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

Title

Interim Report of Detailed Coding/Decoding
Algorithms and Correlation Estimation Techniques

Author(s)Anwar, Khoirul; He, Xin; Hou, Jiancao;
Komulainen, Petri; Matsumoto, Tad; Matth´e,
Maximilian; Wolf, Albrecht; Yi, Na; Zhou, Xiaobo

Citation

ICT‑619555 RESCUE D2.1.1 Version 1.0: 1‑54

Issue Date

2014‑10Type

Research Paper

Text version

publisher

URL

http://hdl.handle.net/10119/13796

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
D2.1.1 Version 1.0
Interim Report of Detailed Coding/Decoding Algorithms andCorrelation Estimation Techniques

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:

10/2014
10/2014
Petri Komulainen
Khoirul Anwar, Xin He, Jiancao Hou, Petri Komulainen,
Tad Matsumoto, Maximilian Matthé, Albrecht Wolf, Na Yi,
Xiaobo Zhou
JAIST, TUD, UNIS, UOULU
WP2 – Code and algorithm design and optimization
PU
R
1.0
54

Abstract: The RESCUE project proposes a novel multi-route communication technology design targeted for
multi-hop networks, based on cooperative decode-and-forward (DF) relaying allowing intra-link errors andutilizing distributed turbo codes. This deliverable provides initial results and descriptions of the consideredcoding/decoding and correlation estimation algorithms. The state-of-the-art in simple relay network models issummarized, and new source-correlation estimation methods and signaling protocols are proposed. According to the numerical results, the decoding performance is close to the theoretical limit when the correlation is
known. Furthermore, more general system models are considered, including non-orthogonal multiple access,multi-hop communication where the destination is more than two hops away from the source, and multipleaccess relaying where two sources utilize a single relay node. In order to support system level development
and simulations, a new simulation abstraction concept is also proposed.

Keyword list: cooperative relaying, decode-and-forward, distributed turbo code, interleave division multiple
access, iterative decoding, lossy forwarding, multi-hop communication, wireless networks

Disclaimer:

RESCUE

D2.1.1 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 design targeted for multi-hop
networks that are subject to dynamic topology changes. This deliverable provides initial results and descriptionsof the coding/decoding and source-correlation estimation algorithms considered in the project.
The RESCUE cooperative protocol consists of decode-and-forward (DF) or extract-and-forward (EF) relayingthat allows intra-link errors, combined with distributed turbo coding that brings improved error protection. The
relaying nodes decode, interleave, and re-encode the data, which causes no bandwidth expansion compared tothe original signal. The possible decoding errors at the relaying nodes result in limited correlation between theforwarded packet copies. The destination combines the packet copies via iterative decoding, taking into accountthe correlations by properly weighting each copy. For the simple network model consisting of a single source, a setof parallel relay nodes, and one destination node, no major performance improvements by code design can be foundsince the performance of the state-of-the-art codes is already close to the theoretical limit when the correlation is
known.
One of the main remaining challenges lies in how to obtain the knowledge of the correlation between the relayed
data sequences to the destination. The decoding errors at relays result in bit-flipping between the original andforwarded sequences. Thus the correlation estimation is essentially bit error probability estimation. At the destination, the estimation is carried out along with the iterative decoding, and each received packet is treated separately.
The estimation has three phases. First, the log-likelihood ratio (LLR) samples to be used for estimation are selected. Then, pairwise bit error rates (BERs) between transmitted packets are estimated. Finally, the pairwise
BERs are used to resolve the actual transmitter-specific BERs. Several novel ideas to each phase are proposed
that, compared to the state-of-the-art methods, result in improved decoding performance and/or reduced complexity. An alternative approach is to estimate the BER already at the relays and then forward the information to thedestination. The estimate can be based on the signal-to-noise ratio (SNR) of the source-relay link. On the other
hand, if a cyclic redundancy check (CRC) is available, it makes sense for the relays to check it in order to identify
correctly decoded packets. It is a future design challenge to find a protocol that provides the best trade-off between
decoding performance, estimation complexity, and signaling overhead.
More general system models and their coding/decoding challenges are also considered. First, non-orthogonal
multiple access for the relay transmissions by employing interleave-division multiple access (IDMA) is proposed.
The approach improves spectral efficiency if multi-user detection (MUD) at the destination is used. Then, amultiple-access relaying model where two sources utilize a single relay node and communicate to a common
destination node is addressed. The relay applies network coding and transmits a single stream to aid the destinationin recovering the two sources.
When the network model is extended to cover more than two hops between the source and the relay, and when there
are multiple parallel relays at each stage, the decoding strategy at the relays needs to be designed. If complexity is
not an issue, the relays may carry out the same type iterative multi-packet combining as the destination does. On
the other hand, at the destination, the errors in the received packet copies may become correlated, when the sameerrors are transmitted by the parallel relays of the second stage. However, the cross-link problem does not seem tobe severe, at least when the error probabilities remain relatively low.
In the system level, and for the higher layer functionalities such as multi-rate control, power control, automatic
repeat request (ARQ) protocol, and medium access control (MAC), it is desirable to be able to run simulations
without the need to implement all the details of the physical layer. To this end, a quality mapping that predicts the
BER distribution at a receiver that combines multiple packet copies is also developed in this document.

