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https://dspace.jaist.ac.jp/

Title

Final Report of The Coding/Decoding Algorithms
and Performance Comparison

Author(s)He, Jiguang; He, Xin; Hou, Jiancao; Jiang,
Weiwei; K¨uhlmorgen, Sebastian; Matsumoto, Tad;
Paatelma, Anton; Qian, Shen; Tervo, Valtteri;
Wolf, Albrecht; Yi, Na

Citation

ICT‑619555 RESCUE D2.1.2 Version 1.0: 1‑54

Issue Date

2016‑07

Type

Research Paper

Text version

publisher

URL

http://hdl.handle.net/10119/13797

RightsThis material is posted here by permission of the
EU FP7 RESCUE Project. http://www.ict‑rescue.eu/
RESCUE is founded by the European Commission
under the 7th Framework Programme,Theme 3‑"ICT"call FP7‑ICT‑2013‑11,Work Programme Topic
1.1"Future Networks"

Description

Japan Advanced Institute of Science and Technology

ICT-619555 RESCUE
D2.1.2 Version 1.0
Final Report of The Coding/Decoding Algorithms andPerformance Comparison
Contractual Date of Delivery to the CEC:
Actual Date of Delivery to the CEC:
Editor:Authors:

Participants:
Work package:
Security:
Nature:Version:Total number of pages:

07/2016
08/2016
Valtteri Tervo
Jiguang He, Xin He, Jiancao Hou, Weiwei Jiang, SebastianKühlmorgen, Tad Matsumoto, Anton Paatelma, Shen Qian,
Valtteri Tervo, Albrecht Wolf, Na Yi
JAIST, TUD, UNIS, UOULU
WP2 – Code and algorithm design and optimization
PU
R
1.0
54

Abstract: This deliverable provides comprehensive analytical and simulation results of the coding/decoding
algorithms used in RESCUE. The algorithms are applied to various frameworks and investigated the applicability in selected cases. We also address the impact of lossy forwarding (LF) relaying in fading channels
and specifically consider the evaluation of frame error rates (FERs) in comparison with lossless decode-andforward (DF). Moreover, the deliverable proposes an algorithm for opportunistic relay selection in LF-based
networks where the best relay can be found using a machine learning method. Remarkable performance gains
are observed in a case where LF concept is applied in multi-antenna scenario, in which relays can transmit
and receive at the same time by using multiple antennas for interference cancelation. Furthermore, we apply
joint decoding (JD) into IEEE 802.11 WiFi standard. In addition, we present an error rate model for RESCUE
physical layer to be used when designing higher layer protocols. After analyzing the results presented in thisdeliverable, we conclude that RESCUE concept is especially suitable for the cases where the retransmissions
are not preferable or not even possible.

Keyword list: 802.11 WiFi, cooperative relaying, decode-and-forward, distributed turbo code, error rate
model, iterative decoding, lossy forwarding, multiple antennas, wireless networks

Disclaimer:

RESCUE

D2.1.2 Version 1.0

Executive Summary
The RESCUE project – “Links-on -the-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments” – proposes a novel multi-route communication technology for multi-hop networks that are
subject to dynamic topology changes. RESCUE is a cooperative communication paradigm consisting of decodeand-forward (DF) relaying that allows intra-link errors, combined with distributed turbo coding (DTC) that brings
improved error protection. The relaying nodes decode and re-encode the data, and even with possible decoding
errors, there exist correlation between the forwarded packet copies because they originate from the same source.
Therefore, destination can improve the reliability of the detection by taking the correlation into account when decoding. The relaying method considered in RESCUE is referred as lossy forwarding (LF) which, in its originalform, means that no integrity check is performed at the relay, but the frame is always forwarded. In this deliverable,
we provide comprehensive analytical and simulation results of the coding algorithms used in RESCUE. Furthermore, we apply the coding algorithms to various frameworks and investigate its applicability in selected cases. The
gains of the forward error correction (FEC) coding and joint decoding (JD) used in RESCUE are evident alreadyfrom D2.1.1. Therefore, in this deliverable we also address the impact of LF relaying by comparing frame error
rate (FER) results with the lossless counterpart that uses the same coding/decoding.
Firstly, we investigate a three-node system, referred as toy scenario 1 (TS1) defined in D1.2.1, by briefly introducing theoretical results considering the outage probabilities of different relaying strategies including a feedbackbased strategy. Furthermore, we deeply investigate the differences between theoretical and practical simulation
results, aiming at finding possible directions for improving the coding/decoding scheme. The second investigatedcase is a system with multiple relays without direct link, referred as toy scenario 2 (TS2), for which we show thesuperiority of LF compared with lossless forwarding in specific cases.
Opportunistic relaying is an attractive solution in order to reduce system complexity. In opportunistic relaying,
the best relay is selected among available relay candidates according to a certain policy. It has been shown that
there is no loss in performance in terms of the diversity-multiplexing tradeoff if only the best relay participates incooperation. In this deliverable, we present an opportunistic relay selection strategy for LF system. Furthermore,a statistical learning method is proposed for practical implementations.
A successive single-input multiple-output (SIMO) erroneous relaying with iterative maximum a posteriori (MAP)
receiver at destination is also proposed in order to allow relays’ transmission and reception at the same time. In
other words, one of the relays can transmit and the other receive resulting in the reduced multiplexing loss. The
proposed scheme allows relays erroneously forward the decoded symbols, and jointly cancels interference andcombines diversity at destination. It has been shown that, without extra cost of time delay and signalling overhead,
the proposed scheme can exhibit up to 8 dB gain by comparing with the conventional selective DF (S-DF) based
schemes.
An intuitive application of RESCUE contributions into current wireless standards is the use of JD in hybrid automatic repeat request (HARQ) to combine the retransmitted erroneous packets at the destination. In this deliverable,
we report the results of applying JD into IEEE 802.11 WiFi standard. We show that with a minor changes, we canachieve performance improvements in terms of FER.
In order to efficiently evaluate and test the higher layer protocols, the abstraction in the physical layer (PHY) is
needed. Therefore, we present an error rate model for RESCUE PHY, which is capable to accurately predict thelink-level performance at low computational complexity and can therefore be utilized for the design and performance evaluation of algorithms and protocols that exploit DTC as well as for system-level simulation.
At the end, we find that LF is beneficial at least in the following cases:
1. Communications in rapidly changing network topology where the retransmissions are not possible.
2. Communications with low power devices where the nodes need to share the load with each other.
For FEC coding/decoding used in RESCUE, we can conclude that it is very simple but remarkably strong performing close to the theoretical limits. Therefore, it has a great potential to be applied in current wireless standards.

Page 2 (54)RESCUE

D2.1.2 Version 1.0

Authors
PartnerName

E-mail / Phone

Japan Advanced Instituteof Science and Technology(JAIST)

Tad Matsumoto
Xin HeShen Qian
Weiwei Jiang

matumoto@jaist.ac.jp
hexin@jaist.ac.jp
shen.qian@jaist.ac.jp
wjiang@jaist.ac.jp

Technical University Dresden(TUD)

Sebastian Kühlmorgen
Albrecht Wolf

sebastian.kuehlmorgen@tu-dresden.dealbrecht.wolf@tu-dresden.de

University of Surrey(UNIS)

Jiancao Hou
Na Yi

j.hou@surrey.ac.uk
n.yi@surrey.ac.uk

University of Oulu
(UOULU)

Valtteri Tervo
Anton Paatelma
Jiguang He

valtteri.tervo@ee.oulu.fi / +358 40 4167991
anton.paatelma@ee.oulu.fi
jhe@ee.oulu.fi

Page 3 (54)RESCUE

D2.1.2 Version 1.0

Table of Contents
Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

List of Acronyms and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2. Study Cases on Lossy Forwarding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1
2.2

2.3
2.4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LF in TS1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 System and Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Outage Probability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2.1 Lossy Forwarding (LF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2.2 Conventional Decode-and-Forward with Joint Decoding (DF-JD) . . . . . . . . . . . . . . . . .
2.2.2.3 Adaptive DF with Joint Decoding (ADF-JD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Numerical Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LF in TS2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
11
11
12
13
14
15
16
17

3. Opportunistic Relay Selection for Lossy-Forwarding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1
3.2
3.3
3.4
3.5
3.6

System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Outage Probability Calculation and Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relay Selection Strategy for Opportunistic LF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistical Learning for Relay Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19
19
21
22
23
24

4. Successive SIMO Erroneous Relaying with Iterative MAP Receiver at Destination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1
4.2
4.3

4.4
4.5

Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Iterative MAP Receiver for Joint Interference Cancellation and Diversity Combining . . . . . . . . . . . . . . . .
4.3.1 The Modified MAP Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Iterative MAP Receiver at Destination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25
25
26
26
27
28
30

5. Application of RESCUE coding to 802.11 WiFi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1
5.2

5.3
5.4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Original IEEE 802.11a/g/p tranceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31
31
31
33
34
34

6. An Error Rate Model for RESCUE PHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Page 4 (54)RESCUE
6.1
6.2

6.3
6.4

6.5

D2.1.2 Version 1.0

System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Error Rate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Blackbox #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Blackbox #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2.1 Construction of simulation tables for Blackbox #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2.2 Generation of bit errors using Blackbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Integration of the Blackbox into Network Simulator ns-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Simulation Scenario and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38
39
39
41
41
41
42
45
45
45
48

7. Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
8. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Appendix A. Converting FER results into Erlang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Page 5 (54)RESCUE

D2.1.2 Version 1.0

List of Acronyms and Abbreviations
Term
16-QAMACC
ADF-JD
ADF
ANN
ARQ
AWGN
BEP
BER
BICM
BLER
BPSK
CBGF
CC
CCC
CEO
CRC
CSI
DF-JD
DF
DTC
FEC
FER
FNN
GI
HARQ
HD
HER
ID
JD
LF
LI
LLR
MAC
MAP
MCS
MI
MRC
MSP
ODF
OFDM
OLS
PCCC
PHY
PSR
QPSK
RD
RESCUE
S-DF
SD
SCCC

Description
16-ary quadrature amplitude modulation
Accumulator
Adaptive decode-and-forward with joint decoding
Adaptive decode-and-forward
Artificial neural network
Automatic repeat request
Additive white Gaussian noise
Bit error probability
Bit error rate
Bit interleaved coded modulation
Block error rate
Binary phase shift keying
Contention-based geographical forwarding
Convolutional code
Constellation constrained capacity
Chief executive officer
Cyclic redundancy check
Channel state information
Conventional decode-and-forward with joint decoding (no lossy forwarding)
Decode-and-forward
Distributed turbo coding
Forward error correction
Frame error rate
Feedforward neural network
Global iteration
Hybrid automatic repeat request
Half-duplex
Header error rate
Iterative decoding
Joint decoding
Lossy forwarding
Local iteration
Log-likelihood ratio
Media access control
Maximum a posteriori
Modulation and coding scheme
Mutual information
Maximal-ratio combining
Modified set partitioning
Opportunistic decode-and-forward (no lossy forwarding)
Orthogonal frequency domain multiplexing
Opportunistic lossy forwarding
Parallel concatenated convolutional codes
Physical layer
Packet success ratio
Quadrature phase shift keying
Relay-destination (sometimes can be written as R-D)
Links-on-the-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments
Selective decode-and-forward
Source-destination (sometimes can be written as S-D))
Serial concatenated convolutional codes

Page 6 (54)RESCUE

SIMO
SINR
SNR
SNRCC
SOTA
SR
SRCC
TSx
USRP
V2I
V2V

D2.1.2 Version 1.0

Single-input multiple-output
Signal-to-interference + noise ratio
Signal-to-noise ratio
Systematic non-recursive convolutional code
State-of-the-art
Source-relay (sometimes can be written as S-R))
Systematic recursive convolutional code
Toy scenario x, x = 1, 2
Universal Software Radio Peripheral
Vehicle-to-infrastructure
Vehicle-to-vehicle

Page 7 (54)RESCUE1.

