Transcript Обзор современных методов помехоустойч

Scientific session
DNIT of the RAS
New optimization
coding theory and its
applied achievements
24.04.2008.
V.V.Zolotarev, SRI RAS
The mainbasis
fundamental
scientificexact
• Theoretical
of
unequivocal
•
•
problemofofan
transition
from
analog
restoration
analog signal
is the
theorem
Communications(connections)
of readout
of academician V.A.Kotelnikov.
computer
At and
transition
of science
our
technological
To digitaland storage of the
civilization to transmission
information to a discrete form the main
• Maintenance of to
a high
level systems, becomes their
requirement
such
of reliability of formation,
conformity
to Shannon
theorem.
processing, transfer
and
storage of figures.
In this
it of
is possible to restore always
• Means
of thecase
decision
- methods
of
in this
theproblem
receiver
the digital
message deformed in
the theory of noiseproof
a channel,
with as much as necessary small
coding
error probability if the length of the code block
will grow.
This theorem has begun the modern
theory
coding.
V.V.Zolotarev.of
The coding
theory
2
Coding -Coding
introduction
of
This isThis
introduction
of redundancy
redundancy
K - the
k information
– the information
Rr--superfluous
symbols
superfluous symbols
++
n=k+r - length of the block
n=k+r - length of the block
R=k/n <1
<1 --code
R=k/n
codespeed
rate
Channel capacity С
is a function of energy in BCS
1
Capacity С
0,8
0,6
WIT
H
0,4
0,2
0
-8
-6
-4
-2
0
2
4
signal/noise ratio, dB
C <1!
V.V.Zolotarev. The coding theory
4
The basic restriction
of the Information Theory
for coding
• Always condition
R <C
must satisfy!
• In this case there are systems of coding which can
provide transfer of the digital information with as
much as small probability of a mistake if the length of
the block of the data will be great enough
(K.Shannon, the theorem of coding existence)
V.V.Zolotarev. The coding theory
5
What is necessary for codes
in communication networks?
• It is - a code gain, CG!, - a measure of signal
•
•
energy effectiveness increase.
Now every one additional dB in CG gives in
communication networks economic benefit in
many millions dollars!
Resource ЭВК can be realized at ERS for
decrease of aerials sizes, and also for increase
in
speed,
reliability
and
distance
of
communication. It is extremely important for
satellite communication systems
such as
VSAT, and also projects micro- and nanosatellites or other high-speed communication
systems. It is achieved only by correct fast
mathematical processing of a digital stream!
V.V.Zolotarev. The coding theory
6
The low estimations of error probabilities decoding
for block codes with R=1/2
Even codes of length n=1000 are inefficient at error
probability in the channel Ro> 0.08. And the theory
asserts it is possible to work successfully at Ро <0.11 !!!
And it occurs at 2500 variants of decisions!
Number of atoms in the Universe is more little!
1,E+00
Вероятность ошибки на блок
234
P0
1,E-01
1,E-02
n=100
1,E-03
1,E-04
1,E-05
n=10000
n=3000
n=1000
n=300
-1 dB
1 dB
0 dB
1,E-06
0,11
0,1
0,09
0,08
0,07
P0 - вероятность ошибки в ДСК
0,06
0,05
Complexity of decoders for
different codes with length n
Exponencial !!!
Asimptotic
complexity
of the decoding
algoritms
maximum
en
VA !!!
minimal
polinomial
~nm
Linear
~n
MTD
1
Quadratic,
~n2
Discr.
algebra
2
3
V.V.Zolotarev. The coding theory
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8
The block multithreshold decoder for
a code with R=1/2, d=5 and I iterations
MTD,complexity-N~d*I*n
V.V.Zolotarev. The coding theory
9
The reasons of high efficiency new
MTD a method
• 1. Procedure is applied special very easy for
•
•
•
•
realization iterative оптимизационная.
2. Special codes with a minimum level of
grouping of mistakes - too a method of
optimization are constructed.
3. Process of many hundreds parameters
special optimization in the decoder was
realized.