Page 2 (54)RESCUE

D2.1.1 Version 1.0

Authors
PartnerName

E-mail / Phone

Japan Advanced Instituteof Science and Technology(JAIST)

Tad Matsumoto
Khoirul Anwar

matumoto@jaist.ac.jp
anwar-k@jaist.ac.jp

Technical University Dresden(TUD)

Maximilian MatthéAlbrecht Wolf

maximilian.matthe@ifn.et.tu-dresden.dealbrecht.wolf@ifn.et.tu-dresden.de

University of Surrey(UNIS)Na Yi
Jiancao Houn.yi@surrey.ac.uk
jiancao.hou@surrey.ac.uk

University of Oulu
(UOULU)

Petri Komulainen
Xiaobo Zhou
Xin Hepetri.komulainen@ee.oulu.fi / +358 294 482971
xiaobo.zhou@ee.oulu.fi
xin.he@ee.oulu.fi

Page 3 (54)RESCUE

D2.1.1 Version 1.0

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

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

3

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

5

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

6

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

8

2. Multi-route Relaying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1

2.2

2.3

System Models and Theoretical Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Single-Relay Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 CEO Relaying Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distributed Turbo Codes – Coding and Decoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Single-Relay Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 CEO Relaying Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2.1 Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2.2 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Single-Relay Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 CEO Relaying Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
11
12
12
14
14
14
16
16
18

3. Source Correlation Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1

3.2

3.3

Source Correlation Estimation at the Destination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 State-of-The-Art Algorithm and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Modification of the SoTA Estimation Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2.1 Threshold Adaptation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2.2 Reducing Estimation Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Novel Approaches for Pairwise Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3.1 Model-Based Unbiased Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3.2 Heuristic Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Numerical Results of Proposed Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4.1 Reference Scenario and State-of-The-Art Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4.2 Performance of Modified Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4.3 Performance of Novel Pairwise Estimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Source Correlation Estimation at Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The Source-Relay (S-R) Correlation Knowledge Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Performance Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3.1 Convergence Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3.2 BER Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20
20
22
22
22
24
24
24
25
25
25
28
31
31
31
32
32
33
34
34

4. Advanced Topologies and Access Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1

Interleave-Division Multiple-Access (IDMA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Code design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Single-User Detection (SUD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Multi-User Detection (MUD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36
36
37
38

Page 4 (54)RESCUE

4.2

4.3

D2.1.1 Version 1.0

4.1.4 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coding and Decoding for Multi-Hop Relaying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 System Model: Coding and Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Joint Adaptive Network and Channel Coding for Orthogonal Multiple Access Relay Channel . . . . . . .
4.3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1.1 Network Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Coding and Decoding Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2.1 Coding Structure at The Source and Relay Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2.2 Joint Network-Channel Decoding Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39
39
40
41
42
42
43
43
43
44
45

5. Support for System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.1
5.2

Multi-Rate Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Interaction with Higher Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Functional Block Diagram and Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Simulation Abstraction for Higher Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47
48
48
49

6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Page 5 (54)RESCUE

D2.1.1 Version 1.0

List of Acronyms and Abbreviations
Term
ACC
AF
ARQ
AWGN
BER
BLER
BPSK
BSC
CDMA
CEO
CF
CI
CRC
CSI
DACC
DF
EBSA
EESM
EM
EF
EXIT
FC
FEC
FER
GI
IDMA
IL
LI
LLR
LTE
MA
MAC
MAC
MAI
MAP
MARC
MARC-IE
MI
MCS
MSE
MUD
OFDM
P2P
PCCC
PHY
QAM
QPSK
RESCUE
S-DF
SDR
SINR

Description
Accumulator
Amplify-and-Forward
Automatic Repeat Request
Additive White Gaussian Noise
Bit Error Rate
Block Error Rate
Binary Phase-Shift Keying
Binary Symmetric Channel
Code-Division Multiple Access
Chief Executive Officer
Compress-and-Forward
Confidence Indicator
Cyclic Redundancy Check
Channel State Information
Doped Accumulator
Decode-and-Forward
EXIT-Constrained Binary Switching Algorithm
Exponential Effective SNR Mapping
Extended Mapping
Extract-and-Forward
Extrinsic Information Transfer Chart
Fusion Center
Forward Error Correction
Frame Error Rate
Global Iteration
Interleave-Division Multiple AccessInterleaver
Local Iteration
Log-Likelihood Ratio
Long-Term Evolution
Multiple AccessMultiple Access Channel
Medium Access Control
Multiple Access Interference
Maximum a Posteriori
Multiple Access Relay Channel
Multiple Access Relay Channel allowing Intra-link Errors
Mutual Information
Modulation and Coding Set
Mean Squared Error
Multi-User Detection
Orthogonal Frequency-Division Multiplexing
Point-to-Point
Parallel Concatenated Convolutional Codes
Physical Layer
Quadrature Amplitude Modulation
Quadrature Phase-Shift Keying
Links-on-the-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments
Selective Decode-and-Forward
Software-Defined Radio
Signal-to-Interference+Noise Ratio

Page 6 (54)RESCUE

SNR
SoTA
SPC
SPC-IrR
S-R
SUD
V2V
WP
WSN

D2.1.1 Version 1.0

Signal-to-Noise Ratio
State-of-The-Art
Single-Parity Check
Single-Parity Check and Irregular Repetition
Source-Relay
Single-User Detection
Vehicle-to-Vehicle
Work Package
Wireless Sensor Network

Page 7 (54)RESCUE1.