D2.1.2 Version 1.0

Introduction

The RESCUE project – “Links-on-the-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments” – aims at designing a communication network that is robust of sudden topologicalchanges. Deliverable D1.1 [D11] defines two examples of such cases: public safety operations that take place inareas where the communication infrastructure is partially inoperable due to a disaster such as an earthquake, orvehicle-to-vehicle (V2V) communication, where cars and other vehicles share, for example, safety-critical information about the road and traffic conditions with each other.
RESCUE technology can be roughly characterized by two main factors: lossy forwarding (LF) and distributed
turbo coding (DTC) for which the joint decoding (JD) is applied at the destination. In other words, RESCUE is acooperative communication paradigm consisting of decode-and-forward (DF) relaying that allows intra-link errors,
combined with DTC that brings improved error protection. The relaying nodes decode and re-encode the data, andthe possible decoding errors at the relaying nodes result in correlation between the forwarded packet copies that thedestination takes into account when decoding. LF in its original form means that no integrity check is performedat the relay, but the frame is always forwarded. Selective decode and forward (S-DF) [D121] can be viewed as a
subcategory of LF, since S-DF uses a reliability criterion or threshold by which the forwarding decision is made.
The basic principles of the RESCUE relaying strategy have been presented in [AM12; ZHA+12; ZCA+12].
In this deliverable, we apply RESCUE technology (LF and JD) in various cases in order to find out the indicators
by which the RESCUE technology should be chosen for a certain application. It is intuitive that JD can improve
the performance in any case, where multiple correlated packet copies are available at the destination. Furthermore,
we find that LF is beneficial at least in the following cases:• Communications in rapidly changing network topology where the retransmissions are not possible.
• Communications with low power devices where the nodes need to share the load with each other.
Communication networks are often designed by defining strict link budgets, which determines how the base stations are located around the target area. The link budget is affected by the limited maximum power that can be used
for transmission, which in turn is regulated by local authority. Modulation and coding schemes (MCSs) shouldbe also defined in such a way that we can have the best tradeoff in throughput and power consumption. Whendesigning the MCSs for a fixed or slowly varying topology, it is not reasonable to aim at detection which is always
error-free, since a large portion of the erroneous frames can be recovered by the automatic repeat request (ARQ)
protocol. Hence, in such networks one should consider a tradeoff between transmit power, MCS and ARQ. The
ARQ protocols developed specifically for RESCUE technology are described in [D31; D32; D33]. However, when
the topology changes quickly, we cannot rely on ARQ. For example, when a car is passing by the relay nodes (fixed
or mobile), there may be only one chance to send the information. If the information was received with errors,
RESCUE technology can be used to recover it. Even if we would have a chance for retransmission from topology
perspective, it is not always desirable. Such examples are the cases where the energy levels of the transmit and/or
the receive nodes are low, and source nodes cannot afford of sending multiple times. In this case, it is not desirable
to use only one link, but rather share the load with other nodes in order to increase the life time of the network.
The rest of the deliverable is organized as follows: In Chapter 2, we investigate LF in two different scenarios. We
show that in a three-node system, referred as toy scenario 1 (TS1) defined in [D121], LF is superior to losslessforwarding when the retransmission from the source is not possible. The second investigated case is a system withmultiple relays without direct link (TS2). In fading channel, depending on the channel realization, this scenario
sometimes falls into the category of chief executive officer (CEO) problem, and sometimes there is multiple losslessframes to be provided from the relays. We show that LF can operate under difficult channel conditions where
lossless forwarding fails. Chapter 3 presents an opportunistic relay selection strategy for LF system. Furthermore,a statistical learning method is proposed for practical implementations. A successive single-input multiple-output(SIMO) erroneous relaying with iterative maximum a posteriori (MAP) receiver at destination is proposed in
Chapter 4. The proposed scheme allows relays erroneously forward the decoded symbols, and jointly cancels
interference and combines diversity at destination. It has been shown that, without extra cost of time delay andsignalling overhead, the proposed scheme can exhibit up to 8 dB gain by comparing with the conventional SDF based schemes. Chapter 5 describes the application of JD for retransmitted frame copies into IEEE 802.11
a/g/p standard. It is shown that the performance can be improved with the expense of increased complexity at

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the destination. The error rate model for RESCUE physical layer (PHY) is presented in Chapter 6. The model,
referred as Blackbox, predicts the link-level performance at a low computational complexity and it has been used
as a PHY abstraction in the work reported in [D32]. Finally, conclusions are drawn in Chapter 7 with the outlook
on the directions of the future research work.

Literature Review on RESCUE Coding Algorithms
Distributed turbo codes was proposed in [VZ03]. Joint source-channel coding for two unknown correlated sources
using channel codes and global iterations was presented in [GZ05]. They used turbo codes for both parallel
branches resulting in the so called super turbo code. They also proposed a way to estimate the correlation at thedestination in a case of two sources.
Performance of the successive coding strategy in the CEO problem was theoretically analyzed in [BS05]. An
iterative joint decoding algorithm for the binary data gathering wireless sensor networks was proposed in [HBP08],
where the convolutional code is applied as the coding scheme at the sensor node to protect the data transmitted
over noisy links between the sensors and the fusion center. In [RYA11], a coding scheme based on the parallel
concatenated convolutional codes (PCCC) was proposed. They used a joint decoding algorithm, which utilizes
the correlation knowledge among the observations of the sensors by weighting the extrinsic log-likelihood ratios(LLRs) by the error probabilities of erroneous observations. Moreover, the capacity of the parallel channel wasderived for verifying the bit error rate (BER) performance by taking into account the error probability of theobserved data sequence. Recent work on the application of turbo trellis coded modulation on cooperative relaying
is reported in [ABN+; ANH16].
In RESCUE, we apply the coding scheme from [PS06] to the relaying structure presented in [GZ05] and extend it
to multiple correlated sources by using the approach in [HBP08]. In [D211; D23], we have proposed the novel decoding algorithm and carefully chosen the coding parameters including code polynomials, doping parameter values
and mapping rules for binary phase shift keying (BPSK), quadrature PSK (QPSK) and 16-ary quadrature amplitude modulation (16-QAM), depending on the quality of the channels. All the functions have been implemented in
C++, integrated to GNURadio system, and tested in simulations. Hence, this is a completely new code design and
up to our best knowledge, there is no existing work with this extend. In top of the new coding scheme, multiple
improvements for state-of-the-art (SOTA) correlation estimation algorithms have been proposed in [D211].

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2.

Study Cases on Lossy Forwarding

2.1

Introduction

The basic principles of RESCUE coding/decoding was presented in [D211]. We start by introducing a single
frame encoder presented in Fig. 2.1 originally proposed in [PS06] for error floor removal in bit interleaved coded
modulation (BICM) with iterative detection. First, a binary information sequence u is interleaved by an interleaver
Π1 . Note that this interleaver is not necessary in point to point (P2P) communications. The purpose of Π1 is toassure independent sources of extrinsic information for JD at the destination.
The first component code C, also referred as an outer code, is a systematic non-recursive convolutional code
[Lee97]. Typically, in serial concatenated codes, the outer code is the stronger one (with lower code rate), however,
it is not a necessary condition to obtain a good code. It is more like a result from the fact that the inner code is
directly concatenated to the channel, which can be treated as a code itself.
After the convolutional code, the binary output sequence is interleaved and passed forward to the inner code. The
inner code consists of two components: 1) a doped accumulator (ACC) [PS06], i.e., memory-1 systematic recursive
convolutional code (SRCC), and 2) modulation mapper, which maps the bits to complex symbols according toa mapping rule M . Inner doping [Ten01], in its original form, is used to trigger the convergence of a serial
concatenated code by replacing some of the coded bits by uncoded bits. This is sometimes needed for nonsystematic codes, which cannot produce enough extrinsic information without having any a priori information
first. RESCUE uses the approach presented in [PS06], which is different compared to [Ten01]. The idea is toreplace some of the uncoded bits by coded bits to enhance the error correction capability of the channel resulting
in the disappearance of the error floor. The doping is characterized by a parameter P, which means that every Pth
bit is taken from the ACC (encoded bit) and the rest are uncoded bits. The impact of the concatenation of ACC
with mapper using various P values has also been investigated in [PS06]. In [PS06], they have also considered theimpact of different mapping rules, which can significantly affect to the convergence properties of the system.
In [D211], the coding structure described above, is applied to DTC-LF, for which the JD is needed at the destination. Novel decoding algorithm was proposed with several correlation estimation strategies. In [D23], the physicallayer implementation was described and the results of system level simulations were provided.
In this chapter, we further analyze the coding/decoding structure. Specifically, we address the situations where
LF can extend the operational range of the network. In other words, if there are errors at the relay, LF relay
forwards and lossless relay does not. Hence, the comparisons made in this chapter, do not consider the overall
resources consumed in the network. In Section 2.2, we briefly introduce some theoretical results for toy scenario
1 (TS1) considering different relaying strategies including a feedback-based strategy. Furthermore, we deeply
investigate the differences between theoretical and practical simulation results, aiming at finding possible directions
for improving the coding/decoding scheme. In Section 2.3, we investigate a case with three relays without direct
link (TS2) and show that LF can help of operating in very difficult channel conditions. The availability of feedback
channel is not analyzed in TS2.

2.2

LF in TS1

In this section, we compare the theoretical bounds of different relaying strategies with practical simulation results.
The system model of TS1 is presented in Section 2.2.1. Outage probabilities of different relaying schemes arederived in Section 2.2.2. Finally, numerical results are shown and discussed in Section 2.2.3.

Figure 2.1.: Structure of the RESCUE encoder.

Page 10 (54)）ncia mi-m
i
R ga
ka
Na

RESCUE（
2.2.1

System and Channel Model

S

R

（

Na Ricka i a n
ga
mi
-m
bR
）

BroadcastD2.1.2 Version 1.0

DRayleigh
We consider a simple, three nodes relaying transmission modelin a time-division channel allocation, as shown inbS sequence bS to a relay (R) and a destination (D) at the first time
Figure 2.2. A source (S) broadcasts the information
slot. In the second time slot, either S or R, or neither of them, transmits the message bS or bR to D, respectively.
Three relaying strategies are considered: 1) LF relaying: R decodes, re-encodes the information and forwards thereceived information sequence to D no matter whether the S-R link error is detected or not; 2) conventional DF
relaying: R keeps silent if error is detected after decoding; 3) Adaptive decode-and-forward (ADF) relaying: S
retransmits if errors are detected after decoding at R.

dSR

R
bR

Broadcast

S
bS

dSD

dRD

D

Figure 2.2.: One-way relaying transmission system.

The received signals y1 via the S-D link and y2 via the R-D link both at D, and the received signal y3 via the S-R
link at R are expressed aspy1 = GSD hSD x1 + nSD ,
(2.1)
p
(2.2)
y2 = GRD hRD x2 + nRD ,py3 = GSR hSR x1 + nSR ,(2.3)
respectively, where Gi j (i j = SD, RD, SR) are the gains related to the distance of each link. hi j and ni j denote thecomplex channel gains and zero-mean additive white Gaussian noise (AWGN) with variance of N0 /2 per dimension, respectively. It is assumed that hi j is constant over one block duration due to the block fading assumption.
x1 and x2 denote the modulated symbols corresponding to the coded and interleaved information sequences, transmitted from S and R, respectively. The S-D, S-R, and R-D links are mutually independent with each other.
Let dSD , dRD and dSR denote the distances between S and D, R and D, and S and R, respectively. The geometricgains of the S-R and R-D links, GSR and GRD , respectively, can be defined as




dSD α
dSD α
GSR =
, GRD =
,
(2.4)
dSR
dRD
where α is the path loss exponent. The gain GSD of the S-D link is normalized to unity.
2.2.2

Outage Probability Analysis

In this section, the expressions of outage probability for various relaying protocols are derived. The outage isdefined as that the information rate exceeds the capacity at corresponding signal-to-noise ratio (SNR). Let TR and
Ci j denote the threshold information rate and channel capacity of the i j link with Gaussian codebook assumption,
respectively.

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Lossy Forwarding (LF)

The information sequence, obtained as the result of decoding at R, is interleaved, re-encoded and transmitted to D,even if decoding errors are detected. The correlation knowledge between the information sequences transmitted
from S and R is utilized in the iterative joint decoding process at D. The outage probability is defined as theprobability that the source coding rate pair of S and R (RS , RR ) falls into the inadmissible area A in Figure 2.3, or
B or C in Figure 2.4. p f represents the bit flipping probability between the information sequence obtained after
decoding at R and the original sequence sent from S [ZCH+14], [QZH+ed].

RR

RR

H(bR)

H(bR)

Admissible Region



H(pf)
H(bS)

RS

H

Figure 2.3.: Rate region for S and R when p f = 0.

RR

H(bR)

e Region

Admissible Region



H(pf)
RS




H(pf)

H(bS)

RS

Figure 2.4.: Rate region for S and R when p f 6= 0.
Let PA , PB , and PC denote the probabilities that (RS , RR ) falls into the inadmissible areas A, B, and C, respectively.
According to the source coding with side information theorem [CT06, Section15.8], [GK11, Section10.4], thePage 12 (54)RESCUE

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outage probability of the LF relaying can be written as
LF
Pout=PA + PB + PC

=Pr[p f = 0, 0 ≤ RS < 1, 0 ≤ RR < H(p0f )],+Pr[0 < p f ≤ 0.5, 0 ≤ RS < H(p f ), RR ≥ 0],+Pr[0 < p f ≤ 0.5, H(p f ) ≤ RS < 1, 0 ≤ RR < H(p f ∗ p0f )].

(2.5)

where p0f represent the crossover probability of the R-D link.
For calculating the outage probability, the relationships between γSD and RS , and that between the instantaneous
channel SNR of the R-D link γRD and RR are established as(2.6)
γi j ≥ Θ(Rk ) = 22Rk − 1 , (k = S, R),
according to Shannon’s lossless source channel separation theorem.
The relationship between p f and γSR can be established as
p f = Λ(γSR ) = H2−1 (1 − log2 (1 + γSR )) ,(2.7)

with the Hamming distortion measure. H2−1 (·) denoting the inverse function of the binary entropy.
Then the outage probability of the LF relaying can be expressed as Z Θ(1)




1
1
γSD
Θ(1 − Θ(γSD ))
PA =
exp −
exp −
1 − exp −dγSD ,
γ SD
γ SR
γ SD
γ RD
γSD =Θ(0)PB =1

Z Θ(1)γSR =Θ(0) γ SR


exp

γSR
γ SR




Θ(1 − Λ(γSR ))1 − exp −dγSR ,
γ SD

(2.8)

(2.9)

and


−γSD
PC =
exp
γ SD
γSD =Θ(1−Λ(γSR )) γSR =Θ(0) γ SDZ Θ(1)

Z Θ(1)

1



1



γSR
exp
γ SR
γ SR




Θ[ξ (γSD , γSR )]1 − expdγSD dγSR ,γ RD(2.10)

where ξ (γSD , γSR ) = H{H −1 [1 − Θ(γSD )] ∗ H −1 [1 − Λ(γSR )]}.

