ISTANBUL TECHNICAL UNIVERSITY F GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY
RELAYING OPPORTUNITIES FOR WIRELESS NETWORKS BY APPLYING NETWORK CODING
Ph.D. THESIS Semiha TED˙IK BA¸SARAN
Department of Electronics and Communications Engineering Telecommunications Engineering Programme
ISTANBUL TECHNICAL UNIVERSITY F GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY
RELAYING OPPORTUNITIES FOR WIRELESS NETWORKS BY APPLYING NETWORK CODING
Ph.D. THESIS Semiha TED˙IK BA¸SARAN
(504132305)
Department of Electronics and Communications Engineering Telecommunications Engineering Programme
Thesis Advisor: Prof. Dr. Güne¸s Zeynep KARABULUT KURT
˙ISTANBUL TEKN˙IK ÜN˙IVERS˙ITES˙I F FEN B˙IL˙IMLER˙I ENST˙ITÜSÜ
KABLOSUZ A ˘GLAR ˙IÇ˙IN A ˘G KODLAMALI AKTARMA FIRSATLARI
DOKTORA TEZ˙I Semiha TED˙IK BA¸SARAN
(504132305)
Elektronik ve Haberle¸sme Mühendisli˘gi Anabilim Dalı Telekomünikasyon Mühendisli˘gi Programı
Tez Danı¸smanı: Prof. Dr. Güne¸s Zeynep KARABULUT KURT
Semiha TED˙IK BA¸SARAN, a Ph.D. student of ITU Graduate School of Science En-gineering and Technology 504132305 successfully defended the thesis entitled “RE-LAYING OPPORTUNITIES FOR WIRELESS NETWORKS BY APPLYING NET-WORK CODING”, which he/she prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.
Thesis Advisor : Prof. Dr. Güne¸s Zeynep KARABULUT KURT ... Istanbul Technical University
Jury Members : Prof. Dr. ˙Ibrahim ALTUNBA¸S ... Istanbul Technical University
Assoc. Prof. Dr. Enver ÖZDEM˙IR ... Istanbul Technical University
Assoc. Prof. Dr. Ali Emre PUSANE ... Bo˘gaziçi University
Assoc. Prof. Dr. Serhat ERKÜÇÜK ... Kadir Has University
Date of Submission : 11 March 2019 Date of Defense : 19 April 2019
FOREWORD
First of all, I would like to express my sincere gratitude to my advisor Professor Güne¸s Karabulut Kurt for believing my abilities to accomplish this research work. I am kindly grateful for her permanent support, result-oriented perspective, availability, constructive suggestions, and scientific guidance that have played key roles to succeed the works investigated in this thesis. I would also like to thank Prof. Frank Kschishang for his valuable contributions and suggestions to the last part of the thesis.
I would like to acknowledge The Scientific and Technological Research Council of Turkey (TUBITAK) for financial support in the project named "Random Network Coding and Designs over GF(q)" under grant no. 113E294 conducted between October 2013 and October 2016. I also acknowledge TUBITAK for financial support based on the Ph.D. Priority Areas Fellowship Program 2211/C since March 2017. I would also like to thank Istanbul Technical University BAP Coordination Unit for financial support.
I would like to thank the members of the thesis steering committee, Professor ˙Ibrahim Altunba¸s and Professor Ali Emre Pusane, for their instructive and valuable contributions during the progression of the dissertation. I specially thank Professor ˙Ibrahim Altunba¸s for his guidance and constructive comments during my graduate education. I am also very grateful to assist his undergraduate courses which helps to improve my instructor capability. I would like to thank Dr. Özge Cepheli for her friendship and support at the beginning of my graduate education. I would also like to thank my colleagues from ITU Wireless Communication Research Laboratory for their friendship.
Finally, I would like to present my special thanks to my parents and sisters for their love, encouragement, and endless support throughout my life. I also appreciate all the support and care of my mom. The major role is of my spouse, Mehmet Ba¸saran, to be extremely supportive of me throughout the thesis process and he has made countless sacrifices to finish this study.
April 2019 Semiha TED˙IK BA¸SARAN
TABLE OF CONTENTS
Page
1. INTRODUCTION ... 1
1.1 Background and Motivation ... 1
1.2 Literature Overview... 2
1.2.1 Network coding ... 2
1.2.2 Random network coded cooperation ... 3
1.2.3 Topology awareness in network coding ... 4
1.2.4 Multi-access schemes for network coded cooperation systems ... 5
1.2.5 Wireless network reliability analysis... 6
1.3 Organization and Contributions of the Thesis... 7
2. NETWORK CODED COOPERATION... 11
2.1 Linear Network Coding... 12
2.1.1 Analog network coding ... 15
2.1.2 Random linear network coding ... 16
2.1.3 Rateless codes in network coding... 17
2.2 Cooperative Communication Aspect of Network Coded Cooperation ... 18
2.3 Conventional Network Coded Cooperation... 20
2.4 Summary and Discussion ... 21
3. DECODING FAILURE PROBABILITY ANALYSIS OF RANDOM NETWORK CODED COOPERATION SYSTEMS ... 23
3.1 RNCC Signaling Model ... 23
3.1.1 Network model ... 26
3.2 Decoding Failure Probability Analysis of RNCC ... 27
3.2.1 Individual link outages ... 27
3.2.2 Calculation of conditional successful decoding probability... 29
3.2.3 Counting full rank and rank deficient matrices ... 30
3.2.4 Relay operations ... 35
3.3 Numerical Results ... 36
3.3.1 Practical implementation results... 41
3.4 Summary and Discussion ... 45
FOREWORD... ix
TABLE OF CONTENTS... xi
ABBREVIATIONS ... xiii
SYMBOLS... xv
LIST OF TABLES ...xvii
LIST OF FIGURES ... xix
SUMMARY ... xxi
4. WIRELESS CHANNEL INDUCED CODING ... 47
4.1 System Model... 47
4.1.1 Conversion of the tripartite network graph to the effective bipartite network graph... 48
4.2 Wireless Channel Induced Coding Solution... 51
4.3 Numerical Results ... 52
4.4 Summary and Discussion ... 55
5. NCC-OFDMA SYSTEM... 57
5.1 Joint Subcarrier and Power Allocation in OFDMA Systems for Outage Minimization ... 58
5.1.1 Joint optimization approaches ... 58
5.1.2 The proposed algorithms ... 60
5.1.3 Numerical results... 62
5.2 Single Relay Selection Scheme for NCC-OFDMA System... 66
5.2.1 OFDMA extension of network coded cooperation... 66
5.2.2 Decoding failure probability analysis of NCC-OFDMA-SRS ... 69
5.2.3 Min-max single relay selection rule ... 69
5.2.4 Decoding failure probability analysis of NCC-OFDMA-SRS... 70
5.2.5 Numerical results... 72
5.3 Summary and Discussion ... 74
6. WIRELESS NETWORK RELIABILITY ANALYSIS FOR ARBITRARY NETWORK TOPOLOGIES... 75
6.1 Outage Polynomials of Wireless Networks... 76
6.1.1 Network outage polynomial calculation based on path enumeration... 78
6.1.2 Network outage polynomial calculation based on cut-set enumeration. 78 6.1.3 Network outage polynomial calculation based on two-terminal polynomial... 79
6.1.4 Bounds on the outage polynomial ... 80
6.1.5 Presence of correlated channels... 81
6.2 Diversity Gain and Ergodic Capacity Analyses for Arbitrary Network Topologies ... 82
6.2.1 Diversity gain analysis... 82
6.2.2 Ergodic network capacity ... 83
6.3 Numerical Results ... 84
6.4 Summary and Discussion ... 89
7. CONCLUSIONS... 93
7.1 On the Efficiency Perspective... 93
7.2 On the Fundamental Limits Perspective... 93
7.3 Future Directions ... 94
REFERENCES... 95
APPENDICES...105
APPENDIX A: An Example of Orbit Counting... 107
ABBREVIATIONS
AF : Amplify-and-Forward ANC : Analog Network Coding ARQ : Automatic Repeat Request AWGN : Additive White Gaussian Noise CC : Cooperative Communication CSI : Channel State Information DF : Decode-and-Forward
DDF : Dynamic Decode-and-Forward FDMA : Frequency-Division Multiple Access HM-OPT : Hungarian Method Based Optimal Solution
HM-RC : Hungarian Method Based Reduced Complexity Solution i.i.d. : Independent and identically distributed
MDS : Maximum Distance Separable LDPC : Low Density Parity Check
LT : Luby Transform
NC : Network Coding
NCC : Network Coded Cooperation
OFDMA : Orthogonal Frequency-Division Multiple Access PNC : Physical Layer Network Coding
QPSK : Quadrature Phase Shift Keying
R2EHK : Random Rotation and Expansion Based Hopcroft-Karp Algorithm