D2.1.1 Version 1.0

Introduction

The RESCUE project – “Links-on-the-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments” – aims to bring forth a novel communication technology design targeted for largely
unplanned multi-hop networks that are further subject to dynamic topology changes. The potential system scenarios for the links-on-the-fly concept have been described in D1.1 [D11]. The first scenario is public safety operations
that take place in areas where the communication infrastructure is partially inoperable due to a disaster such as anearthquake. The second scenario is vehicle-to-vehicle (V2V) communication, where cars and other vehicles share,for example, safety-critical information about the road and traffic conditions with each other. The identified communication applications range from video streaming and text messaging to group communication (push-to-talk),
automatic vehicle/person location, and cooperative collision warning. D1.1 also lists the identified key functional
requirements and design challenges for different protocol layers, from the physical to the network layer.
The RESCUE cooperative protocol consists of decode-and-forward (DF) relaying that allows intra-link errors,
combined with distributed turbo coding that brings improved error protection. The relaying nodes decode andre-encode the data, which causes no bandwidth expansion compared to the original signal. The possible decoding
errors at the relaying nodes result in limited correlation between the forwarded packet copies that the destination
takes into account when decoding. The basic principles of the RESCUE relaying strategy have been presented in[AM12a; ZHA+12; ZCA+12]. The main sources of performance gains in terms of spectral efficiency, transmit
power, and outage probability obtained by the links-on-the-fly technology are:• Route diversity: The signal is relayed via multiple (possibly unreliable) disjoint routes and combined at thedestination. Thus, the probability of successful reception increases.
• Utilizing the broadcast nature of radio transmission: Multiple relay nodes capture the original transmission,and thus more of the received signal energy is exploited.
• Lossy forwarding: The relay nodes allow decoding errors, and thus a higher number of relays are able toassist. Also, a higher portion of the received signal energy is thus exploited.
• Distributed turbo codes and iterative decoding: The parallel relays form together a very powerful lowrate forward error correction (FEC) code, which operates close to Shannon capacity. The decoder at thedestination utilizes source correlation as it knows that the data received via different routes is essentially thesame.
RESCUE is a three-year FP7 project that officially started in November 2013. Work Package 2 (WP2) “codeand algorithm design and optimization” started in the beginning of year 2014, and it will continue until the endof July 2016. In the beginning, the role of WP2 has been to identify, develop, and study channel coding anddecoding methods as well as source-correlation estimation algorithms applicable to the RESCUE system. Recently,
a new research item to study optimal transmit power allocation has started. While WP2 deals mainly with thephysical layer functionality, WP1 addresses the more fundamental information theoretic and wireless access related
aspects of cooperative multi-route relaying. On the other hand, WP3 takes the challenge of designing the necessary
matching packet-based higher layer protocols such as multi-rate coding control, medium access control (MAC),
automatic repeat request (ARQ) protocol, and routing. One essential task of WP2 is to support the development of
the higher layer functionalities. To this end, in order to enable fast system level simulations, totally new methodsof abstraction of the physical layer coding are under development in WP2. Finally, the work from WP2 and WP3will be integrated together by WP4 to implement and demonstrate the operation of the system over-the-air on
an software-defined-radio (SDR) testbed platform. Due to the common objectives, work is carried out in close
cooperation between all the technical work packages.
This deliverable provides initial results and descriptions of the coding/decoding and source-correlation estimation
algorithms considered in the RESCUE project. Chapter 2 addresses a simple network model consisting of a single
source, a set of parallel relay nodes, and one destination node. Here, the state-of-the-art coding and decoding
methods are motivated and reviewed, and some new performance results are shown. The iterative decoding at
the destination can benefit from the knowledge of the bit error probabilities of each of the relayed information
sequences. Thus, one of the needed algorithmic functionalities is correlation estimation that attempts to measure
the bit error probabilities. In Chapter 3, advances in the correlation estimation are presented. In Chapter 4, more

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general system models are considered. These include non-orthogonal channel access for the relay transmissions via
interleave division multiple access (IDMA), multi-hop networks where the destination is more than two hops awayfrom the source, and multiple-access relaying where two source nodes utilize a single relay node and communicate
to a single destination node. Finally, Chapter 5 describes the new simulation abstraction concept, “black box”, thataims to enable system level development and simulations. Furthermore, some preliminary code design choices for
the SDR implementation are disclosed.

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Multi-route Relaying

This chapter addresses a simple multi-route relaying network model consisting of a single source, a set of parallel
relay nodes, and one destination node as shown in Figure 2.1. Communication takes place in two phases. In phaseone, the source transmits and the other nodes receive. In phase two, the relays transmit by using orthogonal radio
resources, for example one at a time. There are one or more relays that take part in forwarding, and the direct
link between the source and the destination may or may not exist. The principles of the coding and decoding
algorithms based on distributed turbo codes, as first proposed in [ZHA+12; AM12a; ZCA+12], are described.
Numerical results of the performance in terms of bit error rate (BER) and frame error rate (FER) are shown forsome basic topologies, and compared to the performance figures predicted by the related theory.

Relay

SourceDestination

Relay

Figure 2.1: The general system model for multi-route relaying.

2.1

System Models and Theoretical Background

The research on cooperative communications using joint source, channel and network coding, has recently attracted
a lot of attention with the recognition of significant importance. In cooperative communication systems, multiple
mobile devices configure a virtual multi-terminal environment, and join in network-level cooperation, rather thanassembling a set of point-to-point (P2P) connections. In this section, we consider the fundamentals of multi-route
relaying problem from the viewpoint of network information theory.
2.1.1

Single-Relay Model

A single-relay model is a special case of the system shown in Figure 2.1, where just one relay node assists thedestination to recover the source information. The single-relay model can be seen as an application of the theorem
for source coding with a helper [GK11], in which the achievable compression rate region of correlated sources
is characterized. An example of the achievable compression rate region is shown in Figure 2.2 (simplified from
[ZCH+14]). The information sent from the source can be recovered by the destination only when the compressed
rate pair falls into this area. For instance, consider the case that two binary information sequences u1 by the source
and u2 by the relay are separately encoded, and jointly decoded at the destination. Here, u1 and u2 are compressedat the rates R1 and R2 , respectively. When applying the compression theorem to the context of transmitting overwireless channels, R1 and R2 translate to the normalized channel capacities of the source-destination and relaydestination channels [ZCH+14]. The achievable rate region is given by
R1 ≥ H(u1 |û2 ),(2.1)
R2 ≥ I(u2 ; û2 ),where û2 is the estimate of u2 at the destination, and H(·|·) indicates conditional entropy and I(·; ·) mutual information. Here, û2 serves as side information for the decoding of u1 , which does not have to be perfect. With thehelp of û2 , R1 can be further reduced to less than the entropy H(u1 ). The correlation of the sources can be modeledby the bit flipping model as a result of channel decoding at the relay [LTA+11], i.e., u2 = u1 ⊕ e and Pr(e = 1) = pe ,where pe is the bit-flipping probability (or BER) and ⊕ denotes binary exclusive OR operation. Assume that theappearance probabilities of the source bits 0 and 1 are equal. Then, H(u1 ) = H(u2 ) = 1, H(u1 |u2 ) = Hb (pe ),where Hb (pe ) = −pe log2 (pe ) − (1 − pe ) log2 (1 − pe ) is the binary entropy function.