2.2.2.2

Conventional Decode-and-Forward with Joint Decoding (DF-JD)

In the conventional DF relaying, S broadcasts the coded information sequence to D and R at the first time slot.
If the transmitted information is successfully recovered at R, the information sequence is forwarded to D at thesecond time slot. R keeps silent if error is detected after decoding at R. A joint decoding process is performed to
combine the signals received from S and R. The outage probability of the conventional DF relaying is defined as
DF−JD
Pout
= Pr {TR > CSD (γSD )|TR > CSR (γSR )} Pr {TR > CSR (γSR )} + PA .

The outage probability can be calculated as
 
 T


 T
2 R −12 R −1DF−JD= 1 − exp
1 − exp −
Pout
γ SR
ΓSD

 Z Θ(1)




1
1
γSD
Θ(1 − Θ(γSD ))
+
exp
exp −
1 − expdγSD .
γ SD
γ SR
γ SD
γ RD
γSD =Θ(0)(2.11)(2.12)

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Adaptive DF with Joint Decoding (ADF-JD)

In ADF-JD transmission, S broadcasts the coded information sequence to D and R at the first time slot. If thetransmitted information is successfully recovered at R, the information sequence is forwarded to D at the second
time slot. The difference compared to conventional DF is that if the S-R transmission fails, S retransmits to D.
D performs joint decoding to retrieve the original message of S. The information sequence is interleaved before
forwarding to D from R when S-R transmission is successful, and also interleaved before retransmission from S
when S-R retransmission fails. The rate region of ADF-JD is shown in Figure 2.5 and Figure 2.6. Similar as thecase of LF, the outage probability is defined as the probability that the source coding rate pairs of S and R (RS , RR )and (RS , R0S ) fall into the inadmissible area D or E shown in Figure 2.5 and Figure 2.6, respectively. R0S is the rateof retransmitted information sequence from S.

RR

R’S

H(bR)

H(bS)

Admissible Region




H(bS)

RS

Figure 2.5.: Rate region for S and R when p f = 0.

R’S

H(bS)

e Region

Admissible Region


RS

H(bS)

RS

Figure 2.6.: Rate region for S and S0 when p f 6= 0.

Page 14 (54)RESCUE

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Let PD and PE denote the probabilities that (RS , RR ) and (RS , R0S ) falls into the inadmissible areas D and E,
respectively. The outage probability of ADF-JD can be defined as
ADF−JD=PD + PEPout
=Pr[p f = 0, 0 ≤ RS < 1, 0 ≤ RR < H(p f )],+Pr[0 < p f ≤ 0.5, 0 ≤ RS < 1, 0 ≤ R0S < H(p f )].

(2.13)

Then, the outage probability can be calculated as Z Θ(1)




1
1
γSD
Θ(1 − Θ(γSD ))ADF−JDPout=
1 − exp
exp −1 − exp
dγSD
γ SD
γ SR
γ SD
γ RD
γSD =Θ(0)








Z Θ(1)
Θ(1 − Θ(γSD ))1γSD1
1 − exp −1 − exp
exp −dγSD ,
+
γ SD
γ SR
γ SD
γSD =Θ(0) γ SD

(2.14)

with the feedback channel is assumed to be lossless and the latency of the feedback transmission is ignored.
2.2.3

Numerical Results and Discussion

In this section, we present the numerical results of the outage probability calculation and the frame-error-rate(FER) performance of the relaying strategies. Since our theoretical analysis assumes capacity achieving code,
outage probability serves as a theoretical bound for FER obtained through simulations. It is worth noting that thegoal of the RESCUE project is not link design but coverage extension by cooperative diversity. Therefore, we
use x-axis as the S-D link SNR per transmission and the power consumed by the relay is not taken into account.
However, the S-D link SNR defines the SNRs of all the other links due to geometric path loss assumption (2.4).
The threshold rate are set to TR = 0.5 and, the path loss exponent is set to α = 3.52 as in [YG11]. In the FER
simulations, we use a serial concatenation of a non-recursive convolutional code with a generator polynomial [3, 2]8
and a doped-accumulator [D211]. The channel code rates are 1/2 for both S and R and binary phase shift keying(BPSK) is used for modulation.
0

10

P

, DF−JD

P

, LF

out
out

Pout, ADF

−1

FER/Outage Probability

10

FER, DF−JD
FER, LF

−2

10

−3

10

−4

10
−10

−5

0
5
Average SNR of S−D link (dB)10

Figure 2.7.: Comparison of the outage probability of the LF, ADF, and the conventional DF system.
Figure 2.7 plots the theoretical outage probability versus average SNR of the S-D link, where all links are sufferingfrom statistically independent block Rayleigh fading. The relay is at the midpoint between the source and the destination. It is found that the 2nd order diversity can be achieved at high SNR region by all the relaying strategies. As
can be seen from the figure, LF relaying system can achieve better performance than the conventional DF system.

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LF is about 1 dB better than conventional DF and 1 dB worse than ADF, respectively, at the outage probability of
0.001. The analytical results are very useful for evaluating the performance of practical code design for different
protocols. The reason for ADF outperforming LF is that ADF has feedback information from R to tell S to retransmit when S-R transmission is failed. The admissible rate region of ADF in Figure 2.6 is increased compared tothat of LF in Figure 2.4, which decreases the outage probability. It is found that the FER and their corresponding
outage curves are consistent with each other, however, there are 1−2 dB gaps in average SNR between the theoretical and simulation results. This is because the channel codes used are not capacity-achieving. The observationfrom simulation results indicates that the outage probability of LF relaying provides a better evaluation for theactual FER performance than that of conventional DF. It is worth of noticing that this comparison does not take
into account the saved resources (time slots or power) in conventional DF if the relay cannot decode.
The impact of the relay location on the outage probability is depicted in Figure 2.8, where the average SNR of
S-D link is kept at 5 dB. In this case, it is assumed that R is located on the line between S (x = 0) and D (x = 1).
With the conventional DF (DF-JD) relaying system, the lowest outage probability is achieved at a certain point(x ≈ 0.4) between S and the midpoint. An interesting observation is that as the relay is located at the midpoint(x = 0.5), the lowest outage probability can be achieved by LF relaying. In general, the lowest outage probability
can be achieved at a point where the contributions of both S-R and R-D links to outage are balanced. Since inconventional DF, the relay stops forwarding the information sequence when errors are found, the quality of the
S-R link has to be good enough, which results in the optimal position shifted closer to the side of the source. In
LF system, the contributions of the two links to the outage probability are balanced because there is a chance thatthe errors occurring in the S-R link can be corrected at the destination, and as a consequence, the optimal locationis the midpoint. With LF relaying the outage curve is symmetric with respect to the midpoint. The FER results
have been obtained for two different relaying strategies presented in [D211]: 1) relay only extracts the systematic
bits, then interleaves, encodes and transmits to destination; 2) relay performs full decoding, interleaves, encodes
and transmits to destination. The FER curves exhibit almost the same tendency as the outage curve, except thatthe lowest FER performance is achieved at around 0.4. This is because the channel code used at S is not capacityachieving and that causes a gap between the theoretical p f value and the simulation result. It is also shown that theoutage performance of LF relaying is superior to that of DF-JD relaying and inferior to that of ADF relaying.
−1

FER/Outage Probability

10

−2

10

−3

10

FER, Extraction
FER, Full Decoding
Pout, conventional DF
Pout, LF
Pout, ADF

−4

10

0.1

0.2

0.3

0.4
0.5
0.6
x−coordinate of relay

0.7

0.8

0.9

Figure 2.8.: Outage probability vs. the relay location, ΓSD = 5 (dB)

2.3

LF in TS2

In this section, we show selected FER results for TS2, i.e., the case with source, three relays and destination.
There is no direct link between the source and the destination and all the existing links are suffering from RayleighPage 16 (54)RESCUE

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0

FER

10

−1

10

−2

10

−8

DF, average SR link SNR: 3 dB
average SR link SNR: 3dB
DF, average SR link SNR: 4 dB
average SR link SNR: 4dB
−6

−4

−2

0

2

4

6

8

10

Average RD link SNR (dB)Figure 2.9.: FER vs. average SNR of RD links in a case with three relays. All the links are Rayleigh fading.
fading. We use a serial concatenation of a non-recursive convolutional code with a generator polynomial [3, 2]8
and a doped-accumulator with the doping rate 1. [D211]. The channel code rates are 1/2 for both S and R andBPSK is used as a modulation. The block length is 1024 bits, and the maximum number of the local decoding
iterations performed at the relay and destination is 3 and 25, respectively.
Firstly, we consider a case where the average SNRs of the links from source to relays (SR) are fixed. Moreover,
we assume that the average SNRs of the SR links are the same. Then we obtain the FER values as a function of
average SNR of relay-destination (RD) links. Here we also assume that the average SNRs of the RD links are
the same. The results are shown in Fig. 2.9. We can observe that LF reduces FER through the whole SNR range
considered. Here again reader should note that the comparison does not take into account the saved resources inconventional DF if the relay cannot decode.
In the other considered case we replace the SR links by bit flipping channel. Specifically, we have selected cases,
for which there is high probability that all the relayed sequences are erroneous1 . In a case of three relays, losslessforwarding can hardly operate due to the high probability of errors at the relays. The results are shown in Fig. 2.10.
We can observe that FER less than 1 can be achieved even in the case where all the relayed sequences are erroneouswith high probability. The case where all the relays can decode without errors is also plotted for comparison.

2.4

Conclusions

The performance of LF in terms of outage probability and FER has been investigated in this chapter. In caseof TS1, we showed that our practical coding/decoding algorithm can reach very close to the theoretical limits.
Furthermore, we showed that 1-2 dB gain can be achieved with LF compared to lossless DF in terms of FER andoutage probability in Rayleigh fading environment. However, if the feedback link is available, ADF can yield thebest performance among the algorithms tested. It is worth of noticing that in terms of the overall transmit power
consumed in the network, the comparison between ADF and LF is fair unlike the comparison between DF-JD with
LF or ADF. Therefore, if the nodes would be able to optimally adapt according to the links, LF does not introduce
any gains in terms of the total transmit power in this simple network model. We could also observe from Fig. 2.7that because the two time slots used in ADF were assumed to be always uncorrelated, all the considered strategies,
ADF, LF and DF-JD can achieve the second order diversity. We also presented FER results for TS2 with various
setups. We showed the superiority of LF compared to lossless DF in cases where the SNRs of the SR links arelow.
1 The smallest considered bit flipping value is 0.005 which means that 99.4% of the frames are erroneous with the block length of 1024.

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0

FER

10

−1

10

−2

10

−8

p = [0.01, 0.01, 0.01]
p = [0.01, 0.005, 0.008]
p = [0, 0, 0], lossless
−6

−4

−2

0

2

4

6

8

10

Average RD link SNR (dB)Figure 2.10.: FER vs. average SNR of RD links in a case with three relays. SR links assume bit flipping.

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Opportunistic Relay Selection for Lossy-Forwarding

In this chapter, an opportunistic relay selection strategy for LF system is proposed. Furthermore, a statisticallearning method is proposed for practical implementations.

3.1

System Model

The opportunistic LF system (OLF) model is depicted in Fig. 3.1, which contains one source S, one destination D
and multiple relays Ri where i ∈ {1, ..., m}. All links suffer from independent block Rayleigh fading, denoted by
hSD , hSRi and hRDi respectively. Hence, for each link, the channel can be expressed as y = h · s + n, where s is thesignal to be transmitted by the corresponding node, and n is the normalized noise with variance σ 2 = N0 /2.

Figure 3.1.: Opportunistic LF system
The overall transmission involves 2 + ε phases. In the first phase, the source node S broadcasts its signal to allother nodes, following a short ε phase for relay selection. In the second phase, only one relay Ri is selected andactivated to help the transmission. The selected relay Ri is performed regardless of successful decoding, since theintra-link errors are allowed in our system. The destination node D jointly decodes the signals from the source
node S and the selected relay Ri . The selection is made by the destination node D with the ε feedback phase. We
assume that full channel state information (CSI) of each link is available at node D.
Furthermore, the source node S, the destination node D and the selected relay Ri composes a LF system [AM12] asshown in Fig. 3.2. The information of S, us , is encoded by using a serial concatenated convolutional code (SCCC).
The received signal in relay is decoded, interleaved by an interleaver π, re-encoded by another SCCC encoder andtransmitted to D. In the destination side, the signals from the source and the relay are jointly decoded. Function
fc is performed to prevent the error propagation due to the intra-link errors. We will use the same structure for ourpractical system simulations in section 3.4.

3.2

Outage Probability Calculation and Approximation

The objective of opportunistic relay selection is to minimize the outage probability for our system. To find the
optimal selection strategy for our system, we first define the best relay R∗ for each transmission as below
Definition 1. If R∗ is selected and a transmission outage happens, then the transmission outage must happen∀R j ∈ {R1 , ..., Rm }\R∗ .
Note that successful transmission is not guaranteed by the best relay. By Definition 1, the best relay R∗ may notnecessarily be single. Multiple relays can be candidates especially in higher signal-to-noise ratio (SNR) region,
one relay from the candidates will be selected randomly in such scenarios.

