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Principles of space communication systems Space for Education, Education for Space
Space for Education, Education for Space ESA Contract No. 4000117400/16NL/NDe
Specialized lectures
Principles of space communication systems
Peter Farkaš
Principles of space communication systems Space for Education, Education for Space
• Connection with previous lectures • Link Budget • Muscles • Essence
– AWGN channel alias DSC channel model – modulation – discrete AWGN channel – why BPSK? – why channel coding?
• Channel Codes • Hard versus soft decoding • Concluding remarks
Layout
2
Principles of space communication systems Space for Education, Education for Space
• Prof. Hubinský
Described very well difficulties and problems with Deep Space Communication (DSC)
• Assoc. Prof. Valko
Mentioned that the bottleneck is channel throughput Often there is lot data and it is impossible (difficult or time consuming) to bring them to Earth
Connection
3
Principles of space communication systems Space for Education, Education for Space
What we will imagine if we hear DSC?
4
Principles of space communication systems Space for Education, Education for Space
5
Image: ESA
Principles of space communication systems Space for Education, Education for Space
ESA's tracking station network Estrack
6
Image: ESA
Principles of space communication systems Space for Education, Education for Space
Spectra for Deep Space Communication Present & Future
7
Visible light 430–770 THz 4.3x1012 to 7.7x1012 Hz
X Ray spectrum 30 petaHz – 30 exaHz (3×1016 Hz to 3×1019
Credit: Augmented snapshot from ESA video
Image: ESA
Principles of space communication systems Space for Education, Education for Space
ESA's tracking station Antenna
8
Image: ESA
Principles of space communication systems Space for Education, Education for Space
ESA's tracking station Demux
9
Image: ESA
Principles of space communication systems Space for Education, Education for Space
ESA's tracking station Demux
10
Image: ESA
Principles of space communication systems Space for Education, Education for Space
11
Image: ESA
This are just a muscles & resource 4 DSC
Principles of space communication systems Space for Education, Education for Space
Are the muscles strong enough?
12
Image: ESA
Principles of space communication systems Space for Education, Education for Space
Are the muscles strong enough?
13
If not can it help to built a bigger HW and use more power ?
Image: ESA
Principles of space communication systems Space for Education, Education for Space
Range equation
14
224)(
m
W
d
Pdp t
Isotropic radiator
Principles of space communication systems Space for Education, Education for Space
Range equation
15
224)(
m
W
d
Pdp t
tP
d
Isotropic radiator
Principles of space communication systems Space for Education, Education for Space
Range equation
16
224)(
m
W
d
Pdp t
tP
d
err AdpP )(
Isotropic radiator
Principles of space communication systems Space for Education, Education for Space
Range equation
17
224)(
m
W
d
Pdp t
tP
d
24 d
APP ert
r
Isotropic radiator
Principles of space communication systems Space for Education, Education for Space
Range equation
18
dB3
dB3
peak
Principles of space communication systems Space for Education, Education for Space
Range equation
19
dB3
dB3
peak
steradians4πoveraverage
intensitypowermaxG
Principles of space communication systems Space for Education, Education for Space
Range equation
20
dB3
dB3
peak
steradians4πoveraverage
intensitypowermaxG
24 d
APGP ertt
r
Principles of space communication systems Space for Education, Education for Space
Range equation
21
2
2;
4
er
err A
AG
24 d
AGPP ertt
r
4
2
rer GA
S
rttrttr
L
GGP
d
GGPP
24
Principles of space communication systems Space for Education, Education for Space
Range equation ->Link Budget
22
S
rttr
L
GGPP
Srtt
S
rttr LGGP
L
GGPP 101010101010 log10log10log10log10log10log10
Principles of space communication systems Space for Education, Education for Space
Link Budget Example: Voyager I
23
WPt 18
MHzfc 8415
md 50002060258167
dBiGt 48
dBiGr 85
Principles of space communication systems Space for Education, Education for Space
Link Budget Example: Voyager I
24
f
c m03565,0
108415
1036
8
Hzfc 8415
md 50002060258167
48283202377047816580955274046428
03565,0
5000206025816742
SL
Principles of space communication systems Space for Education, Education for Space
Link Budget Example: Voyager I
25
f
c m03565,0
108415
1036
8
Hzfc 8415
md 50002060258167
48283202377047816580955274046428
03565,0
5000206025816742
SL
dBLS 317
Principles of space communication systems Space for Education, Education for Space
Link Budget Example: Voyager I
26
mWPt 18000
dB317
dBmPt 5,82
dBiGt 48
dBiGr 8,73
dBmPt 7.112
Principles of space communication systems Space for Education, Education for Space
Link Budget Example: Voyager I
27
mWPt 18000
dB317
dBmPt 5,82
dBiGt 48
dBiGr 8,73
dBmPt 7.112 Is this enough? (for reliable transmission)
Principles of space communication systems Space for Education, Education for Space
Reliability BER
28
rationoisetosignalfBER
At the receiving end !