Problems 1 and 2 - “are very difficult"
The problem 3 - has not appeared at all
V.V.Zolotarev. The coding theory
10
Minimum of calculations at
decoding - in MTD!
(Number of operations per bit,
soft realization)
Usually: N1 ~ d*I, - product
and in MTD: only N2~d+I, - the
sum of key parameters d and I.
It is in ~100 times easier and faster than,
for example, at use of a turbo codes!
It was realized in special TV-system.
Hardware realization MTD at VLSI
1. MTD will consist almost completely of
store elements or shift registers. These are
the fastest elements in VLSI. The share of
other elements in MTD is less than 1 %.
2. MTD may be absolutely parallel one step
algorithm. For this reason MTD for some
values of parameters approximately in 1000
times faster, than for example, a turbo
decoders. A delay - as for the elementary 2input key - absolute minimum .
3. Realization: throughput: up to 1,6Gb/s,
and CG = 7 - 9,5 dB
Chipset of the MTD decoder
at Xilinx for channels with speeds
up to 150 Mb / s
V.V.Zolotarev. The coding theory
13
Multithreshold decoder (MTD) for satellite and space channels, raises efficiency
of their use in 3-10 times, including for EDS. Simple MODEL MTD at Altera for
channels up to 640 Mbit / s. The method can work at information speeds up to
1,6 Gbit / s
MTD for the Space!
V.V.Zolotarev. The coding theory
14
New scientific and technological
revolution – data transmission
with the minimal power
Эффективность новых и старых методов кодирования
при кодовой скорости R=1/2
BER, вероятность ошибки декодера на бит
1,E-01
W
I
T
H
1,E-02
1,E-03
1,E-04
MTD - simple
No coding
VA
1,E-05
The second revolution
The first revolution
1,E-06
MTDCC
1,E-07
0
1
2
3
4
5
6
Ratio Eb/N0
V.V.Zolotarev. The coding theory
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8
9
10
, дБ
15
The symbolical multithreshold decoder for
a code with R=1/2, d=5 and I iterations
-
QMTD-symbolic
V.V.Zolotarev. The coding theory
?
16
Welcome! Visitors of web-site SRI RAS
www.mtdbest.iki.rssi.ru in March, 2008.
USA
Netw
ork
???
More than 18000 visitors of our web-site
from 56 countries have copied more than
7 Gbytes data about MTD algorithms
during last year. V.V.Zolotarev. The coding theory
17
Chipset MTD decoder
at ALTERA basis
V.V.Zolotarev. The coding theory
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Conclusions
1. We have opened iterative MTD algorithms 35 years ago.
2. Complexity of the soft versions MTD is an absolute known
minimum of calculations. A difference with other codes is ~100
times! The rare case in the theory! We outstrip all countries
~ 7 ÷ 10 years.
3. Hard MTD are faster than a other codes ~1000 times!
4. Decisions MTD are almost always optimum even at the big
noise level.
5. MTD - the absolute leader by criteria "complexity efficiency". It is created in Russia!
6. Non-binary codes for MTD - the most unique discovery in the
coding theory during last 30 years. They are unknown abroad!
The Russian scientific school - again in
the group of world leaders in the theory!
V.V.Zolotarev. The coding theory
19
SRI of the Russian Academy of Sciences
in Moscow w.ph.: (495) 333 45 45,
www.mtdbest.iki.rssi.ru,
e-mail: [email protected]
mobil: +7 916 518 86 28
V.V.Zolotarev
24.04.2008.