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Figure 3.2.: System model of LF
According to Definition 1, the outage probability is defined as
Pr(E|ER∗ ) = Pr[(E|ER1 ) ∩ ... ∩ (E|ERm )],(3.1)

where E is the overall outage event for a transmission, ER∗ is the event that the best relay is selected, and ERi is theevent that relay Ri is selected. To calculate the exact outage probability, we can adopt the same technique proposed
in [ZCH+14]. Since the events ERi are correlated to each other, we have to calculate the probability jointly. In[ZCH+14], the authors have calculated the outage probability by triple integrals corresponding to each link. In
consequence, 2m + 1 multiple integrals are required to calculate the outage probability for OLF with m relays. The
computation is intractable even when m is not large.
Therefore, we propose an approximated bound on outage probability based on Bayes’s rule. Since the correlations
among all the events ERi are due to the direct link, which infers that the correlations can be estimated by the outage
probability for SD link that can be expressed as below by the Rayleigh fading assumption
Pr(ESD ) = 1 − exp(−

γth1
),
ΓSD

(3.2)

where ESD is the outage event of SD link, γth1 is the threshold SNR and Γ is the average SNR of SD link. According
to Bayes’s rule, we can estimate equation (3.1) by
Pr(E|ER∗ ) ≈ Pr[ ∩ (E|ERi )|ESD ] × Pr(ESD )Ri ∈S= ∏ Pr[(E|ERi )|ESD ] × Pr(ESD )Ri ∈S∏ Pr[(E|ERi ), ESD ]R ∈S= i
Prm−1 (ESD )∏ Pr(E|ERi )R ∈S= i m−1.
Pr(ESD )(3.3)

The last step is due to ESD ⊆ E|ERi , and Pr(E|ERi ) is the LF outage probability with Ri and provided in [ZCH+14].
Numerical results are shown in Fig. 3.3 for two location configurations1 . The gaps between the approximatedtheoretical bounds and Monte Carlo simulations, according to Definition 1, as the exact bounds, are around 0.5 dB
for 2-relay system and 0.85 dB for 3-relay system. With theoretical bound, we have the proposition below.
Proposition 1. The opportunistic LF system can achieve m + 1 order diversity with m relays.
Proof. According to [QCM15], in high SNR region, Pr(E|ERi ) can be approximated by
Pr(E|ERi ) ≈

C2
C3
C4
C1
+
+
+
Γ2SD Γ2SR(i) ΓSR(i) ΓSD ΓSD ΓRD(i)(3.4)

1 In Location A, average SNRs are the same for all links; in Location B, relays are in the 1/4 point of the line from S to D, the average SNRsof ΓSRi and ΓRDi are ΓSRi = ΓSD + 10 log10 (43.52 ) dB and ΓRDi = ΓSD + 10 log10 [(4/3)3.52 ] dB. The spectrum efficiency for each node is 1.

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m = 1, approximationm = 1, MC
m = 2, approximationm = 2, MC
m = 3, approximationm = 3, MC

Location A−1

10Outage Probability

−2

10

−3

10

Location B

−4

10

−5

10

−6

10

−5

0

5

10

15

20

Eb/No per link (dB)Figure 3.3.: Comparison between approximated theoretical outage probability bound and Monte Carlo simulations
where ΓSD , ΓSD(i) and ΓRD(i) are the average SNRs for SD, SR and RD links with relay Ri respectively, and C1 , . . . ,C4
are constants that are determined by spectrum efficiencies. The outage probability of SD link can also be approximated as
γth1
γth1
Pr(ESD ) = 1 − exp(−
)≈
,
(3.5)
ΓSD
ΓSD
by using the property that e−x ≈ 1 − x when x is small, implying high SNR region. Consequently, by assumingΓ = ΓSD = ΓSRi = ΓRDi , when SNR goes to infinity, equation (3.3) can be expressed asγth1 m−1
C1 +C2 +C3 +C4 m
) ÷(
)
2
Γ
Γ
(C1 +C2 +C3 +C4 )m.
=
m−1 m+1γth1
ΓPr(E|ER∗ ) ≈((3.6)

Obviously m + 1 order diversity can be achieved by equation (3.6).

3.3

Relay Selection Strategy for Opportunistic LF

For the conventional opportunistic decode-and-forward (ODF) system where intra-link error is not allowed, R∗ isgiven byR∗ = arg max{γRi },

(3.7)

Ri

where γRi is the instantaneous SNR of Ri [HB07]. This is directly obtained by the fact that the maximal-ratio
combining (MRC) performed by DF will take more advantage from higher SNR transmission of the relay. However, with intra-link errors, the story will be quite different. According to the theoretical analyses in [ZCH+14],
the transmission over a LF system can be considered as source coding with side-information that is transmitted
by the relay as showed in Fig. 3.2. Hence, to minimize the error after decoding, we want correlation between theside-information and the source information to be as high as possible. In the LF system, the correlation is reducedby the intra-link errors and the RD link errors, which means both SR and RD links have to be taken account equally.
Therefore, the best relay R∗ for our system is given byR∗ = arg min{pi ∗ αi },

(3.8)

Ri

where pi and αi are the intra-link bit-error rates (BER) of SR and RD links respectively when Ri is selected, andpi ∗ αi = (1 − pi )αi + pi (1 − αi ). Point-to-point link BER p can be calculated from Shannon’s lossy source-channel

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0

10

−1

10

Outage Probability

−2

10

−3

10

−4

10

−5

10

m = 1, LF
m = 2, ODF
m = 2, OLF proposed strategy
m = 2, LF ARQ
m = 2, ODF
m = 3, OLF proposed strategy
m = 3, LF ARQ
m = 3, ODF
m = 4, OLF proposed strategy
m = 4, LF ARQ
m = 4, ODF

−6

10

−5

0

5

10

15

20

Eb/No per link (dB)Figure 3.4.: Comparison of the theoretical outage probability of proposed opportunistic relay selection strategy, ARQ method and ODF systemseparation theorem [ZCH+14]H −1 [1 − log(1 + γ) ] γ < γ
th
b
p=
Rc

0
γ ≥ γth ,(3.9)

where Hb−1 (·) : [0, 1] → [0, 0.5] is the inverse binary entropy function, γ is the instantaneous SNR, and γth is thethreshold SNR for coding rate Rc .
To verify our selection strategy, we conduct Monte Carlo simulations with 1, . . . , 4 relays. For comparison, we
propose an automatic repeat request (ARQ) scheme as the optimized case according to Definition 1. In the ARQ
scheme, a relay is only activated when it receives an ARQ message. Whenever the destination node D cannot
successfully decode, it sends an ARQ message to a randomly selected inactivated relay Ri to help the transmission.
The process stops when the destination node D can successfully decode or all relays are activated. An outage
happens when the destination cannot correctly decode the information from the source node S after all relays areactivated. For fair comparison, decoding process in the destination restarts with the signal from the latest activatedrelay.
The numerical results in Fig. 3.4 indicate that the outage performance of proposed selection strategy is almost thesame as the ARQ scheme for different relay numbers. The OLF outperforms conventional ODF system in theentire SNR region. In lower SNR region, the ODF outage probability is even higher than OLF with less number ofrelays. Though we assume symmetric channel here that the average SNR for each link is the same, the proposed
selection strategy can also be used in asymmetric scenarios as the selection is based on instantaneous SNR.

3.4

Statistical Learning for Relay Selection

Our system can be implemented in various configurations especially for higher spectrum efficiency scenarios. For
some specific system implements, the BER may be difficult to be estimated from the CSI, which is required forour theoretical selection strategy. In addition, the performance may also be impacted by some factors, such as
block length, and undisclosed reasons. However, there may exist a hidden pattern to make the selection decisionin specified system implementations. It is possible to build a practical selector without revealing such hidden
patterns. In fact, the issue can be modeled as a typical classification problem that has been solved by statisticallearning methods. For our system, the class is defined as the label of each relay (i for Ri ), and the model aims tofind the most possible label (best relay) given the inputs of instantaneous SNR.
We adopt a supervised machine learning method to select the best relay. In this paper, we utilize a simple fully

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−3.42

10

−1

10

Outage Probability / FER

−3.56

10

9.8

10

10.2

−2

10

−3

10

−4

10

m = 1 LF
m = 1 DFm = 2 LF ARQ
m = 2 OLF ANN selectorm = 2 OLF theoretical selectorm = 2 ODF
m = 3 LF ARQ
m = 3 OLF ANN selectorm = 3 OLF theoretical selectorm = 3 ODF

−5

10

−5

0

5

10

15

Eb/No per link (dB)Figure 3.5.: FER performance of the ANN selector and the theoretical selector (BPSK)connected 3-layer artificial neural network (ANN) for our system. To train an ANN selector for 2 relays, thenumbers of nodes for input layer, hidden layer, and output layer are 5, 10, and 2 respectively. The type of ANN
is feedforward neural network (FNN) [ABM08]. The objective function to find the optimized ANN selector Ω∗
defined asΩ∗ = arg max{1SR∗ [Ω(H)]},(3.10)Ω∈Σ

where Σ is set of all possible ANN selectors. SR∗ and H are the set of best relays according to Definition 1 and theset of CSI for all transmission samples. The CSI we use only contains instantaneous SNR for each link.
To obtain the training data, we adopt traversal simulations for our system with 2 relays. The destination node D
tries decoding jointly with each relay activated respectively. Transmission data are logged into a raw training data
set Sraw as
Sraw = {τ | τ = {SC , h}},(3.11)

where SC is the set of candidate relays with which the transmission outage does not happen, and h is the set of CSI
of each transmission. Finally the valid training data set S is acquired by
S = {τ | τ ∈ Sraw , |τ[SC ]| = 1},(3.12)

since the cases that the number of best relays is 2 or the transmission outage happens are not interesting for a relay
selector.
With the trained ANN selector for 2 relays, selection for multiple relay scenarios can be performed recursivelyasR∗ = Ω(Ω(Ω(R2 , R1 )..., Rm−1 ), Rm ).

3.5(3.13)

Numerical Results

In this section we demonstrate the simulation results for our proposed ANN selector compared with the optimal
ARQ scheme, as well as with the selection strategy for conventional DF system. The common configurations are• Information length: n = 2000

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−1

Outage Probability / FER

10

−2

10

−3

10

−4

10

−5

BPSK m = 2 ARQ
BPSK m = 2 ANN selector
BPSK m = 2 Theoretical selector
QPSK m = 2 ARQ
QPSK m = 2 ANN selector
QPSK m = 2 Theoretical selector
0

5

10

15

20

Es/No per link (dB)Figure 3.6.: Comparison between FER performance of proposed ODF selectors between BPSK and QPSK• Interleavers: random• Number of relays: 1, 2, and 3• SCCC: a [03, 02]8 half-rate non-recursive systematic convolutional code for outer coding, an accumulator
with doping ratio 1 for inner coding.
• Modulation: binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) with gray mapping.
• Decoder: for proposed system, the numbers of iterations are 10 for SCCC and 30 for global iterations
respectively. Intra-link error Pe is known. For conventional DF system, MRC is performed and the numberof iterations is 10.
To train the ANN selector, 5658 items and 3622 items are fed for BPSK and QPSK respectively. The number oftraining iterations is 2000. The ratio of training data to test data is 7:3, and regularizing value λ for cost function is0.5. Both training accuracy and test accuracy for BPSK are near 100%, while for QPSK are both beyond 90%.
Figs. 3.5 and 3.6 demonstrate the frame-error rate (FER) performance of the proposed ANN selector with BPSK
and QPSK modulation and different numbers of relays. The result shows that the performance loss is very little compared to the optimal ARQ scheme. For m-relay scenarios, m + 1 order diversity can be achieved. The
theoretical selector based on equation (3.8) may work well in lower SNR region though, it may cause significant
performance loss as the average SNR increases, and finally make the outage probability converge to the first order
diversity for both 2-relay and 3-relay scenarios.

3.6

Conclusions

An opportunistic LF system was presented in this chapter. A machine learning method has been adopted forpractical relay selection. Theoretical results and simulation results have shown that full diversity order can beachieved by the proposed system. Numerical results have indicated that our system outperforms conventional
opportunistic decode-and-forward system in both theory and practice.

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4.

