IEIIT-BOCNR
DEIS, Università di Bologna
Video Transmission
over Wireless Channel
Bologna, 17.01.2011
Raffaele Soloperto
PhD Student @ DEIS, University of Bologna
Tutor: O.Andrisano
Co-Tutors: G.Pasolini and G.Liva (DLR, DE)
Bologna, 17.01.11 RAFFAELE SOLOPERTO
PhD Outline
� Focus on DVB-T and T2 standards:
� Signal Processing� Linear and Non Linear Predistorsion
� MultiRate – MultiStage Filters
� Channel Coding� LDPC, G-LDPC and DG-LDPC Codes
� Measurements and Tele-Measurements� Instrumentation and programmable circuits
Bologna, 17.01.11 RAFFAELE SOLOPERTO
PhD Outline
� Focus on DVB-T and T2 standards:
� Signal Processing� Linear and Non Linear Predistorsion
� MultiRate – MultiStage Filters
� Channel Coding� LDPC, G-LDPC and DG-LDPC Codes
� Measurements and Tele-Measurements� Instrumentation and programmable circuits
SIG
NA
LP
RO
CE
SS
ING
CH
AN
NE
LC
OD
ING
MEAS. AND TELE MEAS.
VIDEO OVER WIRELESS
II II, III
I, II, III
Bologna, 17.01.11 RAFFAELE SOLOPERTO
PhD Outline
Design of MultiStage and MultiRate Filters withminimum group delay
Signal Processing: MultiStage-MultiRate Filters
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Scientific literature:
I) Ronald E.Crochiere, Lawrence R.Rabiner ���� multistage multiratefilters with minimum number of taps
fixedproj<
II) Raffaele Soloperto, Gianni Pasolini ���� multistage multirate filters withminimum group delay
Bologna, 17.01.11 RAFFAELE SOLOPERTO
MultiStage MultiRate Filter
DEC LPF INTM L
Downsampl.LPF
M
Downsampl.
LPF1Down sampl.
LPFI
MultiRate Decimation(min. number of taps)
M1 MI
ADC
X
X
LPF
LPF
X
X
DAC
cos(2π f0t) cos(2π f0t)
-sen(2π f0t) -sen(2π f0t)
+
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Measurements (1/2)
Fc = 36 MHz
B = 8 MHz
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Measurements (2/2)
Fc = 36 MHz
B = 1 MHz
IEIIT-BOCNR
DEIS, Università di Bologna
Iterative decoding of DG-LDPC codes
Visiting PhD Student at DLR, Munich – DE
(Nov 2009 – July 2010)
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Outline
� Introduction� LDPC codes
� Generalized LDPC codes
� Doubly Generalized LDPC codes� Graph representation
� Decoding algorithm
� Efficient encoding: Quasi-Cyclic DG-LDPC codes
� Conclusions
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Outline
� Introduction� LDPC codes
� Generalized LDPC codes
� Doubly Generalized LDPC codes� Graph representation
� Decoding algorithm
� Efficient encoding: Quasi-Cyclic DG-LDPC codes
� Conclusions
Bologna, 17.01.11 RAFFAELE SOLOPERTO
� Long LDPC/Turbo codes approach Shannon limit
� In the moderate/short block length regime, however, they show a gap from theoretical bounds (~1dB):
� Generalized LDPC codes (Leintmeier ’98, Chiani ’06, Liva ’06)
� Non-binary LDPC codes (Mackay, ’98)
� Doubly Generalized LDPC codes (Chiani/Paolini/Fossorier ’06)
Why DG-LDPC codes?
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Low-Density Parity-Check Codes
� LDPC codes: (sparse) bipartite graph describing the parity-check equations.
=1001110
0101101
0011011
H
=⊕⊕⊕=⊕⊕⊕=⊕⊕⊕
0
0
0
7432
6431
5421
cccc
cccc
cccc
Parity-check equations:
Parity-check matrix of a Hamming (7,4):
Bipartite graph:
Variable nodes
Check nodes
Bologna, 17.01.11 RAFFAELE SOLOPERTO
LDPC codes: decoding on the bipartite graph
� ML decoding is unfeasible even for rather short block lengths…� Belief propagation (BP): iterative, message-passing decoding algorithm.� Sparse graph: the correlation among messages is reduced. BP ≈ ML.� Complexity: graph, nodes, iteration number, etc…
. . .
. . .