rd : Relay-to-Destination Link RLNC : Random Linear Network Coding RNCC : Random Network Coded Cooperation sd : Source-to-Destination Link
SDR : Software Defined Radio SNR : Signal-to-Noise Ratio sr : Source-to-Relay Link
TDMA : Time-Division Multiple Access TWRC : Two-Way Relay Channel
WiCiC : Wireless Channel Induced Coding XOR : Exclusive-Or
SYMBOLS
M : The number of source nodes N : The number of relay nodes
L : The number of coherence bandwidths ℵ : The number of subcarriers
ℵc : The number of subcarriers in each coherence bandwidth
q : The field size
i : The index of source node j : The index of relay node n : The index of subcarrier Si : ithsource node
Rj : jthrelay node
ξn : nthsubcarrier
D : Destination node
xi : The source packet of Si
ˆ
xj,i : The detected version of xi at Rj
αj,i : The code coefficient of xi at Rj
cj : The coded packet of Rj
ysirj : The received signal at Rj when Si transmits
ysid : The received signal at D when Sitransmits
yrjd : The received signal at D when Rj transmits
hsirj : The channel coefficient between Siand Rj
hsid : The channel coefficient between Siand D
hrjd : The channel coefficient between Rj and D
wsirj : The AWGN component at Rj when Si transmits
wsid : The AWGN component at D when Sitransmits
wrjd : The AWGN component at D when Rj transmits
σ2
w : The variance of the AWGN component
u : The link type (sid, sirj, rjd)
Ru : The target transmission rate of link u
G : The graph model of given communication network
V : Vertex set
U : User set
S : Source node set
R : Relay node set
D : Destination node set ¯
γsr : The average SNR value of sr link
¯
γsd : The average SNR value of sd link
¯
γrd : The average SNR value of rd link
H : Channel-outage matrix of sr links G : Channel-outage matrix of rd links φsr : Outage probability of sr links
φrd : Outage probability of rd links
Z : Global encoding matrix of RNCC system A : The network coding matrix
D : The diagonal matrix of the direct transmission of sd links Z0 : The updated version of Z
B : A matrix part of Z with the size of (N − l) × k
C : A matrix part of Z with the size of (N − l) × (M − k) N : Communication network model
E : The directed edge set
C : A cut-set
K : The collection of all cut-sets
L : The collection of all minimal cut-sets M : The collection of all minimum cut-sets S : A designated source vertex
D : A designated terminal vertex vı : ıthvertex
e : thedge
η : The number of directed edges p : The outage probability of the link e
LIST OF TABLES
Page Table 3.1 : Measurement results... 45
LIST OF FIGURES
Page Figure 2.1 : The classical butterfly network demonstrating the throughput
enhancement with NC... 13 Figure 2.2 : (a) NC encoder, (b) Destination view. ... 14 Figure 2.3 : TWRC model... 16 Figure 3.1 : The network model with M source nodes, N relay nodes, and a
single destination node... 24 Figure 3.2 : The decoding failure probability results of RNCC, with respect to
changing number of relay nodes, N, and field size, q when M = 2. . 36 Figure 3.3 : The decoding failure probability results of RNCC, with respect to
changing number of source nodes, M, and field size, q, when N = 4. 37 Figure 3.4 : The decoding failure probability results of RNCC with respect to
average SNR of sd and sr links when q = 8 and ¯γrd = 5 dB. ... 38
Figure 3.5 : The decoding failure probability results of RNCC with respect to average SNR of sd and sr links when q = 64 and ¯γrd = 5 dB... 39
Figure 3.6 : The decoding failure probability results of RNCC with respect to average SNR of sd and rd links when q = 8 and ¯γsr = 5 dB. ... 40
Figure 3.7 : The decoding failure probability results of RNCC with respect to average SNR of sd and rd links when q = 64 and ¯γsr = 5 dB. ... 41
Figure 3.8 : The upper theoretical bounds (t ≤ 1) and simulation results of decoding failure probability for q = 2 and ¯γsr = 20 dB over
various M, N, and ¯γsdvalues... 42
Figure 3.9 : The decoding failure probability results of single relay selection versus N values for varying ¯γsd when M = 4, q = 4, and ¯γsr =
¯
γrd = 15 dB... 43
Figure 3.10: Implementation setup of RNCC. ... 43 Figure 3.11: The decoding failure probability results of real tests with
simulations versus the average SNR value of sd links, γ0
sd when
M = N = 3. ... 44 Figure 4.1 : An example of tripartite graph model of the network given in
Figure 3.1 when M = 2 and N = 3. ... 49 Figure 4.2 : The effective bipartite graph model of the corresponding tripartite
graph. ... 50 Figure 4.3 : The decoding failure probability results of various algorithms
presented using symmetric SNR case when ¯γu = ¯γ, ∀ u and
Figure 4.4 : The decoding failure probability results of various algorithms presented using AS1case where ¯γu → ∞, u ∈ hrjd, ¯γu = ¯γ, u∈
hsirj and AS2 case where ¯γu → ∞, u ∈ hsirj, ¯γu = ¯γ, u ∈ hrjd
for M = 4, N = 7... 54 Figure 4.5 : The decoding failure probability results of various algorithms
presented using symmetric SNR case for varying N values when M = 4. ... 55 Figure 5.1 : (a) Outage probability results of the methods versus noise regime,
(b) Total transmit power (TTP) and total excess power (TEP) results of the methods versus noise regime... 63 Figure 5.2 : (a) Outage probability results of the methods according to
different Ri = R0values versus noise regime when M = 4, ℵ = 8,
and L = 8, (b) TTP and TEP results of the methods according to different R values versus noise regime when M = 4, ℵ = 8, and L = 8. ... 65 Figure 5.3 : a) Outage probability results of the methods according to different
Lvalues versus noise regime for M = 4, ℵ = 8, and Ri = R0 = 2,
(b) TTP and TEP results of the methods according to different L values versus noise regime for M = 4, ℵ = 8, and Ri = R0 = 2. ... 67
Figure 5.4 : The comparison of simulation and theoretical results of the decoding failure probability of NCC-OFDMA-SRS for L = 1, ℵ = 8 over varying values of M and N... 73 Figure 5.5 : The comparison of simulation and theoretical results of the
decoding failure probability of NCC-OFDMA-SRS for M = 4, N = 4, and ℵ = 8 over varying values of L. ... 74 Figure 6.1 : There are six exemplary networks denoted by N1, N2, N3, N4,
N5, and N6 which are presented in (a), (b), (c), (d), (e), and (f)
respectively. N1, N2, N3, N4, N5, and N6 respectively have 3
edges, 4 edges, 2 edges, 6 edges, 4 edges, and 5 edges. ... 85 Figure 6.2 : The comparative results of upper and lower bounds of the outage
polynomial of N1. ... 86
Figure 6.3 : (a) The capacity polynomials results of N1, (b) The ergodic
capacity results of N1... 87
Figure 6.4 : The outage polynomial results of N2 versus ρ. ... 88
Figure 6.5 : (a) The capacity polynomials results of N2 (b) The ergodic
capacity results of N2... 89
Figure 6.6 : The outage polynomial results of all the networks defined in Figure 6.1. ... 90 Figure 6.7 : The ergodic capacity results of all the networks defined in Figure
RELAYING OPPORTUNITIES FOR WIRELESS NETWORKS BY APPLYING NETWORK CODING
SUMMARY
In classical relay-aided communication systems, intermediate nodes are able to store and forward received signals to a destination or other intermediate nodes without modifying the content of the received information packets. However, the next generation communication technologies target high data rate and low latency based on the real-time applications in dense network scenarios. Therefore, the efficient utilization of network resources (power and bandwidth) becomes critical at intermediate nodes in order to both increase the throughput and reduce the transmission delay. Network coding (NC) based on mixing packets at relay nodes is proposed as an efficient solution that meets high throughput and low delay demands.
