Practical Anytime Codes

170 Pages·2016·1.71 MB·Swedish

Practical Anytime Codes
LEEFKE GROSJEAN
Doctoral Thesis
Stockholm, Sweden 2016
KTH School of Electrical Engineering
SE-100 44 Stockholm
ISBN 978-91-7595-937-5 SWEDEN
Akademisk avhandling sommedtillstånd av KunglTekniskahögskolanframlägges
till offentlig granskning för avläggande av teknologie doktorsexamen i telekommu-
nication den 13 Maj 2016 klockan 10:00 i Sal F3, Lindstedtsvägen 26, Stockholm.
© Leefke Grosjean, April 2016
Parts of this thesis have been published under IEEE copyright
Tryck: Universitetsservice US AB
Abstract
The demand of an increasingly networked world is well reflected in modern indus-
trialcontrolsystemswherecommunicationbetweenthedifferentcomponentsofthe
system is more and more taking place over a network. With an increasing number
of components communicating and with hardware devices of low complexity, the
communication resources available per communication link are however very lim-
ited. Yet, despite limited resources, the control signals transmitted over the link
are still required to meet strict real-time and reliability constraints. This requires
entirely new approaches in the intersection of communication and control theory.
In this thesis we consider the problem of stabilizing an unstable linear-quadratic-
Gaussian(LQG)plantwhen the communicationlink betweenthe observerandthe
controlleroftheplantisnoisy. Protectingthedatatransmittedbetweenthesecom-
ponents against transmission errors by using error control schemes is essential in
this contextandthe main subject to this thesis. We proposenovelerror-correcting
codes,so-calledanytimecodes,for this purpose andshowthatthey asymptotically
fulfill the reliability requirements known from theory when used for transmission
over the binary erasure channel (BEC). We identify fundamental problems when
the messages to be transmitted are very short and/or the communication channel
quality is very low. We propose a combinatorialfinite-length analysis which allows
us to identify important parameters for a proper design of anytime codes. Various
modificationsofthebasiccodestructureareexplored,demonstratingtheflexibility
ofthecodesandthecapabilityofthecodestobeadaptedtodifferentpracticalcon-
straints. To cope with communication channels of low quality, different feedback
protocolsareproposedforthe BECandtheAWGNchannelthattogetherwiththe
error-correctingcodesensurethereliabilityconstraintsatshortdelaysevenforvery
short message lengths. In the last part of this thesis, we integrate the proposed
anytime codes in an automatic controlsetup. We specify the different components
necessaryforthisanddeterminethecontrolcostwhencontrollinganunstableLQG
plant over a BEC using either the anytime codes proposed in this thesis or block
codes. We detail the relation between parameters such as channel quality, code
rate, plant instability and resources available and highlight the advantage of us-
ing anytime codes in this context. Throughout the thesis, the performance of the
anytime codes is evaluated using asymptotic analysis,finite-length analysisand/or
simulation results.