Successive SIMO Erroneous Relaying with Iterative MAP Receiverat Destination

4.1

Motivation and Objective

Successive single-input multiple-output (SIMO) relaying as one of promising cooperative communication schemes
can be employed for the purpose of compensating multiplexing loss of conventional half-duplex (HD) constrained
relaying [OS04; FWT+07]. Such scheme allows two HD relays alternately serve as transmitter and receiver tocontinuously transmit data frames for every channel use, and multiple receive antennas is used for interference
cancellation. The optimal performance can be achieved if relays can perfectly decode source’s messages. On
the other hand, the performance is degraded if there exists decoding errors at relays. The authors in [WFT+09;
HLT12] presented simple adaptive retransmission protocols to guarantee perfect decoding for relays at the costof time delay and signalling overhead. Alternatively, the authors in [SZN11; BAP+14] used space-time codes toassist relays to mitigate inter-relay interference at cost of spectral efficiency especially for higher modulations.
In order to improve spectral efficiency and avoid error propagation effects, the successive relaying scheme canperform either conventional selective decode-and-forward (S-DF) relaying [WTG+11] or symbol-level selective
transmission at relays [YMH+15]. At the first strategy, if any one of relays fails to correctly decode received
frame, it will not transmit in the next time slot. Such procedure may largely lose diversity if relays always remainsilent. At the second strategy, instead of discarding the whole frame after detecting decoding errors, relays predict
correctly decoded symbols per frame based on a least-square principle and then forward them to destination to
enjoy diversity. In this case, the complexity at relays is increased and prediction errors still exist.
Motivated by above observations, a successive SIMO erroneous relaying with iterative maximum a posteriori(MAP) receiver at destination is proposed, which aims to avoid high-complexity relays and improve both spectral
efficiency and reliability. Specifically, with multiple receive antennas, relays firstly cancel inter-relay interferencewith QR decomposition, and then forward decoded frames regardless decoding errors. Following, destination
performs the proposed iterative MAP receiver by taking the probability of decoding error at relays into account tojointly cancel interference and combine diversity. Here, the probability of decoding error at relays can be estimatedand forwarded from relays as in [HYM15], or be directly estimated at the destination as in [GZ05]. Throughsimulations, it is shown that, without extra cost of time delay and signalling overhead, the proposed scheme exhibits
up to 8 dB bit-error-rate performance gain by comparing with the conventional S-DF based relaying schemes.

4.2

System Model

Fig.4.1 illustrates the successive SIMO erroneous relaying with one source (S), two relays (R1/R2) and one destination (D). All transmissions are using single antenna, and all receptions are using two antennas. Assume discreteR1

S

R1

D

S

D

Erroneous link

R2
Time slot lR2Interference link

Time slot l+1

Figure 4.1.: Illustration of successive SIMO erroneous relaying.
time block fading channels, which remain static over each time slot. There are L frames being transmitted via
L + 1 time slots, where L is an even number. Source continuously transmits L frames in L time slots, and relays
alternatively decode-and-forward received frames until the (L + 1)th time slot. Here, in the 1st time slot, only relay
one and destination receive the 1st frame from source, and in the (L + 1)th time slot, only destination receives theLth frame from relay two.

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Let YR j (l) ∈ C 2×M and YD (l) ∈ C 2×M be the received signal matrices at the jth , j ∈ {1, 2}, relay, and at destinationin the l th time slot, respectively, where M is the number of symbols per frame. Thus, we have
YR j (l) = HR j (l)X(l) + VR j (l),(4.1)

YD (l) = HD (l)X(l) + VD (l),(4.2)

where X(l) , [xR j (l − 1), xS (l)]T is the transmitted signal matrix in the l th time slot composed by the (l − 1)thth
frame from the j , j 6= j ∈ {1, 2}, relay, i.e., xR j (l − 1) ∈ C M , and the l th frame from source, i.e., xS (l) ∈ C M ;th(·)T is transpose of a matrix; HR j (l) ∈ C 2×2 is the channel matrix from the j relay and source to the jth relay inththe l th time slot; HD (l) ∈ C 2×2 is the channel matrix from the j relay and source to destination in the l th timeslot; VR j (l) ∈ C 2×M and VD (l) ∈ C 2×M are the additive white Gaussian noise (AWGN) matrices at the jth relay
and destination in the l th time slot, respectively.
From (4.1) we can see, there exists inter-relay interference which should be cancelled before decoding the received
frame from source. Such interference can be cancelled by QR decomposition without boosting noise power.
Specifically, let QR j (l) ∈ C 2×2 be the unitary matrix and RR j (l) ∈ C 2×2 be the upper triangular matrix generated
from QR decomposition of the channel matrix HR j (l). Then, the received signal at the jth relay after inter-relay
interference cancellation is given byŶR j (l) = QH
R j (l)YR j (l),
 TxR j (l − 1)
+ QH
= RR j (l)R j (l)VR j (l),xTS (l)(4.3)

where (·)H is hermitian of a matrix. Due to the structure of RR j (l), the desired signal after inter-relay interference
cancellation is the second row of matrix ŶR j (l). In addition, due to the properties of QR j (l), the noise powerin (4.3) remains unchanged. After obtaining the desired signal, the jth relay decodes and forwards it regardlessdecoding errors.

4.3

Iterative MAP Receiver for Joint Interference Cancellation and Diversity Combining

The proposed iterative MAP receiver at destination can be formulated by a two-step iterative process: In step one,the modified MAP detection is implemented to jointly cancel interference and mitigate error propagation effects;
While in step two, the soft information, which was provided by step one, is combined and used for turbo-like
decoder, and then the decoder’s output is fed back to the modified MAP detection for the next iteration. With
above process, the interference generated at destination can be cancelled, meanwhile, diversity of the relaying
scheme is also improved.
4.3.1

The Modified MAP Detection

In order to let the proposed receiver have capability of mitigating error propagation effects, we firstly needs tomodify the conventional MAP detection by taking the probability of decoding error at relays into account. Suchprobability can either be estimated at relays and then forwarded to destination as in [HYM15], or be directly
estimated at destination as in [GZ05]. In detail, start from converting (4.2) to the real-valued equivalent form.
Let ỸD (l) ∈ R 4×M , X̃(l) ∈ R 4×M , and ṼD (l) ∈ R 4×M be real matrices obtained from YD (l), X(l), and VD (l),respectively, asỸD (l) = [R(YD (l))T , I (YD (l))T ]T ,(4.4)

Additionally, let H̃D

X̃(l) = [R(X(l))T , I (X(l))T ]T ,(4.5)

ṼD (l) = [R(VD (l))T , I (VD (l))T ]T .

(4.6)(l) ∈ R 4×4 denote the real matrix obtained from HH̃D (l) =D (l), asR(HD (l)) −I (HD (l))
I (HD (l)) R(HD (l))


.

(4.7)

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Then, the real-valued equivalent form of (4.2) is given byỸD (l) = H̃D (l)X̃(l) + ṼD (l).

(4.8)

For the known channels in AWGN, the optimization problem of the conventional MAP detection for the mth
symbols in the l th time slot can be expressed as [VHK04]#"minx̃(m) (l)

4

(m)

(l)

kỹD (l) − H̃D (l)x̃(m) (l)k2 − ∑ logp(x̃k,m ) ,
{z
} k=1
|

(4.9)

,∆(m) (l)

(m)

(l)

(l)

where x̃(m) (l) and ỹD (l) are the mth column of X̃(l) and ỸD (l), respectively; p(x̃k,m ) is the probability of x̃k,m(l)

happening, where x̃k,m is the symbol in the kth row of x̃(m) (l). In this case, logarithm likelihood ratio (LLR) of thesymbol in the kth row of x̃(m) (l) after MAP detection can be expressed as [VHK04](l)−∆(m) (l)+∑ j logp(x̃ j,m )

(l)

(m)

L[x̃k,m |ỹD (l)] = log∑x:x̃(l) =+1 e
k,m

(l)

∑x:x̃(l) =−1 e−∆(m) (l)+∑ j logp(x̃ j,m ).

(4.10)k,m(l)

Here, p(x̃k,m ), ∀k, are independent because they are consist of symbols from different frames.
As we know, LLRs of the symbols in the 1st and 3rd rows of x̃(m) (l) belong to the erroneously forwarded frame(l)from one of relays. Thus, denote pe as the probability of decoding error at the relay in the l th time slot, then inorder to mitigate error propagation effects, we have
(l)

(l)

(l)

(l)

(l)

(l)

(l)

(l)

(l)

(l)

p(x̂ j,m = +1) = (1 − pe )p(x̃ j,m = +1) + pe p(x̃ j,m = −1),p(x̂ j,m = −1) = (1 − pe )p(x̃ j,m = −1) + pe p(x̃ j,m = +1),(l)where p(x̂ j,m ) denotes the modified probability of the symbol in the jth row of x̃(m) (l), and j ∈ {1, 3}. Then,
(l)

(l)

replacing p(x̃ j,m ) with p(x̂ j,m ) in (4.10) for all cases if j ∈ {1, 3}, LLRs of the symbols in the 2nd and 4th rows ofx̃(m) (l) (i.e. LLRs for the forwarded frame from S, where k ∈ {2, 4}) can be modified as
(l)

(m)

L[x̃k,m |ỹD (l)] = log∑x̃:x̃(l) =+1 e−∆(m) (l)+Θ(m) (l)k,m(m) (l)+Θ(m) (l)∑x̃:x̃(l) =−1 e−∆,(4.11)

k,mand LLRs of the symbols in the 1st and 3rd rows of x̃(m) (l) (i.e. LLRs for the erroneously forwarded frame fromone of relays, where k ∈ {1, 3}) can be modified as(l)(l) (m)L[x̃k,m |ỹD (l)] = log(1 − pe ) ∑

(l)

e−∆

(m) (l)+Θ(m) (l)

(l)

e−∆

(m) (l)+Θ(m) (l)x̃:x̃k,m =+1(l)(1 − pe ) ∑x̃:x̃k,m =−1(l)+ pe ∑(l)e−∆(m) (l)+Θ(m) (l)

(l)

e−∆

(m) (l)+Θ(m) (l)x̃:x̃k,m =−1(l)+ pe ∑

x̃:x̃k,m =+1.

(4.12)

Here, we haveΘ(m) (l) ,∑(l)logp(x̃ j,m ) +j, j∈{2,4}∑(l)logp(x̂ j,m ).

(4.13)j, j∈{1,3}

The derivation of (4.12) is trivial with similar procedure given in [LH09].
4.3.2

Iterative MAP Receiver at Destination

Unlike the work in [VHK04], where the iterative decoding is for multiple antenna point-to-point system and thetransmitted frame in every time slot can be individually decoded, the proposed iterative MAP receiver for the

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successive SIMO erroneous relaying needs to wait all L frames being received via L + 1 time slots and then jointly
decode those frames. Given the probability of decoding error at relays, as we described above, the proposed
iterative MAP receiver at destination can be divided into a two-step iterative process: the modified MAP detection
and the conventional turbo-like decoding.
The detailed iterative MAP receiver at destination is illustrated in Fig.4.2. In the l th time slot, destination simul-

Modified
MAP
detector∏ −r 1
Turbo
decoder∏ −s 1

Z −1
∏r

LLRs
conversion∏s

Z

Figure 4.2.: The proposed iterative MAP recevier.
taneously receives the (l − 1)th frame from one of relays and the l th frame from source. Thus, the modified MAP
detection can be implemented to cancel inter-frame interference and generate LLRs for these two frames based on(4.11) and (4.12). Such detection process continues until all L frames obtain two versions of LLRs from both relay
and source. After that, the two versions of LLRs for each frame are separately deinterleaved and then combined
for the turbo-like decoder. The extrinsic LLRs of the coded bits for each frame after the turbo-like decoder will be
duplicated and separately interleaved for both relay and source. Following, the interleaved LLRs are converted to(l)the probabilities p(x̃k,m ), ∀k, m, l, based on the modulator mapping function and then fed them back to the modified
MAP detection for the next iteration use. In Fig.4.2, Π and Π−1 denote interleaving and deinterleaving, respectively; Z and Z −1 represent forward and backward shifting the frame number, respectively; “LLRs conversion”(l)box is used to convert the interleaved LLRs to p(x̃k,m ), ∀k, m, l.
Remark 1: Similar as [VHK04], random interleavers implemented in Fig.4.2 and also in their corresponding(l)transmitters are used to guarantee p(x̃k,m ), ∀k, m, l, to be independently distributed.
Remark 2: For 2 ≤ l ≤ L time slots, destination simultaneously receives two different frames from one of relays
and source. In this case, the shifter Z is implemented to guarantee the same frame’s LLRs being combined for theturbo-like decoder, and the shifter Z −1 is implemented to guarantee the adjacent frames’ LLRs being converted
into the probabilities at the same time for the modified MAP detection.