Principles of space communication systems Space for Education, Education for Space
Signal to noise ratio
29
N
S
In analog systems In digital systems
Principles of space communication systems Space for Education, Education for Space
Signal to noise ratio
30
N
S
In analog systems In digital systems
dBN
S10log10
Principles of space communication systems Space for Education, Education for Space
Signal to noise ratio
31
N
S
In analog systems In digital systems
dBN
S10log10
0N
Eb
Principles of space communication systems Space for Education, Education for Space
Signal to noise ratio
32
N
S
In analog systems In digital systems
dBN
S10log10
0N
Eb
dBN
Eb
0
10log10
Principles of space communication systems Space for Education, Education for Space
Energy per bit has to be computed!
33
TR
STE
p
b
Principles of space communication systems Space for Education, Education for Space
Can we also use some brain products?
34
Principles of space communication systems Space for Education, Education for Space
Information Theory
35
Claude Elwood Shannon 1916-2001
„Encoder“ „Decoder“
Noise
][bpsCR
0BER...01100010
Image: MFO
Photo: By Jacobs, Konrad – http://owpdb.mfo.de/detail?photo_id=3807, CC BY-SA 2.0 de https://commons.wikimedia.org/w/index.php?curid=45380422
Principles of space communication systems Space for Education, Education for Space
Coding
36
Source coding
Source decoding
Channel Coding
Channel decoding)
Modulator
Demodulator
Channel
Separation principle of IT
Principles of space communication systems Space for Education, Education for Space
Source coding example
37
Source coding
2
11 P
4
12 P
4
13 P
source
Principles of space communication systems Space for Education, Education for Space
Source coding example
38
Source coding
2
11 P
4
12 P
4
12 P
source
00 2
01 2
11 2
Codewords length
Principles of space communication systems Space for Education, Education for Space
Source coding example
39
Source coding
2
11 P
4
12 P
4
12 P
i
J
i
i PPH
1
2log
source
00 2
01 2
11 2
Codewords length
Principles of space communication systems Space for Education, Education for Space
Source coding example
40
Source coding
2
11 P
4
12 P
4
12 P
message
bit
PPH i
i
i
5.1
log3
1
2
source
00 2
01 2
11 2
Codewords length
Principles of space communication systems Space for Education, Education for Space
Source coding example
41
Source coding
2
11 P
4
12 P
4
12 P
binit
bit75.0
2
5.1
source
00 2
01 2
11 2
Codewords length
Principles of space communication systems Space for Education, Education for Space
Source coding example
42
Source coding
2
11 P
4
12 P
4
12 P
0 1
10 2
11 2
source
Codewords
Principles of space communication systems Space for Education, Education for Space
Source coding example
43
Source coding
2
11 P
4
12 P
4
12 P
0 1
10 2
11 2
source
Codewords
message
binitn 5.12.2.
4
11.
2
1}{
Principles of space communication systems Space for Education, Education for Space
Source coding example
44
Source coding
2
11 P
4
12 P
4
12 P
binit
bit1
5.1
5.1
0 1
10 2
11 2
source
Codewords
message
binitn 5.12.2.
4
11.
2
1}{
Principles of space communication systems Space for Education, Education for Space
Coding
45
Source coding
Source decoding
Channel Coding
Channel decoding)
Modulator
Demodulator
Channel
Here is also redundancy: coding, protocols, synchronization …
Principles of space communication systems Space for Education, Education for Space
Energy per bit has to be computed!
46
TR
STE
p
b
Principles of space communication systems Space for Education, Education for Space
DSC Channel ?