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Achievable
Compression
Rate Region

Figure 2.2: The achievable compression rate region of theorem for source coding with a helper.
Now consider a one-way relaying system, where the relay does not aim to perfectly recover the original informationtransmitted by the source, but it only “extracts” the source information, even though the relay knows that extracted
sequence may contain some errors. This greatly reduces the computational complexity at the relay. The extracted
sequence represents an estimate of the original information sequence, which is then interleaved and transmitted
to the common destination. Obviously, the original and extracted sequences are correlated. As shown in [Tho08;
AM12b; AM12a; CIA+12], even though extraction has relative weak error correction performance at the relay,
excellent performance after joint decoding at the destination can still be achieved through the log-likelihood ratio(LLR) exchange between the decoders, where the correlation of the intra-link is taken into account.
Obviously, the performance can be further improved by performing FEC decoding at the relays as well. In thiscase though, the errors in the forwarded sequences become bursty instead of independent. Thus, it is imperativethat the correlation is determined for each code block separately instead of employing average BER estimates.
2.1.2

CEO Relaying ModelIn the single-relay model, there is only one relay, and the direct link between the source and the destination always
exists. As an extension of single-relay model, a relay system with multiple relays and in the case when the direct
link is non-existent (negligible), is also of interest to the RESCUE project. With the links-on-the-fly concept,
all the messages forwarded by the relays are potentially lossy, and the destination intends to recover the original
information transmitted from the source based on the multiple erroneous messages forwarded by the relays. It isclear that if all the forwarded sequences are erroneous, the destination cannot fully recover the original data either.
Instead, some distortion, i.e., non-zero BER, will remain after the iterative joint decoding at the destination as well.
This is called the error floor since it cannot be reduced by increasing the SNRs of the relay-to-destination links.
The problem of combining data from uncertain observers – relays in our case – is referred to as the the chief
executive officer (CEO) problem [BZV96] in network information theory. Here, for simplicity, we assume the error
probabilities happening in the source-relay links are fixed values, and the whole system is referred to as parallel
CEO relaying. It should be emphasized here that the parallel CEO relaying model is equivalent to a wireless sensor
network (WSN) model where the different sensors are observing the same source phenomenon, and the observation
errors are modeled by bit-flipping. In [ZHA+12; HZA+13], we intensively studied the coding/decoding design for
WSNs from the viewpoint of the CEO problem.
The quadratic Gaussian CEO problem in which the source and the multiple observations are assumed to be jointly
Gaussian distributed, was studied in [Ooh98; VB97]. Besides the theoretical work, a successive coding and decoding algorithm was proposed in [BS05] based on the derived rate-distortion function for the parallel Gaussian
CEO problem, and the optimal rate allocation scheme in order to achieve the minimal distortion under a sum-rate
constraint was further considered in [BS09] for the successive coding/decoding strategy. An iterative joint decoding algorithm for the binary data gathering WSNs was proposed in [HBP08], where the convolutional code isapplied as the coding scheme at the sensor node to protect the data transmitted over noisy links between the sensors
and the fusion center (FC). 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

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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 was derived for verifying the bit error
rate (BER) performance by taking into account the error probability of the observed data sequence. In [RA12],an adaptive bi-modal decoder for a binary source estimation involving two sensors was proposed based on themodified extrinsic information transfer (EXIT) chart analysis.
2
Slepian−Wolf losslessBerger−Tung inner bound (lossy)

1.8
1.6
1.4

R2

1.2
1
0.8
0.6
0.4
0.2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

R1

Figure 2.3: The admissible rate region of Slepian-Wolf theorem and rate-distortion region of Berger-Tunginner bound.
Let us take the CEO relaying model with two relays as an example, and let u1 and u2 denote the data sequences
forwarded by the two relays, respectively. Here, the destination aims to resolve both two relayed sequences.
Assume u1 and u2 are described at rates R1 and R2 , respectively, then the rate-distortion derived based on the
Berger-Tung inner bound [GK11] isR1 ≥ I(u1 ; v1 |v2 ),
R2 ≥ I(u2 ; v2 |v1 ),(2.2)
R1 + R2 ≥ I(u1 , u2 ; v1 , v2 ),where v1 and v2 are the descriptions of u1 and u2 , respectively, created and forwarded by the relays. The admissible
rate-distortion region is depicted in Figure 2.3 with some given distortion levels. As a special case, if the distortions
for u1 and u2 are both 0, the problem has already been solved by the Slepian-Wolf theorem [SW73], with which
the admissible rate region is
R1 ≥ H(u1 |u2 ),
R2 ≥ H(u2 |u1 ),(2.3)
R1 + R2 ≥ H(u1 , u2 ).
The admissible rate region of the Slepian-Wolf theorem is also shown in the same figure for comparison. It
is clearly found that by accepting some distortion in u1 and u2 at the destination, the rate-distortion region of
CEO relaying model can be further expanded. This indicates that further compression at the relays is allowed, or
equivalently, in the wireless channel transmission, transmit powers can be reduced.