By using NC, an increase in data rate and low transmission latency become possible since NC has a flexible nature for an extension to multi-source multi-relay case by assigning different code sets to each relay. Thus, NC can be considered as an effective tool that serves to all of the network users. Furthermore, it can be used as a promising solution for scalability problems in dense networks. While predetermined code sets are used in conventional NC, code coefficients are generated randomly in random linear network coding (RLNC). In RLNC, code coefficients have a uniform distribution and they are independently chosen from a finite field. RLNC yields a flexible scheduling opportunity based on the dynamically changing network components and provides improved efficiency. As cooperation emerges due to the naturally occurring broadcasting over wireless channels, the applications of NC and RLNC in wireless networks enable network coded cooperation (NCC) and random network coded cooperation (RNCC), respectively.
In this thesis, we design and characterize various relaying opportunities considering the efficient usage of three types of resources, namely relay, power, and bandwidth, by applying NC in wireless networks. We initially provide a decoding failure probability analysis framework for RNCC systems and propose a relay selection scheme to alleviate the complexity of the usage of all relay nodes. In addition, we propose a topology-aware NC scheme to improve the system reliability. Besides, minimizing power consumption of the wireless systems while maximizing the number of served users is another contribution of the thesis. Designing bandwidth efficient multiple access schemes for NC in frequency-selective channels is also handled. The final main benefit is the determination of the asymptotic performance limitations of unstructured wireless topologies through relating network reliability perspective with max-flow min-cut theorem.
Accordingly, we provide efficient transmission architectures at the relay nodes as a first perspective. A new framework is proposed for computing decoding failure probability
indicating the successful decoding of the source symbols at the destination node, is utilized. Also, the results belonging to a single relay case and a relay selection scheme are investigated. The validity of the presented theoretical expressions is demonstrated through identical simulation results. An implementation scenario is also presented to show the practical usage effectiveness of RLNC in real time applications by using software defined radio nodes.
Conventional NC and RLNC techniques do not take into account the channel conditions while determining network code coefficients. In addition to the characterization of the performance framework of RNCC systems, we propose a new coding scheme called wireless channel induced coding (WiCiC) by considering channel-awareness for the efficient usage of relay nodes in basic operations. We assume that 1-bit quantized channel state information (CSI) is available at the relay nodes, which is a less strict requirement than full CSI knowledge. In the absence of topology awareness, higher field sizes are required to obtain linearly independent codewords because of the wireless channel impairments for RLNC. Due to operating in binary field, the decoding process of the proposed scheme is quite simple compared to conventional network codes and RLNC in higher order fields. In addition, the proposed WiCiC scheme achieves the exact performance of the exhaustive codeword search providing considerably reduced complexity. Therefore, the introduced coding algorithm is convenient for practical implementation thanks to its lower encoding and decoding complexities in wireless networks.
As the second perspective, power efficient solutions are designed for wireless networks by considering the efficient bandwidth utilization. Orthogonal frequency-division multiple access (OFDMA) technique not only provides efficient design freedom for improving spectral and power efficiencies but also overcomes the destructive effects of the frequency-selective channel by exploiting multiuser diversity. It also allows effective assignment of limited radio resources to users. Firstly, the joint assignment problem of subcarriers and limited transmission power is addressed as a combinatorial optimization problem for the OFDMA system. To ensure fairness among users while jointly minimizing the total transmit power, the minimization of the number of outage subcarriers is selected as the objective function. An optimal algorithm based on the application of Hungarian method is proposed by utilizing randomly weighted complete bipartite graphs. A reduced complexity algorithm is presented as well. The proposed algorithms reduce the number of outage users compared to the benchmark works and provide significant power savings.
After defining individually efficient usage scenarios of the limited resources, we jointly optimize the utilization of all of them. To exploit frequency diversity gain while ensuring orthogonality among multiple users, OFDMA technique is considered as a multiple access scheme for NCC systems, referred to as NCC-OFDMA. Owing to its natural characteristics, such as allowing scalability and providing robustness to channel impairments, NCC can be easily adapted to dense network deployments. Since OFDMA offers a flexible design on bandwidth usage by letting smart subcarrier allocation schemes in frequency-selective channels, combining NCC with OFDMA enables feasible transmission schemes for efficient resource utilization. A single relay selection (SRS) technique is used to mitigate the complexity of utilizing all relay nodes. This system model is referred to as NCC-OFDMA-SRS. In addition, the asymptotic
decoding failure probability expressions of the system are obtained, demonstrating that the achievable maximum diversity gain results are attained.
The final goal of the thesis is to determine the outage performance analysis of wireless networks for unstructured network topologies. The performance limitations of an arbitrary network topology, comprised of the links that are prone to errors and erasures, constitute an essential problem. The network reliability perspective of the graph theory is invoked to obtain the network outage polynomial of generalized wireless networks by enumerating paths and cut-sets of its graph representation for both uncorrelated and correlated wireless channels. We evaluate the network outage polynomial by utilizing individual link outages, through the use of path enumeration, cut-set enumeration, and terminal-reliability approaches. A relationship between the max-flow min-cut theorem and key communication performance indicators, namely diversity and coding gains, is established. An ergodic capacity analysis of networks with arbitrary topologies is also provided in terms of network outage polynomial. Accordingly, we provide a comprehensive tool that can be used to specify the asymptotic performance limitations under various implementation schemes.
In summary, we propose various efficient resource utilization schemes from the relay, power, and bandwidth perspectives associating with NC in wireless networks. In addition, we present extensive performance analyses of the proposed schemes from the aspects of diversity gain, outage probability, and decoding performance. Accordingly, we introduce an overall relaying approach which is a candidate to be utilized in next generation wireless networks. Furthermore, we obtain the performance bounds of generalized wireless networks by applying the concepts of graph theory. Therefore, the performance bounds that provide an additional insight into the system restrictions can be preferred to improve system efficiency.
KABLOSUZ A ˘GLAR ˙IÇ˙IN A ˘G KODLAMALI AKTARMA FIRSATLARI
ÖZET
Klasik röle (aktarma dü˘gümü) yardımlı haberle¸sme sistemlerinde, ara dü˘gümler (röle) aldıkları i¸saretlerin içeri˘gini de˘gi¸stirmeden onları sadece depolar ve di˘ger ara dü˘gümlere ya da alıcı dü˘güme iletir. Gelecek nesil haberle¸sme sistemleri ise yüksek veri hızı ve dü¸sük iletim gecikmesi ihtiyaçlarını sa˘glamayı hedeflemektedir. Bu yüzden röle dü˘gümlerindeki i¸slemlerin güç tüketimi ve band geni¸sli˘gi kullanımı açısından daha verimli bir ¸sekilde gerçekle¸stirilmesine ihtiyaç vardır. Band geni¸sli˘gi ve güç gibi sınırlı a˘g kaynaklarının röle dü˘gümlerinde etkili bir ¸sekilde kullanılması, veri iletim hızının artırılması ve iletim gecikmesinin dü¸sürülmesi açısından kritik bir öneme sahiptir. Literatürde önerilen a˘g kodlama (network coding, NC) tekni˘gi bahsedilen bu beklentileri kar¸sılayabilme potansiyeli olan etkili bir çözüm olmaya adaydır.