47
Principles of space communication systems Space for Education, Education for Space
AWGN
• Johnson Thermal Noise
48
Hz
WkT 0
0
)(tn
t
Principles of space communication systems Space for Education, Education for Space
AWGN
• Distribution of samples Thermal noise
49
n
2
2
1)(
n
enp
Principles of space communication systems Space for Education, Education for Space
AWGN
Two sided “frequency world” Model
50
n
)(np
0
f
Hz
WN
20
0
Principles of space communication systems Space for Education, Education for Space
AWGN
One- sided “frequency world” Model
51
n
)(np
0
f
Hz
WN0
0
Principles of space communication systems Space for Education, Education for Space
AWGN
One- sided “frequency world” Model
52
n
)(np
0
f
Hz
WN0
0 W
0.NWN
Principles of space communication systems Space for Education, Education for Space
AWGN channel
• Model, which is too idealistic for terrestrial channels, but is quite accurate for deep space channel.
Model
53
)(ts )()()( tntstr i
)(tn
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
54
sbitWN
SWCW /1log
0
2
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
55
sbitWN
SWCW /1log
0
2
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
56
sbitWN
SWCW /1log
0
2
xy log
1 x
y
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
57
sbitWN
SWCW /1log
0
2
ex xx
1
01lim
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
58
sbitWN
SWCW /1log
0
2
ex xx
1
01lim
sbitWN
S
S
WN
S
NCW /1log
0
200
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
59
sbitWN
SWCW /1log
0
2
ex xx
1
01lim
sbitWN
S
S
WN
S
NCW /1log
0
200
sbitWN
S
WS
NC
S
WN
/1loglim
0
0
20
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
60
sbitWN
SWCW /1log
0
2
ex xx
1
01lim
sbitWN
S
S
WN
S
NCW /1log
0
200
sbitWN
S
WS
NC
S
WN
/1loglim
0
0
20
sbitxxS
NC x /1log
0
lim 1
20
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
61
sbitWN
SWCW /1log
0
2
ex xx
1
01lim
sbitxxS
NC x /1log
0
lim 1
20
sbiteS
NC /log2
0
Principles of space communication systems Space for Education, Education for Space
Formula for AWGN channel capacity
62
sbitWN
SWCW /1log
0
2
ex xx
1
01lim
sbitxxS
NC x /1log
0
lim 1
20
sbiteS
NC /log2
0
sbitN
Se
N
SC /44.1log
0
2
0
Principles of space communication systems Space for Education, Education for Space
Digital modulation
63
Principles of space communication systems Space for Education, Education for Space
Digital modulation
64
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
time T
)(tsi)(ts j
Principles of space communication systems Space for Education, Education for Space
Modulation rate
65
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
time T
)(tsi)(ts j
s
symbolch
TRM
.1
Principles of space communication systems Space for Education, Education for Space
How is conected with transmission rate?
66
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
s
symbolch
TRM
.1
s
bitRp
Principles of space communication systems Space for Education, Education for Space
Digital modulation
67
)(tsi )()()( tntstr i
)(tn
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Matched Filter
)(ˆ tsi
decision (MAP )
Principles of space communication systems Space for Education, Education for Space
Digital modulation BPSK
68
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
TttfAts c 0)2cos()(1
TttfAts c 0)2cos()(2
Principles of space communication systems Space for Education, Education for Space
Digital modulation BPSK
69
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
TttfAts c 0)2cos()(1
TttfAts c 0)2cos()(2
Principles of space communication systems Space for Education, Education for Space
Signal space - geometrical representation
70
“… every waveform of finite length and with a finite frequency spectrum can be represented as a point or radius vector in N-space.” “Thus, each of the m signals considered … can be represented by its own point or radius vector.”