2.2

Distributed Turbo Codes – Coding and Decoding

2.2.1

Single-Relay ModelIn our simple one way relay system, both the relay and the destination receive the signal from the source node
during phase 1. At the relay node, the information (systematic) bits are recovered, either by performing channel
decoding or even by extracting the systematic part of the coded bits, before being re-transmitted. During phase 2,

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the recovered bits (may contain some errors) are interleaved, re-encoded again, and forwarded to the destination
node.
SourcePhase 1
De-M
2
Phase

QPSK

Phase 1

ACC

De-M
De-M
ACC

QPSK

Relay
Destination

Figure 2.4: The structure of the relay system.
The block diagram of the proposed relay system is shown in Figure 2.4. In this system, we do not need strong
codes: only memory-1 half rate (R = 1/2) systematic non-recursive convolutional code (SNRCC) is adopted forboth encoders C1 and C2 . At the source node, the original information bits b1 are first encoded by C1 . After that, theencoded bit sequences are interleaved by Π1 and doped-accumulated by ACC (with a doping rate Pd1 ≥ 1). Then,they are modulated into symbols s by using quadrature phase-shift keying (QPSK) modulation, and transmitted toboth the relay and the destination during the first time slot. The details of the doped accumulator are shown in
Figure 2.5.

M
Figure 2.5: Doped accumulator. The switch selects every Pd th output bit from the accumulator, while theother Pd − 1 outputs are systematic.
At the relay node, the received signals first go through the demapper, ACC−1 and the de-interleaver Π−1
1 . Then,the original information bits u1 are recovered by making hard decisions of the output of the decoder D1 , which isdenoted as u2 . After that, the recovered bits are interleaved by Π0 and then go through the channel encoder C2 ,the interleaver Π2 and the ACC (with doping rate Pd2 ). Then the data are modulated into sr , and transmitted to thedestination during the second time slot.
At the destination node, the received signals ysd and yrd first go through the horizontal decoding processes as canbe seen in Figure 2.4, where the combination of the demapper and the ACC exchange information with the channel
decoders through horizontal iterations (HI) [AM12a]. After every HI, the extrinsic LLRs obtained from the two
decoders D1 and D2 are also exchanged with several vertical iterations (VI), through an LLR updating function fc[GZ05]. The fc function is defined asfc (L, pe ) = ln

(1 − pe ) exp(L) + pe,
(1 − pe ) + pe exp(L)(2.4)

where L represents the input LLR sequence into the fc function, which are Leu1 and Leu2 as shown in Figure 2.4.
Function fc can be obtained by first converting the LLR into the probabilities of the systematic bits being ”0”and ”1”, and then modifying the values by taking into account the knowledge of pe . The purpose of function
fc is to avoid the error propagation while exchanging likelihood information between HI and VI. By doing this,the extrinsic LLR (systematic part) forwarded from the relay helps decoding of the original bits by exploiting thecorrelation knowledge between the source and the relay. Finally, the original information can be recovered bymaking hard decisions of the a posteriori LLRs at the output of D1 .

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2.2.2
2.2.2.1

D2.1.1 Version 1.0
CEO Relaying Model
Transmitter

Figure 2.6 illustrates the CEO relaying model to be analyzed. An uncoded binary source u, where the bits are
independent and evenly distributed between zeros and ones, is transmitted to multiple relays. Since hard decisions
are always performed at the relays, we may simply use a bit-flipping model to randomly generate errors in thedata sequence. The received information uk can be seen as the output of a binary symmetric channel (BSC) withassociated crossover probability pk when u is the input, i.e., uk = u ⊕ ek where ”⊕” denotes the binary exclusive
OR operation. Consequently, the bit sequences are correlated with each other since they have the common input uof the independent BSCs.

ACC

+

+

+

+

BPSK

Joint
Decoder
Source++++RelaysDestination

Figure 2.6: A schematic diagram of a parallel CEO relaying model [HZJ+14].
The k-th relay encodes its data uk by an encoder ENCk and transmits the corresponding coded data to the destination. For simplicity, we assume simple serially concatenated convolutional codes with binary data transmission.
The data uk is, first of all, interleaved by an interleaver Πk,1 whose role is to enable the global iterative decoding
process to utilize the correlation knowledge. The interleaved sequence is then encoded by an encoder Ck resulting
in the coded sequence ck . It is further interleaved by another interleaver Πk,2 , the length of which depends on thecode rate Rck of the encoder Ck . After that, the interleaved version of ck is doped-and-accumulated by a so-called
accumulator ACC [AM12a] with a doping ratio Pd . Finally, the modulated symbol sequence sk ∈ {+1, −1}, generated by binary phase-shift keying (BPSK) modulation for the doped-accumulated binary sequence, is transmitted
over AWGN channels to the destination at different time slots. Therefore, the received signal yk at the destinationfrom the k-th relay is simply expressed asyk = sk + wk ,(2.5)
where wk ∼ C N (0, σ 2 ) is a complex white Gaussian noise sequence with the variance per dimension σ 2 .
2.2.2.2

ReceiverThe block diagram of the joint decoding technique is shown in Figure 2.7. Because of the fact that the received
data sequences from the relays are highly correlated, global iteration (GI) is introduced in the iterative decoding
process with the view to utilizing the correlation knowledge, i.e., the extrinsic LLR is exchanged between GI and
local iteration (LI) to enhance the BER performance.
The decoding process is divided into following steps:

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+_

...
+_

Variable
Node

...
+_

: LI

: GI

Figure 2.7: The joint decoding strategy utilizes correlation knowledge among the relays’ data through global
iteration [HZJ+14].
1. Initialization: The channel state information is fully known to the destination. Thereby, after receiving thesignal yk from the k-th relay, the channel LLR Lck is calculated by
Lck =2ℜ(yk ),
σ2(2.6)

where ℜ(·) takes the real part of a complex value in its argument. In addition, the extrinsic LLR Leck of thecoded bits and the a priori LLR Lauk of the systematic bits, which are corresponding to the a priori LLR fed
back to ACC−1 after interleaving, and the a priori LLR to Dk , respectively, are set to 0.
2. LIs are performed between ACC−1 and Dk , k = 1, · · · , K, simultaneously.
3. The extrinsic LLR Leuk , which is obtained by subtracting the a priori LLR Lauk from the a posteriori LLR
p
Luk , is deinterleaved by Π−1k,1 and then updated through function f c ase
Leu,k = fc {Π−1k,1 (Luk ), pk }.