NC tekni˘gi farklı röle birimlerine farklı kod kümeleri atayabilen, çoklu kullanıcı ve röle durumlarına uyum sa˘glayabilen esnek bir yapıya sahiptir. Bu yüzden NC tekni˘gi, yo˘gun a˘g kullanıcılarının bulundu˘gu durumlarda, ölçeklenebilirlik problemini çözebilecek bir yöntem olarak kullanılmaya uygundur. Ayrıca, NC kullanılarak hem veri iletim hızı artırılabilir hem de dü¸sük iletim gecikmeleri elde edilebilir. Belirlenmi¸s kod kümelerinin kullanıldı˘gı klasik a˘g kodlama yapılarından farklı olarak, kod katsayılarının sonlu bir kümeden rastgele seçilerek üretildi˘gi rastgele a˘g kodlama (random linear network coding, RLNC) tekni˘gi literatürde önerilmi¸stir. RLNC ¸seması, her bir röle dü˘gümünde, kod katsayılarının belirlenen sonlu bir kümeden e¸sit olasılıklı ve ba˘gımsız olarak rastgele üretilmesi prensibine dayanmaktadır. RLNC tekni˘gi özellikle durumları dinamik olarak de˘gi¸sen a˘g bile¸senleri olması durumunda, esnek planlama özelli˘gi sayesinde verimlili˘gin artırılmasını sa˘glar. NC ve RLNC, kablosuz sistemlere uygulandı˘gında ise kablosuz kanalın do˘gası gere˘gi her yöne yayılım yapma özelli˘ginden dolayı sırasıyla i¸sbirlikli a˘g kodlama (network coded cooperation, NCC) ve i¸sbirlikli rastgele a˘g kodlama (random network coded cooperation, RNCC) sistemleri kar¸sımıza çıkmaktadır.
Bu tezde, sınırlı olan röle, güç ve band geni¸sli˘gi kaynaklarının verimli bir ¸sekilde kullanılmasını amaçlayan çe¸sitli aktarma uygulamaları tasarlanmaktadır. Öncelikle, RNCC sisteminin kapsamlı kod çözme ba¸sarısızlı˘gı analizi yapılmaktadır ve klasik NC çalı¸smalarındaki tüm röle dü˘gümlerinin kullanılması gereklili˘ginin getirdi˘gi karma¸sıklık, önerilen tekli röle seçimi tekni˘gi sayesinde azaltılmaktadır. Ek olarak, kodlama katsayıları üretilirken a˘g topolojisinin göz önüne alındı˘gı yeni bir a˘g kodlama ¸seması önerilmi¸stir. Servis sa˘glanan kullanıcı sayısının maksimum seviyeye ta¸sınırken minimum güç harcanması, bu tezin bir di˘ger katkısını olu¸sturmaktadır. Bu kapsamda frekans seçici kanallarda a˘g kodlama içeren, band geni¸sli˘gi açısından verimli bir çoklu eri¸sim ¸seması önerilmi¸stir. Tezin son ana faydası ise, a˘g güvenilirli˘gi ve maksimum akı¸s minimum kesinti (max-flow min-cut) teoremi kullanılarak, herhangi
bir yapılandırılmamı¸s kablosuz a˘g sisteminin kuramsal ba¸sarım ve ergodik kapasite limitlerinin belirlenmesidir.
Öncelikle, bu tez kapsamında ilk bakı¸s açısı olarak röle birimlerinin verimli kullanıldı˘gı iletim teknikleri sunulmaktadır. Kablosuz kanaldaki RNCC sisteminin, kod çözme ba¸sarısızlı˘gı olasılı˘gını hesaplamak için yeni bir ¸sema önerilmektedir. Kod çözme ba¸sarısızlı˘gı hesaplanırken, kodlama matrisinin tam ranklı olması ko¸sulu kullanılmaktadır. Çok röleli sistem modelinin yanı sıra, hem tek röleli hem de tek röle seçimli durumlara ait teorik ifadeler elde edilmektedir. Bu sonuçların geçerlili˘gi, kapsamlı Monte Carlo benzetimleri ile do˘grulanmaktadır. Ayrıca, RLNC tekni˘ginin gerçek zamanlı sistemlerde kullanım avantajını kanıtlamak amacıyla yazılım tabanlı radyo birimlerinden olu¸san bir uygulama senaryosu tanıtılmaktadır.
Geleneksel NC ve RLNC tekniklerinde, kanal durumlarını göz önüne almadan kod katsayıları üretilmektedir. RLNC tekni˘ginin kablosuz kanallarda kapsamlı ba¸sarım analizinin yanı sıra, röle birimlerinin daha etkin bir ¸sekilde kullanılması amacıyla, kablosuz kanalın ba˘glantı durumlarını göz önünde bulunduran yeni bir kodlama ¸seması üzerine çalı¸sılmaktadır. Bu do˘grultuda, ikili tabanda i¸slem yapan, kablosuz kanal tarafından uyarılmı¸s kodlama (wireless channel induced coding, WiCiC) ¸seması önerilmi¸stir. Önerilen WiCiC ¸semasında, ikili alandaki kod katsayıları kanal durum bilgisi (channel state information, CSI) kullanılarak üretilmektedir. Tam CSI’nın bilindi˘gi duruma göre daha az katı bir kural olan 1-bitlik düzeyle¸stirilmi¸s CSI bilgisinin röle birimlerinde mevcut oldu˘gu varsayımı kullanılmaktadır. CSI bilgisinin mevcut olmadı˘gı ya da özellikle kodlama katsayıları üretilirken göz önüne alınmadı˘gı durumlarda, kablosuz kanaldaki bozulmalardan dolayı ba¸sarım kayıplarının önüne geçilmesi için kod katsayılarının daha büyük sonlu kümeden seçilmesi zorunlu hale gelmektedir. Kod katsayılarının ikili alandan seçilmesi, kod çözme karma¸sıklı˘gını klasik NC ve RLNC’ye göre önemli oranda azaltmaktadır. Böylece, önerilen WiCiC ¸seması hem kodlama hem de kod çözme karma¸sıklı˘gının dü¸sük olması sayesinde pratik gerçeklemelerde kullanılmaya oldukça uygun bir tekniktir.
˙Ikinci bakı¸s açısı olarak da güç tüketimi ve band geni¸sli˘ginin verimli kullanıldı˘gı sistemlerin tasarımı üzerine yo˘gunla¸sılmaktadır. Dik frekans bölmeli çoklu eri¸sim (orthogonal frequency-division multiple access, OFDMA) tekni˘gi, hem spektral hem de güç verimlili˘ginin artırılması için tasarım serbestli˘gi sa˘glamaktadır. OFDMA’deki alt ta¸sıyıcılara güç ve frekans ataması i¸slemi, birle¸simsel optimizasyon problemi ¸seklinde tanımlanmaktadır. Kullanıcılar arasında adaleti garanti eden, kesintideki alt ta¸sıyıcı sayısını ve iletim gücünü en aza indirmeyi amaçlayan bir optimizasyon problemi önerilmi¸stir. Hem en iyi hem de en iyiye çok yakın olan daha dü¸sük karma¸sıklı˘ga sahip ikinci bir algoritma önerilmi¸stir. Bu iki algoritma, hem kesinti olasılı˘gı hem de güç tüketimi açısından literatürdeki çalı¸smalara göre önemli avantajlar sa˘glamaktadır.
Kısıtlı kaynakların ayrı ayrı verimli kullanılmasına yönelik çalı¸smaların ardından, bu kaynakların kullanımı ortak olarak optimize edilmi¸stir. Çoklu kullanıcılar arasında dikli˘gi sa˘glayarak frekans çe¸sitleme kazancından yararlanmak amacıyla, OFDMA tekni˘gi, NCC-OFDMA olarak adlandırılan a˘g kodlamalı i¸sbirlikli sistemlerde bir çoklu eri¸sim tekni˘gi olarak dü¸sünülmü¸stür. Frekans seçici kanallarda OFDMA, band geni¸sli˘gi kullanımında akıllı alt ta¸sıyıcı tahsisine izin veren esnek bir yapıya sahiptir. NCC’nin OFDMA ile birle¸stirilmesi, etkin kaynak kullanımı açısından uygulanabilir iletim yapılarına olanak tanımaktadır. Tek bir röle seçimi (single relay selection,
SRS) tekni˘gi, tüm röle dü˘gümlerinin kullanıldı˘gı duruma göre karma¸sıklı˘gı önemli miktarda azaltmaktadır ve bu model, NCC-OFDMA-SRS olarak adlandırılmaktadır. NCC-OFDMA-SRS sisteminin kod çözme ba¸sarısızlı˘gı ifadesinin birinci dereceden yakınsaklı˘gı türetilmi¸stir ve bu sonuçlar benzetimlerle do˘grulanmaktadır. Buna ek olarak, maksimum çe¸sitleme kazancına eri¸sildi˘gini gösteren asimptotik kod çözme ba¸sarısızlı˘gı ifadeleri elde edilmi¸stir.