V. A. Kotelnikov, Theory of Potential Noise Immunity, DrSc. Thesis 1946
Image: By Kremlin.ru, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=18257931
Principles of space communication systems Space for Education, Education for Space
Signal space (GFT)
71
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
ji
jiEdttt i
ji;0
;)()(
)(...)()()( 121211111 tatatats NN
)(...)()()( 22221212 tatatats NN
)(...)()()( 2211 tatatats NMNMMM
Kotelnikov, Theory of Potential Noise Immunity, DrSc. Thesis 1946
Principles of space communication systems Space for Education, Education for Space
Signal space
72
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
ji
jiEdttt i
ji;0
;)()(
),...,,()( 112111 Naaats
),...,,()( 222212 Naaats
),...,,()( 21 MNMMM aaats
Principles of space communication systems Space for Education, Education for Space
Signal space
73
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
ji
jiEdttt i
ji;0
;)()(
),...,,( 112111 Naaas
),...,,( 222212 Naaas
),...,,( 21 MNMMM aaas
Principles of space communication systems Space for Education, Education for Space
Signal space - geometrical representation
74
)(1 t
)(2 t
1a
2a
s
Principles of space communication systems Space for Education, Education for Space
signal as a point in signal space
75
)(1 t
)(2 t
1a
2a
s
Principles of space communication systems Space for Education, Education for Space
Signal space - geometrical representation
76
If to the transmitted signal is added a noise waveform with a vector which can have an arbitrary direction and arbitrary length, then the resulting received waveform will also be characterized by a point in N-space, which most often will not coincide with any of the points corresponding to signals. Depending on the position of this point, the receiver will reproduce some message or other …
V. A. Kotelnikov : Theory of Potential Noise Immunity, DrSc. Thesis, 1946
Principles of space communication systems Space for Education, Education for Space
Signal space - geometrical representation
77
)(1 t
)(2 t
1a
2a
s
r
n
Principles of space communication systems Space for Education, Education for Space
Digital modulation BPSK
78
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
TttfAts c 0)2cos()(1
TttfAts c 0)2cos()(2
Principles of space communication systems Space for Education, Education for Space
Digital modulation BPSK
79
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
TttfAts c 0)2cos()(1
TttfAts c 0)2cos()(2
bEbE
Principles of space communication systems Space for Education, Education for Space
Digital modulation 64-QAM
80
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Principles of space communication systems Space for Education, Education for Space
Optimal receiver (without tr. code)
81
)(tsi )()()( tntstr i
)(tn
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Matched Filter
)(ˆ tsi
decision (MAP )
Principles of space communication systems Space for Education, Education for Space
Error rates depend on Euclidian distance
82
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Principles of space communication systems Space for Education, Education for Space
Transmission rate ? Modulation Rate
83
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Principles of space communication systems Space for Education, Education for Space
Transmission rate ? Modulation Rate
84
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols) symbolbinitMK /log2
Principles of space communication systems Space for Education, Education for Space
Transmission rate ? Modulation Rate
85
Mp RKR .
Modulation alphabet (channel symbols)
Principles of space communication systems Space for Education, Education for Space
Transmission rate ? Modulation Rate
86
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Mp RR
Mp RR 6
Principles of space communication systems Space for Education, Education for Space
Back to IT
87
Principles of space communication systems Space for Education, Education for Space
Dig. Modul. -> discrete AWGN channel
88
Principles of space communication systems Space for Education, Education for Space
Dig. Modul.> discrete (d.)AWGN channel
89
bpM ERERS
Principles of space communication systems Space for Education, Education for Space
1D signal set AWGN channel capacity?
90
R. M. Fano, „Transmission of Information“, MIT Press 1961
symbolbitN
EC /
21log
2
1
0
2
E0s E1s
Principles of space communication systems Space for Education, Education for Space
When we get energy efficient DSC?
91
symbolbitN
EC /
21log
2
1
0
2
J
symbolbit
E
N
E
E
C /
21log
2
1
0
2
Principles of space communication systems Space for Education, Education for Space
C/E [bit per symbol/J] (N0 =1)
92
C/E
[b
it p
er
sym
bo
l/J]
(N
0 =
1)
10log 10 E/ N0
Principles of space communication systems Space for Education, Education for Space
C/E [bit per symbol/J] (N0 =1)
93
C/E
[b
it p
er
sym
bo
l/J]
(N
0 =
1)
10log 10 E/ N0
44.1
Principles of space communication systems Space for Education, Education for Space
When we get energy efficient DSC?
94
J
symbolbit
N
E
E
C /21log
2
1
0
2
Principles of space communication systems Space for Education, Education for Space
When we get energy efficient DSC?