(2.7)

4. A degree K variable node combines K − 1 extrinsic LLRs Leu, j , j 6= k, obtained as the results of LIs, tocalculate the message fed back to the decoder Dk of the k-th LI. Thus, the a priori LLR Lau,k is then obtainedasLau,k = ∑ Leu, j ,
(2.8)
j∈κ\k

where κ = {1, 2, · · · , K} is the set of the indices of the relays, and κ\k means removing k from the set κ.
5. The output of fc (Lau,k , pk ) is interleaved by Πk,1 to form the a priori LLR Lauk which is fed back to Dk in thecorresponding k-th LI.
The decoding process is performed in an iterative manner where Steps 2) to 5) are repeated with the switches
shown in Figure 2.7 being closed except in the final iteration, since the exchanged information between decoders
should be extrinsic according to the turbo principle.
In the final iteration, the switches are all opened, and a hard decision on u is made to make a final estimate û of u,pbased on the a posteriori LLR Lu originated by summing up all the deinterleaved and fc -updated versions of the apposteriori LLR Luk .

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2.3

Numerical Results

2.3.1

Single-Relay Model

Three relay location scenarios are considered, as shown in Figure 2.8. Generally, the relay node can be allocatedcloser to the source node in Location A or closer to the destination in Location B, or the three components keep
the same distance from each other in Location C. The geometric gain of the source-relay (sr) link with regard to
the source-destination (sd) link can be defined as
 α
dsd
,
(2.9)
Gsr =
dsr
where the path loss exponent α is assumed to be 3.52 [YG11] in our simulations. It is straightforward to derive
the geometric-gain of the relay-destination (rd) link Grd in the same way. Moreover, without losing the generality,
the geometric-gain of the source-destination link, Gsd , is fixed to one. Therefore the received signals yi j (i j ∈{sr, sd, rd}) at the relay and the destination node can be expressed as:√(2.10)
ysr = Gsr · hsr · s + nsr ,√ysd = Gsd · hsd · s + nsd ,(2.11)√
yrd = Grd · hrd · sr + nrd ,(2.12)
where s and sr represent the symbols transmitted from the source and the relay, respectively. The fading channel
gain, hi j , is equal to one in the additive white Gaussian noise (AWGN) channel. The notation ni j represents thezero-mean AWGN noise of the three links with variance σi2j . The signal-to-noise ratio (SNR) of source-relay andrelay-destination links at each location scenario are evaluated as follows: given the path loss parameter α equals to
3.52 [YG11], we have SNRsr = SNRsd + 21.19 dB and SNRrd = SNRsd + 4.4 dB in Location A; SNRsr = SNRsd+ 4.4 dB and SNRrd = SNRsd + 21.19 dB in Location B; SNRsd = SNRrd = SNRsr in Location C.

Figure 2.8: Simulation setups for single-relay transmission. dsd denotes the distance of the source-relay link
[CZA+12].
Figure 2.9 shows the BER performances of the proposed relay system using QPSK with natural (Gray) mapping
rule, where the frame length of the transmitted information is set at 10000 bits in the simulations. Based on the
EXIT analysis, 30 horizontal iterations are performed at the destination node and meanwhile 5 vertical iterations
take place between the two decoders D1 and D2 during each horizontal iteration.
The turbo cliff can be achieved by using our technique in the relay system over AWGN channels. It can be seenfrom Figure 2.9 that, when performing the channel decoding at the relay node, the BER performance in Location
A is much better than that of the other cases. The reason is that, when the relay is close to the source, the geometricgain of the intra-link is large and the intra-link error probability pe is very small. In other words, the recovered
bits at the relay node are highly correlated with the original information at the source node, and the decoder D2
at the destination is able to provide very reliable extrinsic LLRs of the information bits, which can be fed into thedecoder D1 as the a priori information. Hence, the Location C’s case has the worst BER performance because
there is no geometric gain when the source, relay and destination nodes are equally separated.
On the other hand, Figure 2.9 also presents the BER curves by using extract-and-forward (EF) relay strategy, where
only the systematic part of the coded bits are extracted, without performing channel decoding at relays. It can beclearly seen that the intra-link BER performance of the EF scheme is worse than that of the decode-and-forward

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0

10A, decoding
B, decoding−1

C, decoding

10

A, extraction
B, extraction
C, extraction
−2

BER

10

−3

10

−4

10

−5

10

−6

−5

−4

−3

−2

−1
SNR

sd

0
(dB)

1

2

3

4

5

Figure 2.9: BER performance of the proposed system with QPSK in AWGN channel [CZA+12].
0

10

P2P
Location A
Location B
Location C−1

Frame Error Rate

10

−2

10

−3

10

0

2

4

6

8
SNRsd (dB)

10

12

14

16

Figure 2.10: FER performance of the proposed system with QPSK in block Rayleigh fading channel[CZA+12].
(DF) scheme. However, it has to be noted that the EF scheme can achieve almost the same BER performance as
DF in Location A. This is because that the intra-link is very strong when the relay is close to the source node, andboth of the DF and EF strategies can almost fully recover the original bits at the relay. When the relay node is close
to the destination as in Location B, there is about 1 dB gap between the BER curves of DF and EF schemes. In thecase of Location C, the BER gap between DF and EF is much smaller than that of Location B’s case.
According to [CBV05], with code rate 1/2, the Shannon/SW limit for Location C for Gaussian codebook is -1.55
dB. Therefore, as can be seen from Figure 2.9, the gap of the proposed system to the theoretical limit in Location
C is 2.75 dB.
Finally, the frame-error-rate (FER) performance in block Rayleigh fading channels is shown in Figure 2.10. Theinterleaver lengths are set at 4400 bits. The point-to-point (P2P) transmissions are simulated for comparison.
Similarly to the AWGN channel cases, the proposed system achieves better FER performance when the relay iscloser to the source.