4.4

Simulation Results

Computer simulations were used to evaluate the bit-error-rate (BER) performance of the proposed successive
SIMO erroneous relaying with iterative MAP receiver at destination. All channels were generated as independent
block Rayleigh fading, which remained static over each transmission time slot. Assumed that there were L = 20
frames being transmitted via L + 1 time slots, and no adaptive retransmission was considered. SNR denoted as thetransmission power normalized by noise power ratio. The quadrature phase-shift keying modulation and turbo-likechannel coding were also considered for the system. In detail, 1/2 rate serial concatenated convolutional code
was used at source and relays, where the first encoder was the non-recursive non-systematic convolutional codewith a generator polynomial G = ([3, 2])8 , and the second encoder was the doped-accumulator with a doping rateequalling 2. Random interleavers were implemented, and simulation results were computed on an average over
10,000 independent channel realizations.
Four baselines were used for comparisons: 1) Perfect decoding at relays: this was served as BER performancebound, where relays can perfectly decode source’s messages all the time and the same iterative decoding at destination as the proposed scheme; 2) Proposed iterative decoding (ID) without pe : relays always forward decoded
symbols regardless decoding errors but the iterative decoding at destination without taking pe into account; 3)Page 28 (54)RESCUE

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0

10

−1

BER

10

−2

10

−3

10

Perfect decoding at relays
Proposed ID with pe
Proposed ID without pe

−4

10
−15

CRC based S−DF
Threshold based S−DF
−10

−5

0

γS,D, S−D link SNR (dB)5

Figure 4.3.: BER versus S-D link SNR with relay-location A in block Rayleigh fading channels and blocklength=1024.
Cyclic redundancy check (CRC) based S-DF: relays only forward if they can perfectly decode source’s messages
and the same iterative decoding at destination as the proposed scheme but without taking pe into account; 4)Threshold based S-DF: relays only forward if decoding errors at relays is less than 15% and the same iterative
decoding at destination as the proposed scheme but without taking pe into account. It is worthwhile to note that all
the presented schemes use the same QR-decomposition detection method at relays as described in Sec. II to cancel
inter-relay interference.
Fig.4.3 shows BER performances of different schemes with relay-location A. Define di, j as the distance between
the ith and jth nodes. Given the distance between source and destination as dS,D = d, we have dS,R1 = dS,R2 =dR1,D = dR2,D = d for relay-location A. As a consequence, based on a simplified suburban area pathloss modelwith the pathloss exponent equalling to 3.52, SNR relationship in dB among S-D, S-R1, S-R2, R1-D, and R2-D
links can be approximated by γS,D = γS,R1 = γS,R2 = γR1,D = γR2,D . As shown in Fig.4.3, the scheme of perfectdecoding at relays undoubtedly gives the best BER performance and enjoys the full diversity gain of 2. Apart from
that, Proposed ID with pe scheme gives the second best BER performance due to the iterative decoding process
at destination by taking the error propagation effects into account. By contrast, Proposed ID without pe scheme
gives the worst BER performance. The BER performances of two S-DF based schemes are in the middle between
Proposed ID with pe scheme and Proposed ID without pe scheme. This is because in this case, the S-DF based
schemes prefer to remain silent rather than propagate decoding errors.
In order to generalize the analysis, we also produced BER performances of different schemes for a different relay location (i.e. relay-location B) in Fig.4.4. In this case, given dS,D = d, we have dS,R1 = dS,R2 = 12 d and
dR1,D = dR2,D = 34 d. Then, similar as the setup of relay-location A, the corresponding SNR relationship in dBamong S-D, S-R1, S-R2, R1-D, and R2-D links can be approximated by γS,R1 = γS,R2 = γS,D + 10.6 dB and
γR1,D = γR2,D = γS,D + 4.4 dB. Such location is the case that relays are close to source. As shown in Fig.4.4,
the same BER performance trend as Fig.4.3 is presented, where Proposed ID with pe scheme gives the second
best BER performance. Comparing Fig.4.3 with Fig.4.4, the BER performance difference between Proposed ID
with pe scheme and the conventional S-DF based schemes in Fig.4.4 is larger than the ones in Fig.4.3, where theperformance difference in Fig.4.4 can exhibit up to 8 dB gain. This is because, when relays are close to source,
their decoding capabilities are increased due to higher received SNR. However, due to the iterative decoding at
destination without taking pe into account, the conventional S-DF based schemes in this case still encounter error
propagation effects plus the increased inter-stream interference at destination.

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10

−1

10

−2

10

−3

BER

10

−4

10

−5

Perfect decoding at relays
Proposed ID with pe−6

Proposed ID without pe

10

10

−7

10
−15

CRC based S−DF
Threshold based S−DF
−10

−5

0

γS,D, S−D link SNR (dB)5

Figure 4.4.: BER versus S-D link SNR with relay-location B in block Rayleigh fading channels and blocklength=1024.

4.5

Summary

In this chapter, a successive SIMO erroneous relaying with iterative MAP receiver at destination has been proposed.
The proposed scheme allows relays erroneously forward the decoded symbols, and jointly cancels interference
and combines diversity at destination. It has been shown that, without extra cost of time delay and signalling
overhead, the proposed scheme can exhibit up to 8 dB gain by comparing with the conventional S-DF based
schemes especially for relay-location B.

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5.

Application of RESCUE coding to 802.11 WiFi

5.1

Introduction

In this chapter, we apply the RESCUE JD technique into IEEE 802.11a/g/p standard. In particular, we investigate
the impact of utilizing JD together with ARQ. It is shown that even with a very small change in standard, we canachieve about 0.5 dB gain in terms of FER vs SNR.
An open source implementation of orthogonal frequency domain multiplexing (OFDM) [Cha66] transceiver forIEEE 802.11a/g/p networks is available online1 for GNU Radio2 . We use this implementation as a basis of our own
experiments. The receiver implementation with the fitting for operation with an Ettus USRP N2103 is described in[BSS+13] and OFDM transmitter using GNU Radio is described for example in [FCV+10].
The high level flow graph of the OFDM tranceiver design in GNU Radio is depicted in Fig. 5.1. The most important
blocks in the flow graph are following:• TUNTAP PDU: Creates ethernet connectivity together with Ethernet Encapsulation block. This makes
possible to use gr-ieee802-11 design as a normal ethernet adapter.
• OFDM MAC: Medium Access Control (MAC) block to take care of MAC layer features as described inIEEE 802.11 standard.
• WiFi PHY Hier: Hierarchical physical layer block which includes all the physical layer features. This block
will be described in more details in section 5.2.1.
• UHD, USRP Sink & UHD, USRP Source: These blocks creates connectivity between flow graph and USRP.

5.2

Implementation

In this section, the physical layer implementation of IEEE 802.11a/g/p is described and the application of JD
with minimum modifications is explained. The original IEEE 802.11a/g/p PHY hierarchical block is opened inFig. 5.2 and it is described in more details in section 5.2.1. The used simulation model including needed changes
in standard is described in section 5.2.2.
5.2.1

Original IEEE 802.11a/g/p tranceiverFig. 5.2 depicts the GNU Radio flow graph of PHY hierarchical block. Data processing for packet coming from
MAC layer is following:
1. OFDM Mapper adds first service field and tail bits to incoming Protocol Data Unit (PDU). After this, data
will go through following processing steps: scrambling, convolutional encoding, puncturing and interleaving. Finally processed PDU will be splitted into symbols.
2. Packer Header Generator creates signal field. It will be mapped to BPSK symbols inside Chunks to Symbols
block. Symbols coming out of OFDM Mapper block will be mapped using current constellation in the other
Chunks to Symbols block. Possible symbol constellations are BPSK, QPSK, 16QAM and 64QAM.
3. OFDM Carrier Allocator maps incoming symbols and pilot symbols to OFDM subcarriers. There is 48 data
symbols in one OFDM symbol. It also appends short and long training sequences into the beginning of theframe.

1 http://www.ccs-labs.org/software/gr-ieee802-11/
2 http://gnuradio.org
3 https://www.ettus.com

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Figure 5.1.: High level flow graph of the OFDM transceiver in GNU Radio.

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Figure 5.2.: Flow graph of the original physical layer functionalities.
4. At this point packet will go through Inverse Fast Fourier Transform (IFFT). Last step in this processig chain
is to add cyclic prefix to OFDM symbols. This will happen inside of OFDM Cyclic Prefixer block.
Samples coming from Pad Source will go through the following processing:
1. Firstly, signal is fed to a packet detector. Packet detection algorithm is described in [Liu03]. Packet detector
blocks will also handle coarse frequency offset correction and remove cyclic prefix.
2. Now sample stream has coarse synchronization and it will go through Fast Fourier Transform (FFT).
3. After FFT, sample stream goes to equalizer. It will correct remaining frequency and phase offset and scale
samples to correct amplitude using information from pilot signals. Pilot signals will be removed and only
data samples will be outputted.
4. Data samples are now fed to OFDM Decode Signal block which decodes the signal. Signal field has rate
field and packet length fields.
5. After the signal field is decoded, OFDM Decode MAC maps symbols back to bits, deinterleaves, depunctures, decodes and descrambles data and then sends it out to Pad Sink.
5.2.2

Simulation ModelIn this section, simulation model, changes in standard and test cases are described. To establish RESCUE coding
on 802.11 OFDM tranceiver, minimum needed change is random bit-interleaver for payload data. This interleaver
will be located before data scrambling. Standard compliant convolutional coding with generator g0 = 1338 andPage 33 (54)RESCUE

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g1 = 1718 is used in implementation.
The simulation model is depicted in Fig. 5.4. It has following new blocks:• Rescue decoder: This block includes all the decoding and demapping functions. It also controls simulations
and prints logs.
• Rescue Packet Generator: Generates data packets using payload generated by Rescue decoder. Generationcommand also includes desired SNR, code rate, modulation and number of packets to generate.
• Rescue channel: AWGN/Rayleigh channel generating Gaussian noise using SNR information.
• Simulation packet detector: This block is used to emulate packet detection.
Simulation model has possibility to forward data through OFDM chain and equalizer or just add noise to data
symbols. Latter one is used in these simulation to investigate theoretical limits of this technology without nonideal
blocks, such as equalizer.
When decoder receives packet it first decodes signal field. If it is successful it decodes the whole packet. If thepacket has errors, decoder checks if header’s address fields match to the stored addresses. Packets with matching
addresses will be added to decode set if any combining is used. In this work, header error rate (HER) will bedefined to cover only address part of the header because it is one of the main limiting factor of this technology. If
HER increases too much it may mask gains coming from joint decoding.
Test cases selected to study the impact of JD in WiFi are the following:• Joint decoding using interleaver: Joint decoding is applied to a standard code.
• Combining LLRs after decoding: Just a simple summation of LLRs.
• No combining
Joint decoder structure for N frame copies can be seen in figure 5.3. It is worth of noticing that the feedback fromthe BCJR to the demapper is not effective because BPSK modulation is used in simulations.

5.3

Numerical Results

All the simulations were run over 2000 generated individual packets with 10 retransmitted copies per packet.
As mentioned in Section 5.2.2, rate 1/2 convolutional coding with generator g0 = 1338 and g1 = 1718 is used
together with BPSK modulation. Frame Error Rate (FER) comparison between joint decoding, LLR combining
after decoding and no combining for one and two copies can be seen in Fig. 5.5 and for 5 and 10 copies in Fig. 5.6.
HER is also plotted to figures. It can be seen from Fig. 5.5 that a small gain is achieved by adding the interleaver
and performing iterative joint decoding. From Fig. 5.6, we can observe that the gain is increased when having more
copies, reaching up to 0.5 dB with 10 frame copies. As already mentioned in Section 5.2.2, it can be also observed
from Fig. 5.6 that HER is restricting the performance of both, combining and JD. In fact, even if ten copies aresent, the number of the copies that are jointly decoded is much less in low SNR regime, because of the erroneousheaders.

5.4

Conclusions

As was seen from numerical results, gain achieved by adding interleaver and performing iterative joint decoding
gives maximum of 0.5 dB more SNR operating range with high number of retransmissions and less with a fewer
number of copies. The limited gain is mainly due to the impact of HER but also due to the fact that the standard code
is not designed for iterative processing. Therefore, this topic should be studied further with different modulation

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Figure 5.3.: Joint decoder for 802.11 simulation.

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Figure 5.4.: Flow graph of the physical layer including RESCUE functionalities.

100

FER

10-1

10-2

10-3

10-4
-4

No combining, 1 copy
No combining, 2 copies
Combining, 2 copies
JD, 2 copies
HER

-3

-2

-1

0

1

2

SNR

Figure 5.5.: BER results for one and two frame copies.

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100

FER

10-1

10-2

10-3

10-4
-4

No combining, 5 copies
No combining, 10 copies
Combining, 5 copies
Combining, 10 copies
JD, 5 copies
JD, 10 copies
HER

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

SNR

Figure 5.6.: BER results for five and ten frame copies.
and coding schemes and possibly even with different forward error correction codes, such as the code designed for
RESCUE.
Even though it would be possible to get more gain by designing better codes for this purpose, 802.11 may bechallenging environment for joint decoding because of its nature as interference limited system. Packet corruptions
because of collisions may dominate instead of Gaussian noise and for that purpose, JD should be combined withinterference cancelation techniques.

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6.

D2.1.2 Version 1.0

An Error Rate Model for RESCUE PHY

This chapter presents a link quality model for a wireless communication system with DTC and LF. The modelmaps the signal-to-interference-plus-noise ratio (SINR) of packet copies received from different links to a mutual
information (MI) parameter and, in a second stage, converts it to a block error rate. The model accurately predicts
the link-level performance at a low computational complexity and can be therefore used as a physical layer (PHY)
abstraction for the computationally-intensive, simulation-based performance evaluation of various functionalities
at higher protocol layers or at the system level. In order to illustrate the usage of the proposed model, we show
the integration of the model into a protocol level simulator assessing the performance improvements of LF and JD.
This work has been published in [THZ+16].

6.1

System Model

A block diagram of a parallel lossy DF relaying model is depicted in Fig. 6.1, where uk = u ⊕ ek denotes thebinary sequence at a relay k after decoding, ⊕ indicates modulo 2 addition, u is the original binary independent
identically distributed (i.i.d.) information sequence from the source, and ek = [ek,1 , ek,2 , . . . , ek,L ] is a bit flipping
sequence defined as
1, with probability pk ,ek,n =(6.1)
0, with probability 1 − pk , n = 1, 2, . . . , L.
Each correlated version of the source sequence uk is interleaved and encoded by a twofold serially concatenatedcode at the relay: First, a systematic non-recursive convolution code (SNRCC) and second, a doped accumulator (ACC) [AM12], i.e., memory-1 systematic recursive convolutional code (SRCC) are deployed. The ACC isused to prevent an error floor at the relay decoder [PS06]. Finally, the modulated sequence sk is transmitted over a
block fading channel, where γk is a fading factor and wk is Gaussian noise.

γ1

e1
u1
u

x1

Map1

y1

s1

γK

eK
uK

Source

Enc1

EncK

xK

MapK

Relays

w1

sK

Joint
Decoder

wK

û

yK

Destination

Figure 6.1.: A schematic diagram of a parallel relaying model [D211].