95
ENERGY EFFICIENT RANGE
J
symbolbit
N
E
E
C /21log
2
1
0
2
2
10
0
N
E
0 1/2 dB35.0log10 10
Principles of space communication systems Space for Education, Education for Space
bps ? in energy efficient range
96
symbolbitN
EC /44.1
0
2
10
0
N
E
How much bps we can get in this range ?
sbitN
ERCRCR M
Mp /44.10
Principles of space communication systems Space for Education, Education for Space
bps ? in energy efficient range
97
symbolbitN
EC /44.1
0
2
10
0
N
E
How much bps we can get in this range ?
sbitN
S
N
ERCRCR M
Mp /44.144.100
Principles of space communication systems Space for Education, Education for Space
bps ? in energy efficient range
98
symbolbitN
EC /44.1
0
2
10
0
N
E
How much bps we can get in this range ?
sbitCN
S
N
ERCRCR M
Mp /44.144.100
Principles of space communication systems Space for Education, Education for Space
Bit Error Rate (BER)?
99
Principles of space communication systems Space for Education, Education for Space
Bit Error Rate (BER)?
100
“energy of a pulse for a given noise power density is the effective determinant of error probability.”
V. A. Kotelnikov, Theory of Potential Noise Immunity, DrSc. Thesis 1946
Principles of space communication systems Space for Education, Education for Space
AWGN channel optimal detection?
• Without coding only hard decision (detection is possible “old fashion”)
Hard detection
101
)(tsi )()()( tntstr i
)(tn
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Matched Filter
)(ˆ tsi
decision (MAP )
Principles of space communication systems Space for Education, Education for Space
AWGN channel optimal detection?
• Without coding only hard decision (detection is possible “old fashion”)
Hard detection
102
)(tsi )()()( tntstr i
)(tn
)(,),(),(1 tststs Mi
Modulation alphabet (channel symbols)
Matched Filter
)(ˆ tsi
decision (MAP )
Rz
Principles of space communication systems Space for Education, Education for Space
Hard decision (detection)
103
z
2
0
1
2
1
0
12
1)/(
ay
eszp
2
0
2
2
1
0
22
1)/(
ay
eszp
Principles of space communication systems Space for Education, Education for Space
BPSK BER
104
0
2
N
EQBER
Principles of space communication systems Space for Education, Education for Space
Uncoded BPSK BER? in energy ef. range
105
1104.2
Principles of space communication systems Space for Education, Education for Space
LESSON LEARNED
106
“If one wants to signal both Energy-efficient and reliably with
binary modulation on deep space channel than one must use channel coding”
J. Massey, DSC & Coding: A Marriage Made in Heaven, Reprint Springer 1992
Principles of space communication systems Space for Education, Education for Space
Channel Coding
• Coding gain up to date codes more than 9 dB at BER =10-5
Coding gain
107
0
log10N
Eb
BER 110
210
310
410
510
5 6 7 8 9 10 [dB]
Mariner 69 2.2 dB Pioneer 9 3 dB . . . Turbo Code 9 dB
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Linear Block Code is a k-dimensional subspace of an n-dimensional vector space over GF(q)
Introduction
108
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
Clasification
109
Linear Nonlinear
Block
Tree
Linear Block Codes
Nonlinear Block Codes
Linear Tree Codes
Nonlinear Tree Codes
Polar Codes
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Linear Block Code is a k-dimensional subspace of an n-dimensional vector space over GF(q)
Introduction
110
Évariste Galois (25 October 1811 – 31 May 1832)
GF(2)
}1,0{
+ 0 1
0 0 1
1 1 0
x 0 1
0 0 0
1 0 1
Principles of space communication systems Space for Education, Education for Space
Repetition Code
111
(111)
(000)
Principles of space communication systems Space for Education, Education for Space
Repetition Code
112
(111)
(000)
Principles of space communication systems Space for Education, Education for Space
Repetition Code
113
(111)
(000)
[3, 1, 3] code
[n, k, dm] code
Principles of space communication systems Space for Education, Education for Space
Repetition Code
114
(000)
[3, 1, 3] code
[n, k, dm] code (111)
