reporter ：林煜星 advisor ： prof. y.m. huang
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1
Iterative Joint Source-Channel Soft-Decision Sequential Decoding Algorithms for
Parallel Concatenated Variable Length Code and Convolutional Code
Reporter：林煜星Advisor： Prof. Y.M. Huang
2
Outline
• Introduction
• Related Research– Transmission Model for BCJR
– Simulation for BCJR Algorithm
• Proposed Methodology– Transmission Model for Sequential
– Simulation for Soft-Decision Sequential Algorithm
• Conclusion
3
DemodulatorChannel Decoder
Source Decoder
User Joint Decoder
資料壓縮
錯誤更正碼
Discrete source
Source Encoder
Channel Encoder
Modulator
Introduction
Channel
4
Related Research
• [1]L. Guivarch, J.C. Carlach and P. Siohan
• [2]M. Jeanne, J.C. Carlach, P. Siohan and L.Guivarch
• [3]M. Jeanne, J.C. Carlach, Pierre Siohan
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Transmission Model for BCJR
Independent Source
or first orderMarkov Source
Huffman CodingTurbo Coding
parallelconcatenation
Additive WhiteGaussian Noise
Channel
Turbo decodingUtilization
of the SUBMAP
HuffmanDecoding
ku
kv
pcP symbols
kdK bits
ku
kv
kx
ky
ˆkd
K bits
ˆkd
P symbols
a priori
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Transmission Model for BCJR-Independent Source or first order Markov Source
Independent Source
or first orderMarkov Source
Huffman CodingTurbo Coding
parallelconcatenation
Additive WhiteGaussian Noise
Channel
Turbo decodingUtilization
of the SUBMAP
HuffmanDecoding
ku
kv
pcP symbols
kdK bits
ku
kv
kx
ky
ˆkd
K bits
ˆkd
P symbols
a priori
7
Transmission Model for BCJR-Independent Source or first order Markov Source(1)
Symbol Probability
A 0.75
B 0.125
C 0.125
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Transmission Model for BCJR-Independent Source or first order Markov Source(2)
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Transmission Model for BCJR-Independent Source or first order
Markov Source(3)
Y↓ X→∣ a b C
a 0.94 0.18 0.18
b 0.03 0.712 0.108
c 0.03 0.108 0.712
0.75
P a P a P a a P b P a b P c P a c
Example:
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Transmission Model for BCJR-Huffman Codign
Independent Source
or first orderMarkov Source
Huffman CodingTurbo Coding
parallelconcatenation
Additive WhiteGaussian Noise
Channel
Turbo decodingUtilization
of the SUBMAP
HuffmanDecoding
ku
kv
pcP symbols
kdK bits
ku
kv
kx
ky
ˆkd
K bits
ˆkd
P symbols
a priori
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VLC Symbol Probability
0 A 0.75
10 B 0.125
11 C 0.125
1 0.125( ) 0.251 0.5P y
P yP y
Transmission Model for BCJR-Huffman Coding
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Transmission Model for BCJR-Turbo Coding parallel concatenation
Independent Source
or first orderMarkov Source
Huffman CodingTurbo Coding
parallelconcatenation
Additive WhiteGaussian Noise
Channel
Turbo decodingUtilization
of the SUBMAP
HuffmanDecoding
ku
kv
pcP symbols
kdK bits
ku
kv
kx
ky
ˆkd
K bits
ˆkd
P symbols
a priori
13
d = (11101)
u
v
Non SystematicConvolution code
Transmission Model for BCJR-Turbo Coding parallel concatenation(1)
14
10
(4,1)
(4,3)
(5,1)
(5,3)
(5,2)
(5,0)(4,0)
(4,2)
(3,1)
(3,3)
(3,0)
(3,2)
(2,1)
(2,3)
(2,0)
(2,2)
(1,1)
(1,3)
(1,0)
(1,2)
(0,1)
(0,3)
(0,0)
(0,2)
11
d = (11101)
01
10
01
00
Transmission Model for BCJR-Turbo Coding parallel concatenation(2)
15
Recursive Systematic Convolution(RSC)
kd 1lu
2lu
2 4
3 41
11, D D D
D DG D
Transmission Model for BCJR-Turbo Coding parallel concatenation(3)
Rate=1/2
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Rate=1/4
2lv
ld
1lv
1lu
2lu
Transmission Model for BCJR-Turbo Coding parallel concatenation(4)
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1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Interleaver
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
Transmission Model for BCJR-Turbo Coding parallel concatenation(5)
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Rate=1/4
2lv
ld
1lv
1lu
2lu
Transmission Model for BCJR-Turbo Coding parallel concatenation(6)
Turbo Code rate1/3
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Turbo Code rate=1/2
ld lu
2lu
2lv
lv
Transmission Model for BCJR-Turbo Coding parallel concatenation(7)
20
Independent Source
or first orderMarkov Source
Huffman CodingTurbo Coding
parallelconcatenation
Additive WhiteGaussian Noise
Channel
Turbo decodingUtilization
of the SUBMAP
HuffmanDecoding
ku
kv
pcP symbols
kdK bits
ku
kv
kx
ky
ˆkd
K bits
ˆkd
P symbols
a priori
Transmission Model for BCJR-AWGN
21
Transmission Model for BCJR-AWGN(1)
22
Independent Source
or first orderMarkov Source
Huffman CodingTurbo Coding
parallelconcatenation
Additive WhiteGaussian Noise
Channel
Turbo decodingUtilization