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2.3.2

D2.1.1 Version 1.0
CEO Relaying Model

A series of simulations has been conducted to verify the results of our proposed coding/decoding techniques. This
subsection provides the results of the simulations. The common parameters assumed in the simulations were set
as follows• Block length n = 10000 bits.
• Interleavers: random.
• Encoder Ck , k = 1, · · · , K: rate Rck = 12 nonrecursive systematic convolutional code with generator polynomial
G = [03, 02]8 , where [·]8 represents the argument is an octal number.
• Doping ratio Pd = 1.
• Decoding algorithm for Dk and ACC−1 : log-maximum a posteriori (MAP).
• The number of iterations: 50 times.
• The SNR of each relay node is assumed to be the same.
Figure 2.11 illustrates the BER performance of the technique presented in [ZHA+12] and [HZA+13] with thenumber of relays K = {2, 4, 6, 8}. The new results of the theoretical analysis presented in [HZJ+14] are also
shown. In the simulations, the error probabilities pk were all set to 0.01. It can be clearly seen that in all the cases,
the BER curves exhibit sharp drop in the values at their corresponding threshold SNR values, like turbo-cliff of theturbo-codes. The difference between the threshold SNR obtained by the simulations and the theoretical analysis
are {1.61, 1.65, 1.88, 1.92} dB for K = {2, 4, 6, 8}. Furthermore, the sharp decrease in BER suddenly plateaus at
higher SNR values, where the error floor appears.
Figure 2.12 shows the BER performance with K = {3, 5, 7}, where the error probabilities pk were set at unevenvalues that are shown in the caption of Figure 2.12. Even in these cases, the BER performance gap to the theoreticallimits are about {1.52, 1.73, 1.8} dB.
0

10

K=2
K=4
K=6
K=8

−1

10

1.61dB
−2

10

−3

10

BER

1.65dB−4

10

1.88dB−5

10

1.92dB
−6

10

−7

10
−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

SNR per sensor (dB)Figure 2.11: BER performance of our proposed technique with the number of relays K = {2, 4, 6, 8}. pk are
set at 0.01. The corresponding SNRlim are plotted in vertical dash-dot lines. The approximatederror floors and the lower bounds plb of the error floors are presented in horizontal dashed anddash-dot lines, respectively [HZJ+14].

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0

10

K=3
K=5
K=7

−1

10

−2

10

1.52 dB

−3

BER

10

1.73 dB

−4

10

−5

10

1.8 dB
−6

10

−7

10

−8

10
−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

SNR per sensor (dB)Figure 2.12: BER performance comparison with the number of relays K = {3, 5, 7}.
The observation error probabilities are distributed as pk = {0.025, 0.075, 0.002}, pk ={0.0145, 0.005, 0.025, 0.015, 0.03}
andpk = {0.01, 0.015, 0.02, 0.05, 0.005, 0.0003, 0.02}[HZJ+14].
It is also found that the error floors shown in Figures 2.11 and 2.12 are placed between the results of the Poissonbinomial approximation (upper bound) and the rate-distortion lower bound. It is clearly seen that the error floors
found by simulations match well with the values obtained in Poisson-binomial approximation. The elimination of
the error floor is impossible since the errors are inserted before encoding at each relay node, even though the floor
can be made very small because of the combined use of LI and GI.

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3.

Source Correlation Estimation

3.1

Source Correlation Estimation at the Destination

In order to utilize the correlation knowledge in the decoding process, the correlations need to be estimated somehow. The estimation may be carried out at the destination as part of the iterative decoding process so that after
each global iteration the estimates are refined. In this section, several methods are described that can improvethe estimation performance of the relay errors. With an improved estimation, the decoding performance of thedestination can be significantly improved. Initially, the state of the art algorithm is repeated and its performance ispresented. Then, the influence of the threshold T is investigated and an adjusted value is proposed. Moreover, theinfluence of the estimation variance on the decoding performance is described and methods for reducing the estimation variance, further improving the decoding performance. In addition to modifications of the state-of-the-art(SoTA) estimator, new estimators are presented. Finally, the performance of the proposed estimators is analyzed
with the help of simulations.
3.1.1

State-of-The-Art Algorithm and Performance

In [HZA+13], we proposed a nonnegative constrained iterative algorithm to estimate the observation error probabilities, which is also referred as the source correlation. Assuming that the bit decision errors made by the relays
are uncorrelated, and that the bit error probability at relay i is pi , the following pairwise equations holdqi j = pi (1 − p j ) + p j (1 − pi ),(3.1)

for i = 1, · · · , K; j = 1, · · · , K; and i 6= j. Here, qi j is the pairwise bit error probability, i.e., the probability that a bitin the sequence of relay i differs from the corresponding bit in the sequence of relay j. We choose K pairs of thecorrelation equations in [HZA+13] to estimate the error probabilities pi as
p̂i + p̂ j − 2 · p̂i · p̂ j = q̂i j ,where, i = 1 · · · K,

j = i + 1 if i = 1 · · · K − 1,
j = 1 if i = K,

(3.2)

where following [GZ05], the a posteriori LLRs at the output of the two decoders are utilized in the pairwise error
probability estimation aspq̂i j =p

exp(Lui ,n ) + exp(Lu j ,n )1 N,∑
N n=1 [1 + exp(Lup i ,n )] · [1 + exp(Lup j ,n )](3.3)

where N represents the number LLR pairs with their absolute values larger than a given threshold T . Since thereliability of q̂i j is influenced by N, it is important to choose an appropriate T value. However, how to determine
the optimal T was not studied in [HZA+13].
We can reformulate (3.2) by introducing the identity matrix I of size K and a matrix J defined by (3.5), into thefollowing form:[(I + J) − 2 · diag(p̂) · J] · p̂ = q̂,(3.4)

where, p̂ = [ p̂1 , p̂2 , · · · , p̂K ]T , and q̂ = [q̂12 , q̂23 , · · · , q̂K1 ]T . The diag(·) is the operator that forms a diagonal matrix
from its argument vector, and J is defined as follows:
0 1 0 0 ···0
0 0 1 0 · · · 0J = . . . .
(3.5)..  .
 .. .. .. ..
. 
1 0 0 0 ···0
Now, our objective is to find a nonnegative vector p̂ that minimizes kAp̂ − q̂k2 , which is formulated as follows:
min kAp̂ − q̂k2
s.t p̂  0,