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• [7,4,3] Hamming Code Introduction
115
1i
2i3i
4i
Hamming 1915 - 1998
Photo: By Source (WP:NFCC#4), Fair use, https://en.wikipedia.org/w/index.php?curid=40177109
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Hamming Code Introduction
116
1i
2i3i
4i
6c
5c 4c
3c 1c0c
2c
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Hamming Code Introduction
117
1i
2i3i
4i
6c
5c 4c
3c 1c0c
2c16 ic
25 ic
34 ic
43 ic
4210 iiic
3212 iiic
4321 iiic
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Hamming Code Generator Matrix Introduction
118
6c
5c 4c
3c 1c0c
2c16 ic
25 ic
34 ic
43 ic
4210 iiic
3212 iiic
4321 iiic
PIG
1101000
0110100
1110010
1010001
G
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
Introduction
119
16 ic 25 ic 34 ic 43 ic 4210 iiic
3212 iiic
4321 iiic
1101000
0110100
1110010
1010001
G
1i
2i
3i
4i
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Generator Matrix Introduction
120
16 ic
25 ic
34 ic
43 ic
4210 iiic
3212 iiic
4321 iiic
Gic
1101000
0110100
1110010
1010001
G
4321 ,,, iiiii
0123456 ,,,,,, cccccccc
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Control equations Introduction
121
6c
5c 4c
3c 1c0c
2c
02456 cccc
01345 cccc
00356 cccc
Principles of space communication systems Space for Education, Education for Space
Channel Coding hard
• Control Matrix Introduction
122
1001011
0101110
0010111
H
0.1.0.0.1.0.1.1 0123456 ccccccc
0.0.0.1.0.1.1.1 0123456 ccccccc
0.0.1.0.1.1.1.0 0123456 ccccccc
IPHT
0
TcH
0
TcH
Principles of space communication systems Space for Education, Education for Space
1001011
0101110
0010111
H
Tanner Graph
123
Principles of space communication systems Space for Education, Education for Space
Reed Solomon Codes
124
121 ..)( tjjj xxxxg
Reed, I. S. and Solomon, G., “Polynomial Codes Over Certain Finite Fields,” SIAM Journal of Applied Math., vol. 8, 1960, pp. 300-304.
MDS non-binary block codes 1 kndm
Principles of space communication systems Space for Education, Education for Space
Reed Solomon Codes
125
121 ..)( tjjj xxxxg
17,188,204
)())()(()(15210
xxxxxg
DVB-T
Principles of space communication systems Space for Education, Education for Space
CCSDS Codes
126
Consultative Committee for Space Data Systems (CCSDS) concatenated coding system that uses RS as the outer code, and a convolutional inner code.
RS encoder
RS decoder
Convolutional Code encoder
Convolutional Code decoder (Viterbi)
Modulator
Demodulator
Channel
Principles of space communication systems Space for Education, Education for Space
Deep Space LDPC- Comand Codes Control matrix A
127
[128, 64, ]
Principles of space communication systems Space for Education, Education for Space
Deep Space LDPC- Comand Codes Generator matrix G
128
[128, 64, ]
Principles of space communication systems Space for Education, Education for Space
Convolutional Codes
129
data
„Logic“
Tree Code Encoder
codeword
...01d
...01c
Principles of space communication systems Space for Education, Education for Space
Convolutional Codes
130
data
„Logic“
Tree Code Encoder
codeword
...01d
...01c
...01c
...01d
Principles of space communication systems Space for Education, Education for Space
Convolutional Code
131
...01d
Principles of space communication systems Space for Education, Education for Space
Convolutional Codes
132
S0= 00
S1= 10
S2= 01
S3= 11
00/0
11/1
01/1
10/1
10/0
01/000/1
11/0
Principles of space communication systems Space for Education, Education for Space
Convolutional Codes
133
S0
S1
S2
S3
0/00 0/00 0/00
1/01
0/00
1/01
0/00
1/01
0/00
1/01
Principles of space communication systems Space for Education, Education for Space
Convolutional Codes
134
Principles of space communication systems Space for Education, Education for Space
AWGN Channel Capacity BPSK + Coding in AWGN channel
135
54321 60 98712 10 11 12
1
5.0
4105 BER
Mariner 69 un-coded
Mariner 69 RM
Pioneer 9 Convol.code
Turbo-code LDPC
rN
E r
dB
B 12log10
0
Principles of space communication systems Space for Education, Education for Space
MAP & ML
136
)/1(
.
.