Tez kapsamında ilgilenilen son konu ise yapılandırılmamı¸s kablosuz a˘gların kesinti ba¸sarımı analizidir. Kablosuz ba˘glantılar hataya ve bozulmaya yatkın oldu˘gu için kablosuz a˘gların ba¸sarım limitlerinin belirlenmesi oldukça önemli ve temel bir problemdir. Bu kapsamda, çizge teorisine ait a˘g güvenilirli˘gi bakı¸s açısı, yol sayma ve kesinti kümesi sayma teknikleri kullanılarak hem ili¸skili hem de ili¸skisiz kanal durumlarında genelle¸stirilmi¸s kablosuz a˘glara ait a˘g kesinti polinomu elde edilmi¸stir. Maksimum akı¸s minimum kesinti teoremi ile çe¸sitleme kazancı ve kodlama kazancı gibi haberle¸sme sistemleri için anahtar ba¸sarım ölçütleri ili¸skilendirilmi¸stir. Ayrıca, a˘g kesinti polinomu kullanılarak raslantısal topolojiler için ergodik kapasite sonuçları elde edilmi¸stir. Bu sayede, yapılandırılmamı¸s kablosuz a˘glar için farklı senaryolardaki, hem ba¸sarım sonuçları hem de asimptotik ba¸sarım limitlerini belirleyebilecek kapsamlı bir hesaplama aracı önerilmi¸stir.
Özet olarak, bu tezde kablosuz a˘glar için NC kullanılarak röle, güç ve band geni¸sli˘gi açısından verimli kaynak kullanım ¸semaları sunulmu¸stur. Bu yapılara ait ayrıntılı çe¸sitleme kazancı, kesinti olasılı˘gı ve kod çözme ba¸sarısızlı˘gı olasılı˘gı sonuçları elde edilmi¸stir. Bu do˘grultuda, gelecek nesil kablosuz sistemlerde kullanılmaya aday olabilecek çok çe¸sitli aktarma uygulamaları önerilmi¸stir. Bu çalı¸smalara ek olarak, çizge teorisi temelleri kullanılarak genelle¸stirilmi¸s kablosuz sistemlere ait ba¸sarım sınırları elde edilmi¸stir. Böylece, kablosuz sistemlerin tasarım a¸samasında sistemin verimlili˘gini artırmak için bu ba¸sarım limitleri kullanılabilecektir.
1. INTRODUCTION
This thesis focuses on various relaying applications by considering the efficient usage of three types of resources, namely relay, power, and bandwidth. The thesis especially aims both to propose a cross-layer optimization scheme for smart relaying in wireless networks and to investigate the system performance utilizing network coding (NC). In addition, the asymptotic performance results of any arbitrary wireless network topology are provided by utilizing individual link outages.
This chapter continues with the background and motivation of the thesis. Afterwards, the literature overview about the related works is given. Finally, the organization and the contributions of the thesis are elaborated in the last section.
1.1 Background and Motivation
In conventional communication systems, functionalities such as routing, error correction and data storage have been designed in accordance with the principle that network nodes perform transmission independently. However, data flow rates from source to destination nodes in a network can be increased by transmitting combinations of data obtained from different source nodes over the network during the same time interval, different from the classical network architecture where data flows are processed independently. Stemming from the early work [1] including the form of multi-level diversity, this technique is referred to as NC in [2]. NC is able to provide efficient usage of network resources and has been attracting increasing attention in recent years.
The application of NC in wireless networks has a disadvantage and an advantage. Firstly, as a disadvantage, error propagation may emerge at destination node due to wireless channel impairments. The initial studies on NC assume error free transmissions [2–4] for wired networks. Although such an assumption may be acceptable for wire-line networks, it is overly optimistic for wireless networks.
error performance between source and destination pairs and can be considered as an advantage. Whether a direct link, also termed as cooperation link, is present or not depends on the corresponding link qualities. These links provide additional cooperative diversity to improve the error performance of wireless networks [5]. Therefore, when the implementation of NC in wireless networks is designed by considering cooperation links, the system is called network coded cooperation (NCC). NCC has higher diversity gain and increased spectral efficiency compared to NC with the help of cooperative communication (CC).
1.2 Literature Overview
In this section, we provide a comprehensive literature overview and present open research problems about the considered issues in the thesis related to NCC from different aspects. Thus, the contributions of the thesis can be easily emphasized as will be defined in the next section.
1.2.1 Network coding
NC is a promising transmission scheduling method based on mixing the source packets at intermediate (relay) nodes according to the selected network code type, as proposed in [2]. Transmission of the mixed source packets from relay nodes, contributes to both the power efficiency and the increased throughput of the systems with a transmission bottleneck. In the pioneering works about NC, exclusive-or (XOR) coding schemes are presented to offer better decoding performance [2, 6]. Following these works, higher field sizes are preferred to design conventional NC schemes to serve multiple source nodes. Although operations in higher order fields give the opportunity to enable communication to a large number of source nodes, the associated high decoding complexity is a non-negligible drawback.
Conventional NC schemes, such as maximum distance separable (MDS) codes, use the optimum codes that satisfy Singleton bounds for static networks [7]. The parity check matrices of MDS codes are used to determine the network code coefficients [8]. These codes are capable of achieving the maximum decoding performance in static network topologies, however, the performance of MDS codes in dynamic network topologies is not sufficient to yield the necessary reliability levels.
We provide the generalized system models of NCC together with the extensive literature overview in Chapter 2.
1.2.2 Random network coded cooperation
In next generation wireless communication systems, every user and every device are always expected to be connected to a network from anywhere. This challenging requirement leads to an excessive increase in data traffic. Control and management of such a traffic load are extremely difficult and are expected soon to be a reality with the new dense network deployments. In dense network deployments, user connections instantaneously change, resulting in a dynamic network topology. Accordingly, the centralized controlling of networks may become quite complex. In such cases, random linear network coding (RLNC) can be selected as a special type of NC to set-up a decentralized control architecture [9, 10]. Relay nodes use network code coefficients, which are selected from a q−element (q is a prime power) finite field Fq, to create
network-coded symbols. Each relay node randomly determines the coding coefficients and generates network coded symbol without a need for a centralized controller. If the number of users changes in the network, the relay node can only increase the number of coding coefficients. The easy implementation of RLNC at the relay nodes improves its flexibility, making it a feasible solution to address dense network problems.
The decoding probability analysis of RLNC is given for erasure channels [11]. The theoretical decoding probability expression of RLNC defined in [11] is an approximation of the exact expression. Another work on RLNC over erasure channels is given in [12], where there is a constraint that the coding coefficients are selected from Fq\{0}. The tightness of the presented bounds is demonstrated with the simulation
results of RLNC. In [13], an analysis model for RLNC is proposed to calculate the bounds on the theoretical decoding probability expression. In [12, 13], the bounds on theoretical decoding probability are expressed tightly independent of q in a limited region. In addition to this constraint, the homogenized networks are also studied in which signal-to-noise ratio (SNR) values of direct and cooperation links are accepted as identical. However, this assumption is not widely acceptable for wireless links when calculating the upper bounds on decoding probability. Therefore, [13] does not provide the closed form expressions for generalized wireless channel conditions. On
the other hand, tight bounds (upper and lower) of RLNC in which coding coefficients are selected from Fq\{0}, are presented in [14] ignoring source to destination links,
for multi-source multi-relay scheme. An optimized framework is proposed to minimize overhearing probability while guaranteeing successful decoding for a legitimate user by transmitting random network coded symbols from a source node over erasure channels in [15]. Predefined delay and reliability constraints are also considered when performing simulations and obtaining theoretical derivations in [15]. The exact decoding probability expressions of RLNC in the field F2 are given by considering
erasure patterns [16].
As cooperation emerges due to the naturally occurring broadcasting in wireless links, the application of RLNC in wireless networks enables random network coded cooperation (RNCC). The decoding probability results of RNCC are presented by using coding at source nodes to assist a single relay node [17].
Although there are related studies in the literature [10–17], a comprehensive approach for calculating the successful decoding probability of RNCC under wireless channel conditions still remains an open issue.