At the destination, soft demapping is applied by calculating the log-likelihood ratio (LLR) Lxk with the received
sequence yk and known channel state information. Each relay decoder in Fig. 6.2 has two matching BCJR algorithms [BCJ+74]. In general, the joint decoder is structured in two main parts: (1) the local iteration (LI), where
the relay sequence is decoded, and (2) the global iteration (GI), where the information exchange among all relay
sequences is performed. In GI the LLR update function [AM12], based on the knowledge of pk , updates the LLRs
Leuk accordingly1 . If the LLRs Leuk are not improving anymore, the final estimation of u is determined by harddecision of the sum of all Leuk . For a detailed explanation of the joint decoder, we refer to [HZA+13].

1 The value of p can be estimated at the relay and transmitted to the destination or it can be estimated during the decoding process.
k

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y1

Demap1

Lx1

Lau1
Decoder1
Leu1

UpdateFunction

Leu1
Lau1
Variable
Node

Lpu

û

LauK
yK

DemapK

LxK

LeuK
DecoderK
LauK

UpdateFunction

LeuK

Local Iteration
Global Iteration

Figure 6.2.: The joint decoding strategy utilizes correlation knowledge among the relays data through global
iteration [HZK+15].

6.2

Error Rate Model

The MI-based metric is well suited for the link-level abstraction of the system model where same data is received
through multiple parallel links. Fig. 6.3 divides the abstraction model into two components, Blackbox #1 and #2,
which illustrate the deterministic and stochastic parts, respectively. The idea is to use the MI metric given byBlackbox #1 to match with simulation based results stored in Blackbox #2. To be more specific, Blackbox #1
compresses a given set of parameters into a one single scalar, which is further mapped with simulation results inBlackbox #2. In the following we describe the content of both parts of the abstraction model.

Stage 1
Extraction of quality
measures and compression
BEP atrelays rk
p1 .. pK

SINR between
relay rk anddestination
SINR1 .. SINRKBlackbox#1

MutualInformation
MI

Idealistic BEP

Stage 2Mapping

Blackbox#2

Number oferrors per
packet E

pidealModulation Code
order
rate

Code Number
block of parallel
length L links K

Figure 6.3.: PHY abstraction for link-level performance in multi-path relay networks with LF and joint
decoding.

6.2.1

Blackbox #1

Blackbox #1 was originally described in [D211]. The BER after JD at the destination depends on the bit error
probability (BEP) at the relay k (pk ), the SINR of the link between relay k and the destination (SINRk ), and thePage 39 (54)RESCUE

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used modulation and coding scheme (MCS). Next, we show how these parameters are mapped to a single scalarMI.
A simplified version of the “achievable rate region” from [ZCH+14] is shown in Fig. 6.4. The figure corresponds
to a three-node system model, where the destination receives two copies of the same data packet, one directly fromthe source and another from a relay node. Here, the relay may be unable to decode correctly, and the resulting
BER at the relay is p. The axes R1 and R2 represent the scaled channel constellation constrained capacities (CCCs)k), withof the source-to-destination link and the relay-to-destination link, respectively, given by Rk = C(MRkk,SINR
c Mk
C(Mk , SINRk ) being the CCC of AWGN channel of the parallel link k depending on the modulation and SINRk .
The scaling is performed with the spectral efficiency depending on the number of bits per symbol Mk in complex
modulation and the channel code rate Rkc used at the relay k.
Theoretically, if the rate pair falls into the achievable rate region, error-free decoding at the destination is possible.
Note that the rate region is information theoretic and independent of the code design and decoder implementation.
We assume that the source sequences u1 and u2 have full entropy, i.e., H(u1 ) = 1 and H(u2 ) = 1, respectively.

Figure 6.4.: Rate region for a three-node system.
The bound of the admissible rate region consists of the straight line a, i.e. R1 + (1 − Hb (pk )) = 1 and the curve b.
Here Hb (pk ) = −pk log2 pk − (1 − pk ) log2 (1 − pk ) denotes the binary entropy associated with probability pk . In
order to simplify the model, we approximate the curve by the straight c as R1 + (1 − Hb (pk )) R2 = 1. By combining
the two lines, we get an expression for the approximated admissible rate region as
R1 + min{1 − Hb (pk ), (1 − Hb (pk ))R2 } ≥ 1.

(6.2)

We further propose to generalize the combining of MI over any number of parallel incoming links so that
MI = ∑ Mk
k


Mk =

Rk ,
min{(1 − Hb (pk ))Rk , 1 − Hb (pk )},pk = 0pk > 0.

(6.3)

In theory, when MI per bit is unity, there are no errors after JD. Note that if there are errors in the transmitter, corresponding MI remains always below unity. Otherwise, MI can get larger values. If all parallel links have sufferedof errors before the last hop (a chief executive officer (CEO) problem [HZK+15]), an error floor occurs [WMF15].
Blackbox #1 also calculates the error floor p f loor by using the method described in [D121, Sec. 4.1.4.1].
By employing Shannon’s source-channel separation theorem [CT91], the distortion (BER) at the output of thereceiver can be lower bounded by the inverse of the binary entropy function [ZCH+14] as
pe = Hb−1 (1 − MI),

(6.4)

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which equals to zero when MI ≥ 1. Now, the idealistic BEP pideal can be approximated as an upper bound of theerror floor and MI as
pideal = max{pe , pfloor }.
(6.5)
We call the mapping from the link-specific SINRs and transmitter BERs into the MI and pideal as Blackbox #1. It
employs a very simple deterministic mapping that is independent of the coding and decoding scheme, and requires
no simulations. It predicts optimistic performance that corresponds to infinite packet sizes. It is also worth ofnoticing that due to the summation of MIs in (6.3), the theory assumes that the erroneous bits do not interfere indecoding process, i.e., erroneous bits are treated as erasures.
6.2.2

Blackbox #2

It is well known that in block codes, the number of bit errors per packet is not uniformly distributed. In order toobtain MCS and packet length dependent BER performance results, we propose to concatenate Blackbox #1 withBlackbox #2 that employs a mapping obtained via simulations in the AWGN channel. Note that these results apply
also in block fading channels. The idea is to obtain the random packet-by-packet decoding performance in termsof BER. In the following, we will describe the construction of mapping tables used in Blackbox #2 for K parallel
links.

6.2.2.1

Construction of simulation tables for Blackbox #2

Since Blackbox #1 is able to do the compression of channel quality measures to a single scalar, we can significantly
reduce the number of simulation tables needed. For the simulations, we can perform the following simplifications:set pk = 0 for all k, since pk is already taken into account when calculating MI through (6.3). Furthermore, since
the simulation results and the theoretical results are compared only in terms of the sum of the MIs over the links,
we can set SINRk = γ̂, ∀k, and sweep γ̂ through an appropriate SINR range. The simulations have to be performed
separately for all MCSs considered.
Simulations were performed by sending 10,000 packets (8,000 bits each for QPSK, 8,400 for 16-QAM and multirate) through the channel of each parallel link with orthogonal channel access. The output of the simulations
was the number of errors in each packet after JD at the destination. Empirically, it was found that the errors are
distributed approximately according to a distribution defined asP(α, µ, σ 2 ) = αδ (0) + (1 − α)N (µ, σ 2 ),(6.6)

where α is the probability that the number of errors in a packet is zero, δ (·) is the Dirac delta function, andN (µ, σ 2 ) denotes the normal distribution with mean µ and variance σ 2 . An intuitive explanation for (6.6) is that
α portion of the packets are error-free, and for the remaining part, the error distribution follows Gaussian.
The parameter values pk = 0 and SINRk = γ̂ are fed to Blackbox #1 which outputs MI. For this given pk and SINRkvalues, we run simulations and then fit the simulation data to the distribution given above, resulting in numericalvalues of parameters α, µ, and σ 2 corresponding MI output from Blackbox #1. As a result, we can construct atable with four columns that corresponds to MI, α, µ, and σ 2 , respectively.

6.2.2.2

Generation of bit errors using Blackbox

Since the resolution for the MI values listed in the table is finite, linear interpolation can be used to obtain numericalvalues for the distribution parameters between the quantized points. For the cases where at least one error-freecomponent exists at the relay, errors can be generated directly from (6.6). In the case of CEO problem, there exists
an error floor which is composed of uniformly distributed errors which further need to be considered by adding
E = E + E f loor , where E f loor is the number of errors induced by error floor. The generation of the number ofbit errors E is described in Algorithm 1. The operation E = max{0, E} is used to prevent negative values of E.
Symbol L at line 13 denotes the length of a block.

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Algorithm 1: Bit error generation for multi-path relay networks with LF and JD.
1: Input parameters p1 , p2 , . . . , pK ,SINR1 , SINR2 , . . . , SINRK
2: Calculate MI using (6.3)
3: Find α, µ, σ 2 matching the values on the tables with MI
using linear interpolation
4: Generate uniformly distributed random number ρ ∈ [0, 1]
5: if ρ > α then
6:
Generate E from N (µ, σ 2 )and choose E = max{0, E}.
7: else8:E =0
9: end if
10: Calculate p f loor using the methodfrom [Xia15, Sec. 4.1.4.1]
11: if p f loor > 0 then12:
Initialize E f loor = 0
13:
for i = 1, 2, . . . , L do
14:
Generate uniformly distributed random numberρ f loor ∈ [0, 1]
15:
if ρ f loor < p f loor then16:
E f loor = E f loor + 1
17:
end if18:
end for19:
E = E + E f loor
20: end if

6.3

Validation

In this section, we will analyze the accuracy of Blackbox in terms of BER and BLER in AWGN channel. Two
different MCSs are used: quadrature phase shift keying (QPSK) with channel code rate 1/2 and 16-ary quadratureamplitude modulation (QAM) with channel code rate 3/4. The channel code parameters are shown in Table 6.1.
Natural mapping and modified set partitioning mapping (MSP) are used for QPSK and 16-QAM, respectively.
We define four test cases:• Case 1: QPSK with three parallel links:
p = [p1 , p2 , p3 ]=[0 0 0].
• Case 2: Two parallel links, one uses QPSK and one uses 16-QAM: p=[0 0].
• Case 3: QPSK with three parallel links: p=[0.01 0.02 0].
• Case 4: QPSK with three parallel links:
p=[0.01 0.02 0.05].
Cases 1 and 2 represent cases where exactly the same data is transmitted through independent links. From the relay
network perspective, this means that all routes are error-free before the last hop (relay-destination link). Case 3 isa case where one of the routes is error-free and two of them have suffered from errors before the last hop. Case 4
represents a CEO problem.

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Table 6.1.: MCS parameters
QPSK

16-QAM

Overall rate

1/2

3/4

Inner code
Doping
Puncture pattern
Inner code rate
(after puncturing)
MemoryDoped ACC with puncturing
8
1
[0 1]
[0 1]
1

1

1

1

Outer code
Polynomial description

CC
{3,2}

Puncture pattern

NACC with puncturing{7,5}[1 0 1] for even positions,[1 1 0] for odd

Outer code rate
(after puncturing)
Memory

1/2

3/4

1

2

0.16
Simulations, SNR=-4.5 dB
Blackbox, SNR=-4.5 dB
Simulations, SNR=-4.4 dB
Blackbox, SNR=-4.4 dB
Simulations, SNR=-4.3 dB
Blackbox, SNR=-4.3 dB

0.14
0.12

Probability

0.1
0.08
0.06
0.04
0.02
0
0

100

200

300

400

500

600

700

Number of errors
Figure 6.5.: Error distributions for Case 1 obtained by Blackbox and simulations.

The first step is to validate the error distribution defined in (6.6). The error distributions for Case 1 obtained using
Blackbox and chain simulations with three SNR values are shown in Fig. 6.5. The SNR values are chosen from thewaterfall region, since it is the most difficult region to track. It can be seen that the distributions match very well,although slight deviation is obtained in SNR=-4.3 dB.
Figs. 6.6 and 6.7 show the average BER and BLER, respectively, obtained using Blackbox and through simulations.
The value of pideal is taken directly from Blackbox #1 and BLERideal = 1 − (1 − pideal )L . We can see that in cases 1

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and 2, the curves exactly match. For cases 3 and 4, it can be observed that the result provided by the Blackbox
is optimistic compared to the simulations. Possible approaches to improve the accuracy are to improve the JD
performance, improve the accuracy of the theoretical results used in Blackbox #1 and/or to find better matchingerror distributions. However, this investigation to improve the accuracy of the model in Cases 3 and 4 is left as a
future study.

100
10-1
10-2

BER

10-3
10-4
10-5
10-6
10-7
10-8
-10

case 1, Blackbox
case 1, simulationcase 2, Blackbox
case 2, simulationcase 3, Blackbox
case 3, simulationcase 4, Blackbox
case 4, simulationcase 1, pideal

-8

-6

-4

-2

0

2

SNR (dB)

Figure 6.6.: Average BER results obtained by Blackbox and simulations.

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100

10-1

BLER

10-2

10-3

case 1, Blackbox
case 1, simulationcase 2, Blackbox
case 2, simulationcase 3, Blackbox
case 3, simulationcase 4, Blackbox
case 4, simulationcase 1, BLERideal

10-4

10-5

10-6
-10

-8

-6

-4

-2

0

2

4

SNR (dB)
Figure 6.7.: BLER results obtained by Blackbox and simulations.