)/1( iiii zsP
II
I
zsP
izz
2
0
1
2
1
0
12
1)/(
ay
eszp
2
0
2
2
1
0
22
1)/(
ay
eszp
Principles of space communication systems Space for Education, Education for Space
MAP & ML
137
)1(
)1(
.
.
)1/(
)1/(
i
i
ii
ii
sP
sP
II
I
szp
szp)/1(
.
.
)/1( iiii zsP
II
I
zsP
izz
2
0
1
2
1
0
12
1)/(
ay
eszp
2
0
2
2
1
0
22
1)/(
ay
eszp
Principles of space communication systems Space for Education, Education for Space
MAP & ML
138
)1/(
)1/(
2
1
ii
ii
szp
szp
l
lLR (def.):
Principles of space communication systems Space for Education, Education for Space
Without coding
139
MAP 1)1(
)1(
)1/(
)1/(
i
i
ii
ii
vP
vP
vzp
vzp
0
)()()ˆ( vLyLvL c Without C
1ln)1(
)1(ln
)1/(
)1/(ln
i
i
ii
ii
vP
vP
vzp
vzp
Principles of space communication systems Space for Education, Education for Space
With coding
140
)()()ˆ( vLzLvL c )ˆ()()()ˆ( vLvLzLvL ec
Without C With C
Ext.
A’priory
channel
)ˆ(vLeReal number: (signature – Hard absolute value- reliability
Principles of space communication systems Space for Education, Education for Space
Turbocode
141
Interl.
4iS 3iS1
1
1
1
1
1
1
1
2iS 1iS1
1
1
1
1
1
1
1
iS1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1iS1
1
1
1
1
1
1
1
4iS 3iS1
1
1
1
1
1
1
1
2iS 1iS1
1
1
1
1
1
1
1
iS1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1iS1
1
1
1
1
1
1
1
...011100d
...011100)1( dc
...01)2( c
...01)3( c
12)(
ii xs
12)1( ii xs
}1,1{ is}1,0{ic}1,0{id
Principles of space communication systems Space for Education, Education for Space
Turbo - decoding
142
)(vLApriory
SISO I )(vLIe
)ˆ()()()ˆ( vLvLyLvL ec
)()()ˆ( vLyLvL c )(yLc
SISO II
)(vLIIe
iii nvy
Principles of space communication systems Space for Education, Education for Space
LDPC code decoding
143
0111001011
1010111010
1101011100
0110110101
1001100111
H
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10
z1
z2 z3 z4
z5
Principles of space communication systems Space for Education, Education for Space
Tanner Graph & Belief Propagation
144
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10
z1 z2 z3 z4 z5
+ + + + +
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
145
binit
bit
n
kRC
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
146
binit
bit
n
kRC
bitRRR CMp
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
147
binit
bit
n
kRC
bitRRR CMp
Fourier bandwidth W is proportional to C
p
MR
RR
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
148
binit
bit
n
kRC
bitRRR CMp
Fourier bandwidth W is proportional to C
p
MR
RR
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
149
binit
bit
n
kRC
bitRRR CMp
Fourier bandwidth W is proportional to C
p
MR
RR
Shannon Bandwidth for dimensional signal set MRB
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
150
s
bit
NB
SBCB
2
1log2
1
02
1MRB
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
151
s
bit
NB
SBCB
2
1log2
1
02
1MRB
s
bit
NR
SRC
M
MRM
2
1log2
1
02
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
152
bCMM ERRERS
s
bit
NR
SRC
M
MRM
2
1log2
1
02
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
153
bCMM ERRERS
s
bit
NR
SRC
M
MRM
2
1log2
1
02
s
bit
N
ER
ER
SC bC
bC
RM
2
1log2
1
02
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
154
s
bit
N
ER
ER
SC bC
bC
RM
2
1log2
1
02
C
CMR
2
2
1ln
0
0
N
ER
N
ER
bC
bC
Principles of space communication systems Space for Education, Education for Space
Penalty binary code & BPSK
155
2
1CR 76.0 dB2.1
bC ERE
Principles of space communication systems Space for Education, Education for Space
CONCLUSION
156
In future we will need efficient reliable codes with not too complex decoding and as short codewords as possible Visible light and X ray spectrum can offer more Hz And so higher throughput
Principles of space communication systems Space for Education, Education for Space
Thank you for you attention
157
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