Sammanfattning
Efterfrågan av en alltmer ihopkopplad värld återspeglas bland annat i moderna
industriella styrsystem där kommunikationen mellan de olika komponenterna allt
oftareskeröverettnätverk. Eftersomantaletkomponentersomkommunicerarmed
varandra ökar, medans hårdvaruenheternas komplexitet är fortsatt låg, blir kom-
munikationsresurserna per kommunikationslänk alltmer begränsade. Trots detta
måste styrsignalerna som skickas över länken uppfylla strikta krav på tillåtna
tidsfördröjningar och nödvändig tillförlitlighet. Detta kräver helt nya metoder i
gränssnittet mellan kommunikationsteknik och reglerteknik. I denna avhandlin-
gen undersöker vi problemet med att stabilisera ett instabilt linjärt kvadratiskt
Gaussiskt (LQG) system när kommunikationslänken mellan observatören och reg-
ulatorn är störd av brus. Att skydda styrsignalerna mot störningar i kommunika-
tionskanalenmedhjälpavfelkorrigerandekoderärviktigtidettasammanhangoch
är huvudtemat för denna avhandlingen. Vi föreslår nya felkorrigerande koder, så
kallade anytime-koder, och visar att de asymptotiskt uppnår kraven på tillförlit-
lighetfrånteorinför dataöverförningöveren binär raderingskanal(BEC). Vi iden-
tifierargrundläggandeproblemnär meddelandena somska skickasär väldigtkorta
eller om kommunikationskanalenär av dålig kvalitet. Vi föreslår en kombinatorisk
analys för meddelanden med ändlig blocklängd som tillåter oss att identifiera vik-
tigakonstruktionsparametrar. Olikamodifieringaravdengrundläggandekodstruk-
turenundersökssompåvisarflexibilitetenhoskodernaochmöjlighetenattanpassa
koderna till diverse praktiska begränsningar. För att även använda koderna för
kommunikationskanaler med mycket brus föreslår vi olika återkopplingsprotokoll
som tillämpas vid överförning över BEC eller AWGN kanalen. I sista delen av
avhandlingenintegrerarviddeföreslagnakodernaiettreglerteknisktsammanhang.
Vi specificerarde olika komponenternaochberäknarkontrollkostnadenför ett sce-
nario där vi ska stabilisera ett instabilt LQG system och kommunikationslänken
mellanobservatörenochregulatornmodellerassomen BEC kanal. Det föregående
görs för både de föreslagna koderna och för blockkoder. Vi specificerar sambandet
mellan parametrarna såsom kanalkvalitet, kodhastighet, instabilitet, och tillgäng-
liga resurser. Dessutom lyfter vi fram fördelarna med att använda anytime-koder
för detta sammanhang. Genom hela avhandlingen utvärderas kodernas prestanda
med hjälp av asymptotisk analys, ändlig-blocklängdsanalysoch/eller simuleringar.
v

Acknowledgements
Now that this five-year journey of my Ph.D. studies comes to an end, I would like
to thank all the people that have supported me during this time. I would like to
express my sincere gratitude to Prof. Lars Kildehøj Rasmussen, Associate Prof.
RagnarThobaben,andProf. MikaelSkoglund. Mikaelgaveme the opportunityto
jointheCommunicationTheorydepartmentandunderthesupervisionofLarsand
Ragnar I started to explore the academic world. I am deeply grateful to Lars and
Ragnar for their guidance, for their research insights, their enthusiastic encour-
agement, and the independence they gave me when conducting my Ph.D. studies.
Discussions with them have always been interesting, challenging, stimulating and
as well lots of fun. Moreover I am truly thankful to them for their contribution in
making this an open-minded, flexible and solution-driven workplace. Having had
two children during my time atthe department, I highly appreciate how smooth it
went to combine this with my Ph.D. studies.
I am honored to have collaborated with Associate Prof. Joakim Jaldén and
Associate Prof. Mats Bengtsson in teaching. I thank all my current and former
colleagues from Floor 3 and 4 for creating such a nice working atmosphere. In
particular, I would like to mention Dr. Kittipong Kittichokechai, Dr. Nicolas
Schrammar, Dr. Isaac Skog, Dr. Dave Zachariah, Dr. Mattias Andersson, Dr.
Ricardo Blasco Serrano, and Dr. Dennis Sundman. Special thanks to Raine Tiivel
for her diligence in taking care of the administrative issues and Joakim Jaldén for
doing the quality review of this thesis.
I would like to thank Associate Prof. Michael Lentmaier for taking the time to
act as faculty opponent and Prof. Catherine Douillard, Dr. Ingmar Land and
Associate Prof. Carlo Fischione for acting as grading committee.
I want to thank my parents Meike and Olaf and my sisters Kerrin and Jomtje for
their greatsupport fromfar away. Lastbut not least,I wantto thank my husband
Julien and my children for filling every day with love and happiness.
Leefke Grosjean
Stockholm, April 2016
vii