Channel observations(noisy symbol samples)
„bit reliabilites“
y1 y2 y3 yn. . .
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Generalized LDPC
…
…Single Parity-Check
Low-density parity-check codes(large number of simple nodes)
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Generalized LDPC
…
… Block code(ex. Hamming)
Block turbo codes (BTC) andgeneralized low-density codes (GLDC)(trade-off between node count and complexity)
HHHH
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Generalized LDPC
…
… Block code(ex. Hamming)
Block turbo codes (BTC) andgeneralized low-density codes (GLDC)(trade-off between node count and complexity)
Error floors are lowered
Unbalancing of the edcoding complexity: all the complexity at the SCN!
Super Check Node can be stronger than conventional CN
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Getting closer to the limits in the short/moderate length
Balancing the decoder complexity at CNs and VNs
DG-LDPC codes
“Generalized Stability Condition for Generalized and Doubly-Generalized LDPC Codes”,E.Paolini, M.P.C. Fossorier, M.Chiani, ISIT2007, Nice, France, June24 – June29, 2007
“Generalized and Doubly Generalized LDPC codes with random component codes for the binary erasure channel”, E.Paolini, M.P.C. Fossorier, M.Chiani, IEEE Transaction on Information Theory, Vol. 56, No 4, April 2010
“On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes”, M.F. Flanagan, E. Paolini, M. Chiani, and M.P.C. Fossorier, Forty-Sixth Annual Allerton Conference, Allerton House, UIUC, Illinois, USA, September 23-26, 2008
STATE OF THE ART
“Doubly-Generalized LDPC codes: stability bound over the BEC”, E.Paolini, M.P.C. Fossorier, M.Chiani, IEEE Transaction on Information Theory, Vol. 55, No. 3, March 2009
Bologna, 17.01.11 RAFFAELE SOLOPERTO
� Motivation of our work:
� Simplify decoding algorithm
(new stopping criterions)
� Efficient encoding
(design of QC-DGLDPC codes)
DG-LDPC codes
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Outline
� Introduction� LDPC codes
� Generalized LDPC codes
� Doubly Generalized LDPC codes� Graph representation
� Decoding algorithm
� Efficient encoding: Quasi-Cyclic DG-LDPC codes
� Conclusions
Bologna, 17.01.11 RAFFAELE SOLOPERTO
DG-LDPC GraphN
ois
y c
od
ew
ord
The Tanner graph of DG-LDPC codes can be obteined from that of LDPC codes with original VNs and CNs replaced by Super Variable Nodes and Super Check Nodes respectively.
Legend:
Bologna, 17.01.11 RAFFAELE SOLOPERTO
DG-LDPC Graph
SVNs and SCNs are subcodes with lengths equal to the degrees of their corresponding super nodes!
SVNs degree
(dvx, kvx): subcode for the SVN
dvx: block length of the subcode
kvx: dimension of the subcode
Kv1
no
isy
co
de
wo
rd b
its
SUPER VARIABLE NODE
Bologna, 17.01.11 RAFFAELE SOLOPERTO
DG-LDPC Graph
SVNs and SCNs are subcodes with lengths equal to the degrees of their corresponding super nodes!
SCNs degree
(dcy, kcy): subcode for the SCN
dcy: block length of the subcode kcy: dimension of the subcode
SUPER CHECK NODE
Bologna, 17.01.11 RAFFAELE SOLOPERTO
DG-LDPC. Decoding algorithm
Iterative decoding based on belief propagation (BP)
A Priori information at the i-th iteration
Extrinsic information at the i-th iteration
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Decoding Algorithm
ITERATIONS
SVN
SCN
SUPER CHECK NODE ELABORATION
SUPER VARIABLE NODE ELABORATION
APP LLR TRANSMITTED BIT
HARD DECISION
SYNDROME CHECK
Bologna, 17.01.11 RAFFAELE SOLOPERTO
EXIT Chart
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Stopping Criterions
Simulation on standard PC (Pentium IV, 3.00GHz, 3.00GB RAM)
Example: DG-LDPC code
500 SVNs (SPC(7,6))
500 SCNs (Hamm(7,4))
R = 0.5
Transmitted codewords = 1000
Eb/N0 = 1.8 dB (CER = 10-4)
State of the art
Proposed solutions
da
ta r
ate
[K
bp
s]
• STEP STOP: evaluation of parity-check equations every N iterations.
