with IBM PC!
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Comparison of efficiency binary
and symbolical MTD
Symbolic MTD
Binary MTD
P2(∑>6)
~0,08
Pq(∑>9)
0,3
~0,00005
0,25
d=11
Pthr(e)
0,2
0,15
P(e)
0,1
0,05
Pj~0,03
0
0
1
2
3
4
5
6
7
8
9
10
11
Error probability as funcion of bad checknumber J
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Non-binary MTD - variant 1
In ~10000000 times less operation number in MTD
Performance long codes RS and QMTD for R=1/2
Decoder error probabilities
Ps(e)
1,E+00
1,E-01
1,E-02
1,E-03
M32b1
1,E-04
RS256
М400
1,E-05
M4000
1,E-06
RS4096
1,E-07
M32b2
1,E-08
1,E-09
RS65536
1,E-10
0,3
0,29 0,28 0,27 0,26 0,25 0,24 0,23 0,22 0,21 0,2 0,19 0,18 0,17 0,16 0,15
Channel error probabilities in QСК, P0
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Non-binary MTD - variant 2
Performance long codes RS and QMTD for R=19/20
In ~100000 times less operation number in MTD
1,E+00
1,E-01
RS256
Ps
Decoder Ps(e)
1,E-02
1,E-03
RS4096
RS1024
1,E-04
1,E-05
R=7/8 n256
M80Kb2
1,E-06
M80Kb1
1,E-07
1,E-08
0,025
0,023
0,021
0,019
0,017
0,015
0,013
0,011
Channel symbol
error
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MTDprobabilities P0
0,009
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Reference book
«Error correcting codes.
Methods and Algorithms»
под редакцией
Ю.Б.Зубарева
Authors: V.V. Zolotarev, G.V. Ovechkin
Издательство
«Горячая линия - Телеком», 2004г.
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V.V.Zolotarev
Theory and Algotithms of
Multithreshold decoding
Под редакцией
члена-корреспондента РАН
Ю.Б.Зубарева
Издательства
«Радио и связь»,
«Горячая линия - Телеком»
2006 г.
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Conclusions
1We have invented effective iterative MTD
algorithms 35 years ago.
2. QMTD appeared in1985.
3. It alwais better than RS codes, since
our codes are very long, decoding is
extremely simple, and symbol size does
not depend of code length at all!
4. QMTD is usually almost optimum
decoder (OD) even for large noise level
5. RS decoder with equal effectiveness is
in 1000 ÷ 10 5 times more slow.
6. MTD – is the absolute leader forever!
WE SUGGEST TO WORK TOGETHER!
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In Russia: e-mail: [email protected]
Work ph.: +7 495 333 45 45, +7 495 573 51 32
mоb.: +7 916 518 86 28,
V.V.Zolotarev, S.V. Averin
www.mtdbest.iki.rssi.ru
16.07.2007
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ИКИ РАН ОРТ
т.+7-(495)-333-45-45
E-mail: [email protected]
моб.: +7-916-518-86-28
www.mtdbest.iki.rssi.ru
16.07.2007 г.
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