6.4

Application

We have integrated the Blackbox into the popular ns-3 simulator and carried out a simulation-based performance
evaluation for a representative scenario. This section explains the implementation design for the ns-3 enhancements
and presents the performance results.
6.4.1

Integration of the Blackbox into Network Simulator ns-3

ns-3 is a discrete-event simulator, which models the operation of the system as a discrete sequence of events intime. Key components of a network based on ns-3 models are nodes, applications, channels and network devices,
the latter model the link-level including PHY and MAC. For scalability reasons and to enable simulations at low
computational costs, ns-3 implements PHY abstractions to predict the link layer performance. A MI-link quality
model has already been integrated into the ns-3 distribution [MMR+12]. However, this model does not consider
relaying. Therefore, we have implemented the error rate model for LF and JD and integrated it into ns-32 .
For our studies we have used the ns-3 wifi module, which simulates the IEEE 802.11 PHY and MAC. The integration of the PHY abstraction takes place inside the WifiPhy and the yans classes, more specifically in the send andreceive functions. We make use of packet tags, a ns-3 feature that allows appending additional information to apacket and thereby to enhance existing protocols by functions for LF and JD.
6.4.2

Simulation Scenario and Results

The network under consideration consists of a single source, multiple (two or three) relays and a single destination.
We study the effect of joint decoding and quantify the advantage of using more relays with respect to the reliability.
2 The implementation of the Blackbox for ns-3 is available as open source at https://mns.ifn.et.tu-dresden.de/Research/

Projects/Pages/RESCUE.aspx.

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The nodes execute a WiFi-like PHY and MAC (IEEE 802.11a) extended by LF and JD. For multi-path packet
routing we apply an enhanced version of contention-based geographical forwarding (CBGF) [KFF16]. The channel
is modeled by a log-distance path loss with a channel exponent of 3 and Nakagami distribution with shape factor 1,
which corresponds to a Rayleigh fading channel. For details of the scenario and models we refer to [KFF16].
We measure the packet success ratio (PSR) – the ratio of successfully received packets at the destination and thesent packets from the source – the number of packet copies (decoding attempts) required for error-free decoding– over the transmit power in dBm, whereas all nodes have the same transmit power. In LF+JD-On packets witherrors are forwarded at the relays (lossy forwarding – LF) and combined at the destination (joint decoding - JD)
whereas in LF+JD-Off the relays forward only those packets that are correct and at the destination joint decoding
is disabled, thus the destination needs to wait until an error-free packet arrives.
To illustrate the functioning of the Blackbox, we consider the PSR with respect to the number of decoding attempts,
which corresponds to the number of received packet copies, whereas the summation over the per-packet-copy PSR
yields the overall PSR (Fig. 6.8 top Accumulated).
The PSR grows for the two-copies and three-copies cases (Fig. 6.8 center and bottom) to a maximum and decreases
for higher transmit power values. The reason for the decay is that with a high transmit power the destination is able
to successfully decode the first arriving packet copy (see Fig. 6.8 top). For three packet copies, at approximately
25 dBm the two curves intersect (Fig. 6.8, bottom) because with LF+JD-On the Blackbox was already able todecode the packet correctly with 2 packet copies and does not require additional packet copies, whereas LF+JDOff need to wait for the third error-free packet copy. If we regard the blue curve in Fig. 6.8 as the baseline then the
difference between the red and blue curves gives the gain achieved by LF and JD.

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100

P SR (%) – 2 Packet CopiesRESCUE5080

Accumulated

Accumulated

54.3 %

62.6 %

60
40
20

2 Relays

3 Relays

LF+JD-On
LF+JD-OffLF+JD-On
LF+JD-OffLF+JD-On
LF+JD-OffLF+JD-On
LF+JD-Off

0

40

LF+JD
Gain

2 Relays

LF+JD
Gain

3 Relays

30
20
10

P SR (%) – 3 Packet Copies

010

LF+JD-On
LF+JD-Off

8

2 Relays

6

LF+JD-On
LF+JD-Off

LF+JD
Gain

3 Relays

LF+JD
Gain

4
2
0
10

20
30
40
Transmit Power (dBm)

10

20
30
40
Transmit Power (dBm)

45

Figure 6.8.: Packet success ratio (PSR) over transmit power [dBm] for the number of decoding attempts (1,2 or 3 packet copies). The top figures also show the accumulated PSR (sum of all packet copy
curves). The error-bars refer to two standard deviations.

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Conclusion

We introduced a model that is capable of predicting the BLER in a wireless communication system with distributed
turbo coding, where the destination receives multiple copies of potentially corrupted packets and reconstructs thesource information. We have verified the accuracy of the model for the AWGN channel with several modulation andcoding schemes. Furthermore, we have demonstrated the application of the error rate model in a protocol simulator
and quantified the gains of distributed source coding approach in a state-of-the-art ad hoc routing protocol. The
proposed model represents a PHY abstraction that is capable to accurately predict the link-level performance at low
computational complexity and can therefore be utilized for the design and performance evaluation of algorithms
and protocols that exploit distributed turbo coding as well as for system-level simulation.

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Conclusion and Future WorkIn this deliverable, we have provided comprehensive analytical and simulation results of the coding algorithms
used in RESCUE. Furthermore, we have applied the coding algorithms to various frameworks and investigatedtheir applicability in selected cases. Deliverable [D211] presented the basic structure of RESCUE coding/decoding
algorithms, however, most of the reported results showed bit error rates (BERs) in AWGN channel, which is indeed
enough when investigating the coding gain obtained by the developed coding algorithms. It was shown in [D211]
that the RESCUE coding/decoding can achieve BERs less than 2 dB away from the theoretical limits. As the strong
error correction capability of RESCUE forward error correction (FEC) code is evident, in this deliverable, we also
wanted to address the impact of LF. It is well known, that the majority of the performance increase in cooperative
relaying is due to spatial diversity introduced by the relay channels. Therefore, in Chapter 2, we have looked at theperformance of the proposed algorithms in fading channels. Specifically, we investigated two scenarios: ,• TS1: A system with source, relay and destination, where there exist links between every nodes, and• TS2: A system with source, multiple relays and destination, where the direct link between the source anddestination does not exist.
For TS1, we can conclude that if the channel realizations are independent in time, i.e., two successive time slots areuncorrelated, it is often better to use source-destination (SD) link multiple times rather than use the relay channel.
However, this requires the availability of the feedback channel. For TS2, we can conclude that LF can operate inwider SNR range than lossless DF.
Chapter 3 described the opportunistic relay selection taking into account the errors occurred in source-relay channels. A statistical learning method for relay selection was also proposed. In the presence of multiple relays, it
is important to be able to select the best ones for communication in order to reduce the network traffic. Performance improvements of LF over the lossless DF in terms of required SNR were observed in the considered systemmodel.
Chapter 4 presented a successive SIMO erroneous relaying with iterative MAP receiver for multiplexing loss
compensation of HD constrained relaying. Such scheme allows two HD relays alternately serve as transmitter andreceiver to continuously transmit data frames for every channel use, and multiple receive antennas can be used forinterference cancellation. It was shown that, without extra cost of time delay and signalling overhead, the proposed
scheme can reduce the SNR requirement by 8 dB compared with the conventional S-DF based schemes.
Chapter 5 described the application of JD into IEEE 802.11a/g/p standard. The objective was to apply RESCUE
coding/decoding with minimal changes to standard. Therefore, we did not consider LF, but we relied on multiple
frame copies induced by ARQ. The only change in standard is that the interleaver shuffling the information bits
before encoding should be different for each frame copy. It was shown that the FER can be decreased with a costof increased complexity at the receiver. Even though it would be possible to get even more gain by designingbetter codes for this purpose, 802.11 may be challenging environment for joint decoding because of its nature asinterference limited system. Packet corruptions because of collisions may dominate instead of Gaussian noise andfor that purpose, JD should be combined with interference cancelation techniques.
Chapter 6 described the RESCUE PHY abstraction. The model maps the SINR of packet copies received fromdifferent links to a mutual information parameter and, in a second stage, converts it to a block error rate. The
proposed model is able to accurately predict the link-level performance at low computational complexity and cantherefore be utilized for the design and performance evaluation of algorithms and protocols that exploit distributed
turbo coding as well as for system-level simulation.
Theoretical results reported in Chapter 2 shows that in TS1, where the relay is placed on the line between source
and relay, the optimal relay position is at the midpoint, and the performance is symmetric around it. However,
we have observed during the RESCUE project that in interference-free scenario, the RESCUE coding/decoding
algorithms have the best performance when the relay is closer to the source and when relay is moved closer to thedestination, the performance gets worse w.r.t the theoretical limit. Even though the performance is very good also
for lossy frames and naturally we cannot choose the relay positions in RESCUE use cases, this indicates that there
are space for improvement. One of the most important parts in JD is the LLR update function that compensates the

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loss produced by source-relay link. This function enables the interaction between the two decoders by scaling the
LLRs with the BEP between the sequences. RESCUE coding/decoding uses novel estimation algorithms reported
in [D211] to find the average BEP. The LLR update function reduces the SNR of all the bits. This raises up aquestion can we do better than applying this single function to all bits? Is one confidence indicator value about
the source-relay channel enough to compensate the loss? The results say that yes, however, does it compensate
too much? However, the benefit of the used compensation function is simplicity. Another way to improve theperformance of coding/decoding of lossy frames is to investigate the asymmetric scenario. As mentioned earlier,
we insist on simplicity and practicality and therefore we use the same code in source and relays. However, we
could design better matching codes that adapt with the error probability value at the relay.
Most of the results provided in [D211] and in this deliverable investigate interference-free scenarios. Chapter 4
provided interesting initial results for the case where multiple nodes have an access to the same channel. Unlikein the interference-free system considered earlier, it was observed that the performance improvement in LF-based
strategy compared with the lossless relaying increases especially when the relays are closer to the source. Thisis because, when relays are close to source, their decoding capabilities are increased due to higher received SNR.
However, the lossless DF suffers of reduced spatial diversity gain even if only a few bits are erroneous at therelays. The threshold-based S-DF might provide better performance, but the increased multi-stream interference
and error propagation effects at the destination will let it lose its performance. This indicates that the multi-antennainterference cancelation based on LF is a promising research direction.
The TS1 results shown in Chapter 2 also indicates that in this simple three-node model with geometric path loss
assumption, the availability of the feedback link makes LF meaningless. In other words, in this simple system
it is better to retransmit from the source rather than forwarding the lossy frames from the relay. However, ARQ
may not be always possible. One of the main use cases in RESCUE is public safety and especially disaster typeof situations where infrastructure is partially down. In those cases, we do not necessarily have the control entity,
but the source just transmits hoping that someone can hear. The final destination does not necessarily know thatsomeone has transmitted. On the other hand, once the packet has arrived to destination, the network topology may
have changed already such that the retransmission is not possible. As already mentioned in Chapter 1, we canconclude that LF is beneficial at least in the following cases:
1. Communications in rapidly changing network topology where the retransmissions are not possible.
2. Communications with low power devices where the nodes need to share the load with each other.
In top of the public safety example described above, case 1 includes examples such as V2V and V2I where car
is passing by the relay nodes and the source have only one chance to transmit the data. Another case where thefeedback is not available is an asymmetric structure where destination can only receive or there is not enough power
to send the feedback. Public safety also includes the security aspect, for which there can be a situation where thesource wants to be visible as short time as possible and therefore, avoid retransmissions. Case 2 includes examples
such as low power sensor nodes, where we want to balance the power consumption between the sensors.
In the following, we would like to point out some numerical results obtained during the RESCUE project. It has
been shown in [AM12], that the coding/decoding algorithms used in RESCUE can reduce the required transmit
power at least 1/4 per bit in AWGN channel compared to conventional distributed turbo code. In Chapter 2, weshowed that LF can reduce the FER more than 1/2 compared to the lossless DF in fading channels. By using
the Erlang formulation presented in Appendix A, we can also have significant capacity and spectral efficiency
improvements in specific SNR values.
As a conclusion on RESCUE coding/decoding algorithms, we can state that the code is very simple but remarkably
strong performing close to the theoretical limits. As stated already in Chapter 1, this is a completely new code
design and up to our best knowledge, there is no existing work with this extend.

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on Comm., Special Section on Coding and Coding Theory-Based Signal Processing for WirelessCommunications E95-B.12 (2012), pp. 3654–3662.

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Appendix A

D2.1.2 Version 1.0

Converting FER results into Erlang

The Erlang B formula determines the probability that a call is blocked and is a measure of the grade of service fora trunked system which provides no queuing for blocked calls. The Erlang B formula is given by [Rap+96]
Pb =

Em
m!
,
m Ei
∑i=0 i!

(A.1)

where m is the number of parallel resources, E = λ h is the offered traffic, λ is the mean arrival rate, and h is themean call holding time. The FER and the mean call holding time is related as
h=

1
1
=
,
FSR 1 − FER(A.2)

where FSR denotes frame success rate.

AWGN Example
Consider Fig. 3-21 in [D23]. At SNR=1.6 dB, the FERs for lossy and lossless schemes are 0.138 and 0.98,
respectively. Let m = 1 and Pb = 0.03. Using A.1 and A.2 we get the call arrival rates 0.027 and 6.19 · 10−4 , i.e.,
lossy forwarding increases the Erlang capacity in the SNR 43.1 times.

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