of the SUBMAP
HuffmanDecoding
ku
kv
pcP symbols
kdK bits
ku
kv
kx
ky
ˆkd
K bits
ˆkd
P symbols
a priori
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP
,k k kx y r
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BCJR1
priori
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(5)
BCJR2
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MAP Decoder
1( ) P K
k kAPP d d R
Define
1
1
1
( , )
( ) ( )
, , , , 0,1k
k
k k
N
k k k
d
k k k k k k k
m P m R
m P R m
r m m P d m r m d
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(1)
1 1
K
KR r r
0,1kd
25
( 1)( 0)( ) ln k
k
APP dAPP dkd
Logarithm of Likelihood Ratio(LLR)
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0 0
01
0 0
, ,
, ,ln
M M
k k k km mM M
k k k km m
r m m m m
r m m m m
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(2)
Recall
1
1ln( ) maxn
ii ne e
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(4,1)
(4,3)10
01
00
11
(5,1)
(5,3)10
01
00
11
(5,2)
10
0 0 1 1( ) MN m 0 0 0m
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(3)
27
(0,0)
(2,3) (3,3)
(5,0)
2 3 3 3 1
3 3,2,3r2
2 1(3 , )P R 3 3 21,3 , 3P r 5
4 33P R
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(4)
( 1) ?kAPP d
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BCJR1
priori
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(5)
BCJR2
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11
0 0
01
0 0
, ,
, ,ln
M M
k k k km mM M
k k k km m
r m m m m
kr m m m m
d
k c k kLa L x Le
Pr (1)
0 0)
1
Pr (ln k
k
iP
Pk iLa
22
cL
Transmission Model for BCJR-Turbo decoding Utilization of the SUBMAP(6)
30
Simulation for BCJR Algorithm
• The end of the transmission occurs when either the maximum bit error number fixed to 1000, or the maximum transmitted bits equal to 10 000 000 is reached.
• Input date into blocks of 4096 bits
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Simulation for BCJR Algorithm(1)
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0 0.5 1 1.5 2 Eb/N0
BER
1NP2NP3NP4NP1P2P3P4P
1NP： 1次 iteration independent sourceNo Use a priori probability
1NP： 1次 iteration independent sourceUse a priori probability
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1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Eb/N0
BER
1NP
2NP
3NP
4NP
1MP
2MP
3MP
4MP
Simulation for BCJR Algorithm(2)1NP：1次 iterationMarkov SourceNo use a proiri probability
1MP：1次 iterationMarkov SourceUse Markvo a prioriprobability
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1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0 0.5 1 1.5 2
Eb/N0
BER
12D22D32D42D13D23D33D43D
Simulation for BCJR Algorithm(3)12D：1次 iterationIndependent SourceUse a priori probabilityBit time(level)、 Convolutionstate
13D：1次 iterationIndependent SourceUse a priori probabilityBit time(level)、 tree stateConvolution state
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Proposed Methodology
• [4]Catherine Lamy, Lisa Perros-Meilhac
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Sequential
priori
Transmission Model for Sequential-Sequential Decoding
BCJR2
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1( ) Pr ......... 0,1N
k k kAPP d d R d
1 1
0 0
ln Pr ln Prpk
K n
k pk k k k kk k
pi c cr c r iy c y
ky 1 : if 0kr
0 : Otherwise
:pkc Code word bits
Transmission Model for Sequential-Sequential Decoding(1)
37(0,0)
0
(0,0)
3
1
(0,0)
(1,1)
1100
y=(10)
|r|=(13)
(1,0)
(0,0)(1,1)
(1,0)
Origin node
Open
y=(00)
|r|=(21)
1
4
(2,1)
1100 (2,0)
(2,1)
(1,1)
(2,0)
(1,0)
(1,0)4
1
(3,1)
1100
y=(11)
|r|=(21)
(3,0)(3,1)
(3,0)(2,0)
(2,0)
Close
4
2
(4,3)
01
10
y=(11)
|r|=(31)
(4,2)
(2,1)
(3,0)
(4,3)
(1,1)
(4,2)
(3,1)
(3,1)(5,0)
y=(00)
|r|=(12)
(5,1)
2
5
00
11
(5,0)
(2,1)
(3,0)
(4,3)
(1,1)
(5,1)
(4,2)(4,2)
Example:r=(-1, 3,2,1,-2,-1,-3,-1,1,2)y=(1,0,0,0,1,1,1,1,0,0)
2
3
4
4
4
5
Transmission Model for Sequential-Sequential Decoding(2)
38
1
1
( 1)( 0)1( ) ln APP d
APP dd
2 3 1
2
2
( 1)( 0)2( ) ln APP d
APP dd
2 4 2
Transmission Model for Sequential-Sequential Decoding(2)
39
Simulation for Sequential Algorithm
1.0E-02
1.0E-01
1.0E+00
0 0.5 1 1.5 2
Eb/N0
BER
3D1
3D2
3D3
3D4
2D1
2D2
2D3
2D4
2D1：1次 iterationIndependent SourceUse a priori probabilityBit time(level)、 Convolutionstate
3D1：1次 iterationIndependent SourceUse a priori probabilityBit time(level)、 Convolutionstate、 tree state
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1.0E-03
1.0E-02
1.0E-01
1.0E+00
0 0.5 1 1.5 2
Eb/N0
BER
2D1
2D2
2D3
2D4
1NP
1P
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• Heuristic方法求 Sequential Decoder Soft-Output value運用在 Iterative解碼架構，雖然使錯誤降低，節省運算時間，但解碼效果無法接近 Tubro Decoder的解碼效果，為來將繼續研究更佳的方法求 Sequential Decoder Soft-Output value使解碼效果更逼近 Turbo Decoder的解碼效果
Conclusion
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