Contents
1 Introduction 1
1.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Outline and Contributions of the Thesis . . . . . . . . . . . . . . 7
1.5 Notation and Acronyms . . . . . . . . . . . . . . . . . . . . . . . 11
2 Preliminaries 13
2.1 Communication Theory . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 The Communication System . . . . . . . . . . . . . . . . 14
2.1.2 Binary Memoryless Symmetric Channels . . . . . . . . . . 14
2.1.3 Log-LikelihoodRatios . . . . . . . . . . . . . . . . . . . . 16
2.1.4 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Anytime Information Theory . . . . . . . . . . . . . . . . . . . . 19
2.2.1 The Anytime Communication System . . . . . . . . . . . 19
2.2.2 Anytime Capacity . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Anytime Reliability . . . . . . . . . . . . . . . . . . . . . 21
2.3 Control Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Control System Setup . . . . . . . . . . . . . . . . . . . . 21
2.3.2 LQG Control . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 LQG Control Over Noisy Channels . . . . . . . . . . . . . 23
2.4 LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2 ProtographEnsembles . . . . . . . . . . . . . . . . . . . . 26
2.4.3 Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.4 Stopping Sets and Trapping Sets . . . . . . . . . . . . . . 33
2.4.5 P-EXIT Analysis . . . . . . . . . . . . . . . . . . . . . . . 33
2.5 LDPC-ConvolutionalCodes . . . . . . . . . . . . . . . . . . . . . 34
2.5.1 Structure and Basic Definitions . . . . . . . . . . . . . . . 34
2.5.2 Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5.3 Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.4 Termination of LDPC-CCs . . . . . . . . . . . . . . . . . 38
ix
x Contents
3 LDPC Convolutional Anytime Codes 39
3.1 Code Development . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 Anytime System Model . . . . . . . . . . . . . . . . . . . 39
3.1.2 Code Structure . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.3 Encoding and Decoding . . . . . . . . . . . . . . . . . . . 43
3.1.4 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Performance on the BEC . . . . . . . . . . . . . . . . . . . . . . 45
3.2.1 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . 45
3.2.2 Finite-Length Behavior . . . . . . . . . . . . . . . . . . . 58
3.2.3 Finite-Length Analysis . . . . . . . . . . . . . . . . . . . . 61
3.2.4 Turning Point. . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.5 Transmission Over the Standard BEC . . . . . . . . . . . 66
3.3 Performance on the AWGN Channel . . . . . . . . . . . . . . . . 68
3.3.1 Asymptotic Performance Analysis . . . . . . . . . . . . . 69
3.3.2 Finite-Length Behavior . . . . . . . . . . . . . . . . . . . 71
3.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Comparison With Other Anytime Codes . . . . . . . . . . . . . . 72
3.4.1 Comparison with Toeplitz Codes . . . . . . . . . . . . . . 72
3.4.2 Comparison with Spatially Coupled Anytime Codes . . . 72
3.4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4 Modified Code Structures 79
4.1 Increasing the Degrees in the Protograph . . . . . . . . . . . . . 80
4.1.1 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.1.2 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . 80
4.1.3 Finite-Length Behavior . . . . . . . . . . . . . . . . . . . 81
4.1.4 Finite-Length Analysis . . . . . . . . . . . . . . . . . . . . 83
4.1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Decreasing the Degrees in the Protograph . . . . . . . . . . . . . 83
4.2.1 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.2 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . 84
4.2.3 Finite-Length Behavior . . . . . . . . . . . . . . . . . . . 84
4.2.4 Finite-Length Analysis . . . . . . . . . . . . . . . . . . . . 85
4.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Decreasing the Rate of the Code . . . . . . . . . . . . . . . . . . 87
4.3.1 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3.2 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . 87
4.3.3 Finite-Length Behavior . . . . . . . . . . . . . . . . . . . 88
4.3.4 Finite-Length Analysis . . . . . . . . . . . . . . . . . . . . 89
4.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4 Limiting the Memory of the Code. . . . . . . . . . . . . . . . . . 90
4.4.1 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4.2 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . 91
4.4.3 Finite-Length Behavior . . . . . . . . . . . . . . . . . . . 91