V.V.Zolotarev. The coding theory
20
Further there are help
slides - appendices to the
report
V.V.Zolotarev. The coding theory
21
Whenever possible - to code easier!!! An
example of the coder for свёрточного a code
with code speed R=1/2
V.V.Zolotarev. The coding theory
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Differenr philosophy in coding theory
1
Abroad
Effectiveness
0,8
0,6
0,4
Russia,
MTD
0,2
0
0
0,2
0,4
0,6
0,8
1
Algorithm throughput
V.V.Zolotarev. The coding theory
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Complexity of various algorithms
of decoding
Codes and algorithms
Algorithm Viterbi
Algebraic codes
Turbo codes
Low dencity parity codes
Majority codes- only in Russia - MTD which almost
always converges to optimum
(total search!) the decision, but
with linear complexity
V.V.Zolotarev. The coding theory
Complexity
2n
n2
C1*n
C2*n
C3*n
С3 <C2 <C1
24
Convolutionale multithreshold decoder
for a code with R=1/2, d=5 and 3 iterations
uˆ
vˆ
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
4
5
6
6
5
4
3
2
1
0
6
5
4
3
2
1
0
6
5
4
3
2
1
0
T1
T2
T3
Fig. 1. The multithreshold decoder сверточного JUICE with R=1/2, d=5 and nA=14
V.V.Zolotarev. The coding theory
25
The reasons of high efficiency new
МПД a method
• 1. Procedure is applied special very easy
for realization iterative
оптимизационная.
• 2. Special codes with a minimum level of
grouping of mistakes - a method of
optimization are constructed.
• 3. Special optimization of many hundreds
parameters of the decoder is carried out.
• Problems(Tasks) 1 and 2 - "very difficult"
• The problem(task) 3 - was not put at all
Multithreshold decoding (MTD)
– MTD repeatedly changes symbols of the accepted
message and can achieve at linear complexity of
realization the decision of the optimum decoder
(OD).
– It is a result of the iterative approach application to
the error correction. It was revealed at USSR at 22
years earlier, than in the West.
– Usually "price" of optimum decoding
– (as for Viterbi algorithm, VA) - full search, and
complexity MTD - only linear function of a code
length!!!
V.V.Zolotarev. The coding theory
27
–
What is necessary from codes
for communication networks?
• Prof. Berlecamp (USA) had said in 1980 in the review :
• " It - a code gain! ", - a measure of effect of increase
•
•
•
in energy of the signal, estimated as ~ $1 million per
1 dB CG.
Now it is even more important as it is shown on ours
website SRI RAS www.mtdbest.iki.rssi.ru
Now every additional one dB CG gives in the big
networks economic benefit in hundred millions dollars!
Resource CG can be realized for decrease in the sizes
of aerials, and also for increase in speed, reliability
and distance of communication. It is extremely
important for satellite systems of communication such
as VSAT, and also projects micro- and nano- satellites
or other high-speed systems of communication.
The main fundamental scientific
The main
scientific
problem
offundamental
transition from
analog
problem
of transition from analog
Communications(connections)
Communications
computer
and computerand
science
science to
digital one
Tothe
digital
• Maintenance of a high level
•
of reliability
of formation, on
Maintenance
completely new
processing, transfer and
theoretical
principles of a high level of
storage of figures.
• Means of theof
decision
of
reliability
transmission
and storage of
this problem - methods of
data.
the theory of noiseproof
coding
•
The most successful decisions of this
problem are offered with the theory of
noiseproof coding
V.V.Zolotarev. The coding theory
29
The main problems
of coding technology
• 1. To decode - it is easier!.
• 2. Reliability - is higher!
• 3. Maximum to take into account
Conditions of coding in real systems of
communication
• 4. How it may be reached?
Multithreshold Decoders!!!
• Why? They are extremely simple and
very affective!
Limiting opportunities of codes
Пропускная способность канала и
скорость R1
Зависимость пропускной способности ДСК и скорости R1
от вероятности ошибки в канале Po
1,00
0,90
C
0,80
0,70
Capacity of the channel
0,60
C
0,50
R1
0,40
0,30
R1
0,20
0,10
0,00
0,000
0,050
0,100
0,150
0,200
0,250
0,300
0,350
0,400
0,450
0,500
Po - вероятность ошибки в канале
V.V.Zolotarev. The coding theory
31
Зависимость предельной энергетики канала Eb/N0
от кодовой скорости R
7
6
5
Eb/N0, дБ
.
4
АВ
3
"жёсткий", М=2
2
"мягкий", М=16
1
0
-1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
R - кодовая скорость
V.V.Zolotarev. The coding theory
32
Limiting code cain (CG) in the
case of the condition R <C
V.V.Zolotarev. The coding theory
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