1.2.3 Topology awareness in network coding
In the literature, there are limited works about topology-aware coding. An NC scheme with limited physical layer awareness is used for rate maximization in [18]. An adaptive NC scheme providing rate maximization is proposed for satellite communication networks for time-varying channels [19]. Another study about NC with physical layer awareness focuses on using multiple interfaces [20]. In [21], the optimal coding schemes, which are based on generator matrix MDS schemes in small field sizes for simple multiple access networks, are obtained. There is also an assumption that each source node is connected to the same number of relay nodes in [21]. The link failures between relay nodes and the destination node are ignored as well. In the previous multicast NC works,failed relay-to-destination links are mostly neglected [18–21]. In addition to this fact, the maximum flow perspective has not been considered in the literature with the integrated channel approach. Although the system
model of [21] proposes an efficient coding mechanism, a joint design framework for efficient NC according to channel states has not been taken into account yet.
1.2.4 Multi-access schemes for network coded cooperation systems
Increasing data rate demands of wireless network users enforce the efficient usage of spectrum while reducing the transmission power. Transmission of multiple nodes can be ensured by using either time-division multiple access (TDMA) or frequency-division multiple access (FDMA). As an efficient implementation of FDMA, orthogonal frequency-division multiple access (OFDMA) can be used to serve multiple nodes under the condition of frequency-selective channels [22], that may be encountered in both phases. In TDMA networks, NCC are completed in two orthogonal time slots [8]. On the other hand, making use of OFDMA, the system under consideration is able to utilize orthogonal frequency bands. Therefore, the transmission phases can be executed using orthogonal subcarriers, reducing the total transmission time. Furthermore, OFDMA provides frequency diversity by allowing flexible assignment of subcarriers to multiple nodes.
OFDMA is a competent technique to provide sufficient design freedom to improve spectral and power efficiencies while overcoming the destructive effects of the frequency-selective channel, by exploiting multiuser diversity and allowing efficient utilization of limited radio resources. The assignment of radio resources, namely subcarriers and the transmission power, is conventionally accomplished with the targets of the maximization of each SNR of each link or sum-rate maximization of the total system [9, 23–31]. In these approaches, waterfilling technique is used to allocate the limited power among subcarriers. However, the weighted sum-rate maximization does not guarantee the maximum number of non-outage subcarriers. On the other hand, with a goal of maximizing the number of non-outage subcarriers, the frequency-selective channel in OFDMA is separated into multiple subcarriers. Different from the majority of the works targeting rate (or SNR) maximization, the minimization of the number of outage users in OFDMA networks through a graph-based approach is considered in [32, 33]. A Hungarian method based subcarrier allocation algorithm is proposed to minimize the outage probability while ensuring fairness with providing theoretical approximation formula [32]. They also propose a
subcarrier allocation algorithm, random rotation and expansion based Hopcroft-Karp (R2EHK) algorithm, extended from Hopcroft-Karp algorithm in order to obtain
maximum cardinality matching, by using an unweighted bipartite graph without considering power allocation [33]. In [34], a suboptimal power allocation approach is proposed as an extension of R2EHK.
Both NCC and OFDMA techniques improve the robustness and provide reliable communication against the fading channel impairments. A system combining NCC and OFDMA, referred to as NCC-OFDMA, is shown to provide a significant diversity gain, through the diversity multiplexing trade-off analysis in [35]. On the other hand, the joint resource allocation problem for NCC-OFDMA systems is an open issue from the aspects of fairness among users, high-level functionalities, and practical implementation.
1.2.5 Wireless network reliability analysis
In [36], Shannon and Moore provide a reliability analysis of relay-aided systems by considering the unreliability probabilities of relay nodes. It is proven that the end-to-end reliability of a given network can be increased through these unreliable relay nodes. When a sufficient number of relay nodes is used, the probability of network unreliability approaches to zero [36]. However, transforming a complex network into an equivalent serial-parallel projection may not always be possible. When the serial-parallel representation of a given network is not available, the reliability analysis of generalized networks becomes more challenging. There are various methods proposed to calculate network reliability, including state enumeration, factorizing, path enumeration, and cut-set enumeration [37–40].
Although network reliability is a well-studied subject, its extension to wireless networks is still relatively unexplored [41–45]. As the popularity of wireless communication systems increases compared to their wired counterparts in many different areas, the reliability analysis of wireless communication becomes more important, yet challenging since wireless links are more prone to errors and erasures. Accordingly, an unrealistic deterministic channel model is used when investigating the interference effect of the wireless channels [41]. The reliability analysis of wireless multi-hop networks is conducted regarding shadowing effect of the wireless channel
in [42, 43]. However, [42, 43] do not consider the correlation effect of shadowing and this gap is filled by [44]. The reliability analysis of wireless multi-hop networks, which proposes a mathematical model to represent the network reliability of correlated shadowing wireless channel, is given in [45].
Network outage polynomial basically defines the zero capacity of any corresponding graph. The investigation of network capacity is an interesting problem since the maximum capacity of any network is limited by the size of the minimum cut of the graph. Therefore, the ergodic capacity results of any network can be calculated by using capacity polynomials. In the literature, there are some studies about the calculation of capacity polynomials that determine the maximum flow of arbitrary networks with random capacity edges by using subset decomposition method [46,47]. In [46], a subspace decomposition principle is used to determine maximum flow of arbitrary networks with random capacity edges. The maximum flow analysis of arbitrary networks with random edge capacities based on Bernoulli distribution is conducted in [47].
The aforementioned works have focused on obtaining only network reliability expressions without considering any fundamental performance analysis.
1.3 Organization and Contributions of the Thesis
In order to meet the expectations of next generation communication systems, the classical transmission techniques must be reconsidered according to the requirements of the parameters including high data rate, low latency, easy implementation and scalability. By increasing the number of connected devices and requiring integration of a diverse set of services, new technology demands arise. Various relaying approaches can be considered to increase throughput and to improve the robustness of the system. NCC is a candidate for smart relaying applications, that can be used in the next generation communication technologies. Due to its natural characteristics such as allowing scalability and providing robustness to channel impairments, NC and NCC can be easily adapted to the target network, alleviating the expected implementation issues in dense network deployments. We plan to show that NC/NCC is a convenient technique for future relaying opportunities to satisfy the requirements of the next
generation communication systems through performing both theoretical analyses and simulations in this thesis.
The thesis also handles multiple resource scheduling problems (such as OFDMA subcarrier selection, determining transmit power levels of these subcarriers, and selection of relays that aids to reliable communication) for wireless networks. The effects of different coding techniques on the system performance are also determined. Accordingly, we make contributions in terms of efficient usage of limited radio and peripheral resources (power, bandwidth, and time). The performance bounds of arbitrary network topologies are introduced as well.
The organization flow and the main contributions of the thesis that provide innovations to the literature and research area are explained below by emphasizing the uniqueness of the thesis from different aspects.
Chapter 2 includes the review of NCC systems by explaining the signaling model. In addition to reviewing the state-of-the-art in NCC systems, we aim to provide a comprehensive baseline that helps to compare numerous distinct systems proposed in the literature. We explain the conventional NC types in detail and present an overview of the literature on the applications of NCC.
The extensive tutorial about NCC whose substantial parts are given in this chapter is presented in the following book chapter and the journal paper.
B1: Basaran, S. T., Heidarpour, A.R., Gokceli, S., Kurt, G.K., Uysal, M., and Altunbas, I., (2018). Implementation of Network Coding in Wireless Systems, Network Coding and Subspace Designs, Springer, pp. 295–317.
J1: Basaran, S. T., Kurt, G.K., Uysal, M. and Altunbas, I. (2016). A Tutorial on Network Coded Cooperation, IEEE Communications Surveys and Tutorials, 18(4), 2970–2990.
Chapter 3 handles the performance analysis of RNCC systems and also investigates the system performance for both single relay and relay selection schemes. We introduce a generalized framework to analyze the decoding failure performance of RNCC. We also provide the decoding failure probability expressions of single relay and relay selection schemes with reduced complexity due to the simplicity of network topology according
to the multi-relay case. We validate the theoretical results with simulations to ensure the reliability of derivations.
The study explained in this chapter has been presented in the following journal paper. J2: Basaran, S. T., Gokceli, S., Kurt, G. K., Ozdemir, E. and Yaraneri, E. (2017). Error Performance Analysis of Random Network Coded Cooperation Systems, IEEE Transactions on Wireless Communications, 16(8), 5325–5337.