• THRESHOLD STOP: evaluation of parity-check equations after a fixed number of iterations (threshold)
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Iterative decoding simulator
In principle, we can simulate all possible iteratively – decodable codes
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Iterative decoding simulatorIn principle, we can simulate all possible iteratively – decodable codes
π
C C
…
…
Convolutional turbo codes(small number of complex nodes)
Convolutionalcode
…
… Block code(ex. Hamming)
Block turbo codes (BTC) andgeneralized low-density codes (GLDC)
(trade-off between node count and complexity)
HHHH
…
…
Low-density parity-check codes(large number of simple nodes)
Singleparity-check
IEIIT-BOCNR
DEIS, Università di Bologna
RESULTS
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Outline
� Introduction� LDPC codes
� Generalized LDPC codes
� Doubly Generalized LDPC codes� Graph representation
� Decoding algorithm
� Efficient encoding: Quasi-Cyclic DG-LDPC codes
� Conclusions
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Protographs
� Protograph: small graph with N variable nodes and M check nodes
� Each check/variable node in a protograph identifies a check/variable node type
� Multiple, parallel edges are allowed.
Type A Type B
Type c Type d Type e
Bologna, 17.01.11 RAFFAELE SOLOPERTO
� Derived graph: obtained by q replicas on the protograph.
� Cyclic edge permutations: the DG-LDPC code is quasi-cyclic (QC).
� Shift-register-based encoder.
Protographs
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Proof (sketch):
� Expand rows/columns of Γ according to the rule
� Permute rows/columns of according to a defined algorithm (not shown here)
� HDGLDPC is block circulant
Protographs
THE CODE IS QUASI-CYCLIC
Proposition. A sufficient condition for having a QC DG-LDPC is that the protograph is expanded by means of circulant permutation matrices
HDGLDPC
Bologna, 17.01.11 RAFFAELE SOLOPERTO
7 SCNs Hamm(15,11)
15 SVNs Hamm(7,4)
Q = 30
# SVNs = 450
# SCNs = 210
# bits = 1800
R = 0.533
Kv1 = 4
dv1 = 7
dc1 = 15
Protographs example (1/3)
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Adjaceny Matrix
HQC-DGLDPC
Protographs example (2/3)
Rows/columns expansion
Rows/columns permuation
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Protographs example (3/3)
Performance of a (1800, 960) QC-DGLDPC code and DG-LDPC code in terms of CER on the AWGN channel
There is NO degradation of performance between a QC code and unstructured code!
Q = 30
# SVNs = 450
# SCNs = 210
R = 0.533
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Outline
� Introduction� LDPC codes
� Generalized LDPC codes
� Doubly Generalized LDPC codes� Graph representation
� Decoding algorithm
� Efficient encoding: Quasi-Cyclic DG-LDPC codes
� Conclusions
Bologna, 17.01.11 RAFFAELE SOLOPERTO
� Signal Processing:� design of MultiRate MultiStages Filters with minimum group
delay
� Channel Coding:� General Purpose decoder machine for iterative codes (LDPC,
G-LDPC, DG-LDPC..)� efficient encoding: Quasi Cyclic codes
� Mesearements and TeleMeasurements:� remotization of instrumentation and programmable circuits� remotization of the connections by means of a programmable
matrix
Conclusions
Bologna, 17.01.11 RAFFAELE SOLOPERTO
Publication
Bologna, 17.01.11 RAFFAELE SOLOPERTO
”Sistema di filtraggio, Cancellatore d’eco, Studio delle prestazioni delsistema e Pianificazione di rete.”
”Sistema di filtraggio multistadio, Precorrezione non lieare, Cancellatored’eco.”
”Sistema di filtraggio multistadio, Precorrezione non lieare, Precorrezionelineare, Cancellatore d’eco.”
”Sistema di filtraggio multistadio, Precorrezione non lieare, Precorrezionelineare, Cancellatore d’eco, Modulatore.”
”Attività di misura per la caratterizzazione del Cancellatore d’eco afinestra fissa, con tecnologia ad impulsi e LMS.”
”Deliverable Finale DVB2006 (Polo tecnologico TV digitale)”:- DVB-T Echo Canceller (design & implementation);- DVB-T Echo Canceller (measurements).
DELIVERABLES – DVB2006
Bologna, 17.01.11 RAFFAELE SOLOPERTO
THANK YOU!