Chapter 4 introduces a channel induced coding policy to maximize successful decoding probability of NC system. The proposed wireless channel induced coding (WiCiC) scheme is induced by the wireless channel while the code coefficients are determined according to channel state information (CSI), also providing the opportunity to operate in binary field. We assume that 1-bit quantized CSI is available at relay nodes. The proposed WiCiC scheme achieves the exact performance of the exhaustive codeword search with considerably reduced complexity. Thus, the presented coding algorithm is convenient for practical implementations thanks to its lower encoding and decoding complexities for wireless relay networks.
The study explained in this chapter has been presented in the following journal paper. J3: Basaran, S. T. and Kurt, G.K. Wireless Channel Induced Coding, under review. Chapter 5 includes OFDMA extension of NCC systems along with the proposed subcarrier allocation scheme. We initially propose two joint subcarrier and power allocation algorithms based on Hungarian method. While the first algorithm provides the optimal solution, the second algorithm has a reduced computational complexity and its performance converges to the optimal solution at high SNR values. As for our main contribution, the proposed optimization framework addresses the problem of minimizing the number of outage subcarriers in downlink OFDMA systems, by assigning multiple data rates per user while minimizing the total power over a randomly weighted complete bipartite graph model. The proposed approaches provide power savings compared to the benchmark results in the literature. In the second part of Chapter 5, the decoding failure probability analysis of NCC-OFDMA system with a single relay selection (SRS) technique is presented. This system model is referred to as NCC-OFDMA-SRS and is used to mitigate the complexity of utilizing all relay nodes. Both the theoretical decoding failure probability expressions and the diversity gain of
NCC-OFDMA-SRS are obtained when R2EHKalgorithm is used to assign subcarriers
to users. The theoretical expressions are verified by Monte Carlo simulations.
The studies explained in this chapter have been presented in the following journal and the conference papers.
J4: Basaran, S.T. and Kurt, G.K. (2016). Joint subcarrier and power allocation in OFDMA systems for outage minimization, IEEE Communications Letters, 20(10), 2007–2010.
C1: Basaran, S.T., Kurt, G.K. and Chatzigeorgiou, I. (2018). On the performance of NCC-OFDMA with Single Relay Selection, in Proc. Global Information Infrastructure and Networking Symposium, Thessaloniki, Greece, 23-25 October. Chapter 6 introduces a framework to calculate the network outage polynomial as a tool in order to obtain network outage performance of communication networks. We determine the network outage polynomial of some simple directed networks in both correlated and uncorrelated channels. Accordingly, three methods, namely the path-enumeration method, the cut-set enumeration method, and the terminal reliability based method, are proposed. We derive the diversity and coding gains of a wireless network for arbitrary topology based on its graph properties. We establish a relationship between the max-flow min-cut theorem of graph theory and the diversity gain. In addition, we show that the diversity gain corresponds to the size of the minimum cut of the wireless network graph. We also provide the ergodic capacity analysis of networks in terms of individual link outage probability. In addition, an upper bound for the achievable transmission rate is determined.
The work explained in this chapter has been presented in the following journal paper. J5: Basaran, S.T., Kurt, G.K. and Kschishang, F. Wireless Network Reliability Analysis for Arbitrary Network Topologies, IEEE Transactions on Communications, under review.
Chapter 7 concludes the thesis by providing the main outcomes and summarizes the contributions of the chapters. We also give suggestions regarding possible research topics for the extension of this work.
2. NETWORK CODED COOPERATION
In this chapter, our primary motivation is to provide an overview of the state-of-the-art in NCC systems from both NC and CC perspectives while providing details about various code types. The signaling model of NCC is generalized in the next chapters for different application scenarios.
In wireless networks, the multi-path fading channel can significantly affect the link quality, making the channel more prone to transmission errors. Furthermore, the number of end-users along with their corresponding data rate requirements constantly increases in wireless networks, while the network resources such as frequency spectrum and power remain limited. Wireless communication systems have a broadcast nature through the use of omnidirectional transmission antennas, enabling several nodes, possibly including the destination to receive multiple replicas of the transmission. They also provide spatial diversity through the independent fading channels between distinct node pairs. CC can exploit the spatial diversity, and it can therefore combat the performance degrading effects of the wireless fading channels. Making use of the broadcast nature of the wireless channel, when the source node transmits, the relay nodes (receiving many copies of the transmission signals) can repeat or process the received signals. The destination may capture the source signal, due to the occurrence of direct link between the source and destination. The destination may also receive the signals transmitted from the relays. At the end of the transmission process, the destination combines all received replicas of the information signal in order to significantly improve the error performance of the system.
In classical network set-ups, data flows between source-destination pairs are designed individually, without utilizing from any shared infrastructure. The relay nodes, that enable data flows between source-destination pairs, store and forward the data packets, making use of the well-known law of "commodity flow" paradigm [4]. Although commodity flows can be frequently encountered, (as in the design of vehicular traffic networks), when routing data flows, relay nodes can in fact combine the transmitted
information packets, instead of simply storing and forwarding [48]. To combine information packets, relay nodes can utilize different coding techniques. Using such smart relay nodes, the data transmission rates can be increased. In this sense, it can be concluded that NC is an alternative to the routing approaches defined in [49].
In order to obtain full benefit of NC in wireless networks, NC techniques have to be considered jointly with CC to eliminate the destructive effects of wireless channels. For example, the direct link between the source and the destination in addition to the transmission over the relay node, is only natural with the goal of robust and reliable transmission with possibly lower power consumption.
The main characteristics of NC and CC are combined in the NCC system. In the first phase of NCC, also called broadcast phase, all source nodes transmit information bearing symbols to both relay and destination nodes. This is enabled by the broadcast nature of the wireless channels, where the direct links between source and destination nodes may exist. Note that the broadcast phase is also referred to as the direct transmission phase [50]. In the second phase of NCC, the relaying phase, the relay nodes transmit the network coded symbols to the destination node. The destination jointly processes the signals received from source and relay nodes in order to correctly estimate the transmitted information packets. The existence of direct links between source nodes and the destination increases the diversity gain of the NCC system compared to the basic NC system where the direct link is not exploited. Note that this conventional NCC system can be easily generalized to multiple destination nodes case in an efficient manner.
Based on the preliminary work [51], NCC systems have been attracting great interest from a diverse set of researchers including mathematicians, computer scientists and electrical engineers. In the next section, linear network coding and its various coding types are examined.
2.1 Linear Network Coding
In their seminal work, Ahlswede et al. have shown that the maximum network capacity of a network coded system is given by the max-flow min-cut theorem [2]. This theorem states that the maximum amount of data flow transmitted from the source node to the
S
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1R
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1D
2 𝑥1 𝑥2 𝑥1 𝑥2 𝑥1+ 𝑥2 𝑥1+ 𝑥2 𝑥1+ 𝑥2Figure 2.1 : The classical butterfly network demonstrating the throughput enhancement with NC.
destination node is equal to the minimum capacity of network cuts (A cut in graph theory defines a partition of the vertices of a graph into two disjoint subsets.) separating the source and destination, representing the bottleneck of the network. It is proven that the maximum network throughput (i.e. minimum cut) can be achieved for acyclic networks with linear network codes (A cycle of a graph is a subset of the edges of that graph forming a path so that the first node of the path is the same as the node of the path. However, an acyclic graph does not contain any cycle.) [52]. The popularity of the NC approaches is increased among the researchers due to their inherent advantages [53, 54].
The provided benefits of linear NC are explained commonly over a butterfly network shown in Figure 2.1, representing the quintessential network topology, where the advantages of NC is clearly illustrated in [2]. In this set-up, the single source is labeled as S and generates two information packets, x1 and x2. R1, R2, R3, and R4 represent
the forwarding relay nodes and the destinations are denoted by D1 and D2. The goal
is to transmit the packets, x1 and x2, to both destinations, D1 and D2. When relay
nodes only forward the incoming information packets, x1 and x2, it is clear that the
link between R3 and R4 creates a bottleneck, enabling the transmission of only x1 (or
x2). Instead of simply forwarding received packets, if the relay node processes the
incoming packets, the throughput can be increased. Specifically, when R3 forwards
x1+ x2, then D1 or D2receive x1and x1+ x2or x2and x1+ x2, respectively. Noting
that (x1 + x2)− x2 = x1 and (x1 + x2)− x1 = x2, it can be deduced that both
𝑥1 𝑥2 𝑥𝑀 𝑐𝑗= 𝑖=1 𝑀 𝛼𝑗,𝑖𝑥𝑖
D
𝑐2= 𝑖=1 𝑀 𝛼2,𝑖𝑥𝑖 𝑐1= 𝑖=1 𝑀 𝛼1,𝑖𝑥𝑖 𝑐𝑁= 𝑖=1 𝑀 𝛼𝑁,𝑖𝑥𝑖R
𝑗 (a) 𝑥1 𝑥2 𝑥𝑀 𝑐𝑗= 𝑖=1 𝑀 𝛼𝑗,𝑖𝑥𝑖D
𝑐2= 𝑖=1 𝑀 𝛼2,𝑖𝑥𝑖 𝑐1= 𝑖=1 𝑀 𝛼1,𝑖𝑥𝑖 𝑐𝑁= 𝑖=1 𝑀 𝛼𝑁,𝑖𝑥𝑖R
𝑗 (b)Figure 2.2 : (a) NC encoder, (b) Destination view.
In a more generalized linear NC view, the coded packets are the linear combinations of the input packets. This is illustrated in Figure 2.2 for M source and N relay nodes (N ≥ M). Here, the ithincoming packet, x
i, is detected at the jth relay node, Rj. Rj
linearly combines these detected packets as
cj = M
X
i=1
αj,ixi, (2.1)
where the error free transmission is assumed. Although this is a valid assumption for wired networks, where transmission error rates can be kept negligibly low, this simplifying assumption can be overly optimistic in the presence of wireless communication channels. The coefficients, αj,i, can be obtained from a predetermined
MDS code or generated randomly as an RLNC. In order to recover coded M packets with linear network codes, the destination node, D, requires at least M linearly independent combinations of transmitted packets. Conventionally, the Gaussian elimination can be used to solve the set of linear equations over Fq to recover
x = [x1, . . . , xM]from the received packets. It is worth noting here that an erroneous
estimate at the relay nodes may cause an error at the destination, due to the error propagation through the wireless network. As another decoding approach, the received signals at both broadcast and relaying phases can be used to perform maximum likelihood detection [55].
Most of the NC systems consider the case where code coefficients are available at D [52, 56]. These systems can be referred to as coherent NC. However, the code coefficients can still be reproduced at the destination, for example by transmitting redundant symbols through the network. These systems are referred to as non-coherent
coding [57–60]. In [57], a code construction method is proposed to correct different combinations of errors and erasures in non-coherent RLNC. In [58,59], the asymptotic capacity region of the non-coherent NC is derived for multiple source nodes. The capacity of an NC system when relay nodes perform deterministic or randomized linear non-coherent is calculated in [60]. The NC at relay nodes can also be performed through nonlinear mappings on the received packets in [61]; however, our main focus remains in the linear network codes. Linear network codes can be mainly categorized into three subsections, namely analog network coding (ANC), RLNC, and rateless codes, as will be presented subsequently.
2.1.1 Analog network coding
As mentioned earlier, in the majority of the NC techniques, NC is applied at the bit (or symbol) level through the operations in Fq, and the associated performance
analyses do not consider any transmission error. An exception to this consideration is ANC that inherently takes the impact of the wireless communication channel into account. In ANC, NC is applied at the signal level meaning that coded symbols are obtained by utilizing received signals, instead of estimated bits or symbols. With the aid of characteristics of wireless communication channels, NC is performed without explicitly receiving transmitted packets; however, a combination of these packets is detected.
As the main application example of ANC, two-way relay channel (TWRC) is considered. In the TWRC topology, we have two source-destination pairs S1 and S2
as shown in Figure 2.3. S1 targets to transmit x1 to S2 while S2 targets to transmit
x2 to S1 [62]. Using binary linear NC, this operation can be completed in three time
slots (as opposed to the four time slot routing solution). However in ANC, the relay node obtains a linear superposition of the transmitted signals in a single time slot. The linear superposition is encountered due to the wireless channel nature. The relay node then transmits a combination of the received signals. Thus, NC is performed over the complex number set (hence the term analog), instead of a finite field Fq. To complete
the transmission, ANC takes two time slots instead of the three time slots as in NC approach, as illustrated in Figure 2.3.
𝑥1 𝑥2
𝑥1+ 𝑥2 𝑥1+ 𝑥2
S1
R
S2
Figure 2.3 : TWRC model.
Another variation of ANC is the so-called physical layer network coding (PNC). PNC is based on the demodulation of received signals transmitted from the source nodes in the physical layer [6]. Different from ANC, the modulated signal is decided according to superposition of two received signals sent from the source nodes at the relay node. In PNC, when the relay node receives signals form both S1 and S2 nodes simultaneously
(solid lines in Figure 2.3), the relay node are able to jointly estimate the transmitted packets x1and x2by simply calculating and transmitting x1+x2. Such a joint detection
is possible due to the physical characteristics of the wireless channels. Specifically, the channel gains of source-destination links are highly likely to be distinct values. As for the (almost impossible) same gain case, a joint detection of received bits would not be possible, similar to the rank conditions in linear NC. Once x1+ x2 is detected by both
S1and S2, x2 (x1) can be obtained at S1 (S2) thanks to having a priori knowledge of x1
(x2). Following the seminal works, [62] and [63], there has been a surge of research
activities in the field of both ANC and PNC [64, 65]. As examples, in [64], a joint decoding scheme is proposed for PNC in TWRC with reduced complexity. In [65], a two-phase spectrum sharing protocol based on an ANC strategy for TWRC is provided.
2.1.2 Random linear network coding
When the network topology varies in time or simply unknown at a centralized controller, RLNC as proposed in [9], can be resorted. RLNC is applied as a linear network code, and RLNC coefficients are selected uniformly and independently from Fq. The principles of linear NC also hold in RLNC [9, 66, 67].
RLNC has several applications including peer-to-peer [68] and multicast communi-cations [69, 70]. In [69], two RLNC based transmission methods are proposed for efficient usage of power and delay reduction for multicast scenarios. The robustness of RLNC is substantiated for Byzantine modification of information symbols in distributed multicast networks. Note that when using deterministic network codes,
such as MDS codes, the channel conditions have an impact on the error performance. As preliminary examples, in [71] and [72], the impact of the imperfect propagation conditions are considered where the decoding performance is investigated. In addition, the decoding failure analysis is conducted for RLNC without cooperation links in [72].
2.1.3 Rateless codes in network coding
The network codes can be conventionally designed according to the network topology. The apparent example of this fact is the butterfly network as given in Figure 2.1. For more generalized settings, low density parity check (LDPC) codes or MDS codes such as Reed-Solomon codes are suitable candidates for NC [73]. These conventional techniques have fixed-rate codes. On the other hand, if the relay node decides to transmit signals by considering the channel link quality, rateless codes can be applied. The cluster of rateless codes is ignited by fountain codes, Luby Transform (LT) codes and Raptor codes [74, 75]. Fountain codes produce limitless number of outputs from a given input vector. Each output symbol is generated randomly and independently from the remaining other symbols. LT codes are computationally efficient forms of the fountain codes [74]. The corresponding encoding and decoding schemes are quite simple. Raptor codes are also a class of fountain codes with fast encoding and decoding algorithms. In this technique, before LT coding, precoded input symbols are first encoded with a high-rate code (e.g. an LDPC code). The precoded symbols are then encoded by a suitable LT code with a constant average degree [75]. In the literature, there are many applications of rateless codes for NC in wireless networks [76–85]. In [76], an experimental testbed is implemented to determine the development of fountain codes over mobile communication and satellite links. Rateless coding scheme is extended to multiple input single output systems for additive white Gaussian noise (AWGN) channels [77]. The performance of LT and Raptor codes are compared in [78] for binary symmetric and AWGN channels. In [79], a combined erasure correction code of rateless scheme and feedback channel is proposed to minimize the processing time and memory requirements of transmitter and receiver structures. On-the-fly verification of rateless error codes is investigated by using discrete-log-based hash scheme to authenticate the completeness of downloaded data in [80]. In [81, 82], a fountain code based relaying protocol that improves the system performance, is