(3.6)

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K=4 (Estimated)
K=4 (Known)
K=7 (Estimated)
K=7 (Known)
K=12 (Estimated)
K=12 (Known)
K=16 (Estimated)
K=16 (Known)

−1

10

−2

Bit Error Rate (BER)

10

−3

10

−4

10

−5

10

−6

10
−13

−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

SNR (dB)

Figure 3.1: BER performance comparison for different numbers of relays [HZA+13].
where, A = [(I + J) − 2 · diag(p̂) · J]. Now, vector p̂ is also inside matrix A. Therefore, problem (3.6) is solved
multiple times, and matrix A is updated in every iteration. The iterative algorithm is summarized in Algorithm
1. In this algorithm, we use the standard nonnegative least squares (lsqnonneg) [CP07] proposed by Lawson and
Hanson.
Algorithm 1: p estimator
Input: q̂, ε, Pre-defined maximum iterations ITm
Output: p̂  0 such that p̂=arg min kAp̂ − q̂k2
Initialization: p̂(0) = 0, Calculate A and ∆(0) = kAp̂(0) − q̂k2
for h = 1 to ITm do
Calculate p̂(h) by solving (3.6) using lsqnonneg algorithm;
Update A = [(I + J) − 2 · diag(p̂(h) ) · J];∆(h) = kAp̂(h) − q̂k2 ;if ∆(h) ≥ ∆(h − 1) then
Stop;
end
if kp̂(h) − p̂(h−1) k2 ≤ ε thenp̂ = p̂(h) ;
Stop;
end
end
p̂ = p̂(ITm ) ;Figure 3.1 shows the BER performances in AWGN channel for the cases where estimated p̂ and known p areused at the destination, with the number K of relays as a parameter. The decoding errors at relays were generated
via the bit-flipping model with pi = 0.01 for all i. At each relay, a half rate memory-1 nonrecursive systematic
convolutional code and a doped accumulator with doping ratio 1 was used. In the error probability estimator, Tand ε were set to 2 and 10−6 , respectively, and the maximum iteration times, ITm , were set at 20.
It is found from the figure that the BER performance can be improved by increasing the number of relays K. WithK = 4, the error floor can not be reduced to less than 10−4 by increasing per-link SNR, however it can be reduced
to less than 10−6 with K ≥ 7. Nevertheless, we believe that it is impossible to totally eliminate the error floor,
even though it may happen at a very small BER region. The reason is because we can not completely eliminate thedistortion due to the observation error, which is common to the CEO problems. Compared with the case where p
is known, only 0.3 − 0.5 dB loss in per-link SNR is observed when using estimated p̂, and the loss depends on thenumber K of the relays.

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3.1.2
3.1.2.1

D2.1.1 Version 1.0
Modification of the SoTA Estimation Algorithms
Threshold Adaptation

According to (3.3), the pairwise error probability is estimated based on a subset of the received samples, which
are selected based on the magnitude of their decoded LLR, where the threshold is given by T . The thresholdhas a significant influence on the position of the waterfall region. The optimal estimation threshold can be foundby computing a look-up table for optimal thresholds for each link’s SNR by simulating the decoding processwith random data in an AWGN channel. Hence, the look-up table is pre-defined by simulations. The according
algorithm is provided in Algorithm 2.
Algorithm 2: Computation of look-up table for optimal threshold
Input: ε, maximum iteration M, SNR list
Output: Look-up table T (SNR)
Initialization: T (SNR) = 2.5
for n = 1 to length(SNR) dot n,m = T (SNR[n − 1])for m = 1 to M do
Run Joint Decoder simulation with SNR(n) and T = t n,m , Output p̂(n,m)
if MSE(p̂(n,m) )≤ ε thenT (SNR(n)) = t n,mExit forend
if MSE(p̂(n,m) )≥MSE(p̂(n,m−1) ) thenT (SNR(n)) = t n,m−1
Exit forend
t n,m+1 = t n,m − 0.05
end
end
Basically, for each SNR the optimal threshold is determined as the T which minimizes the mean squared error
between estimated and correct bit flipping probability pk . It is assumed that the optimal T decreseases withincreasing SNR, since decoding performance in the horizontal iterations in the destination is more reliable on its
own and hence the LLR after horizontal iterations can also be considered more reliable at smaller values.

3.1.2.2

Reducing Estimation VarianceIn the SoTA estimation algorithm, the error probability of the relays is calculated based on the estimated pairwise
error probability between the relays. Though this estimator tends to be unbiased (see Section 3.1.4.1) at higher
SNR, the variance of the estimated errors is also an important aspect, since it determines the accuracy of every
single run of the estimator.
In particular, if the actual relay error is very low, it may happen during global decoding iterations that the reference
estimator calculates an error probability close to zero. In this case, the update function fc does not damp therelay’s LLR and hence other relays are outvoted by this particular relay. Accordingly, the BER at the destination isdetermined by the error of this particular relay. The behaviour of this singular estimation is illustrated in Figure 3.2.
Hence, it is not only necessary to have an unbiased estimation but also an accurate estimation with low variance.
In the following, two approaches for reducing the estimation variance are described.
Estimation with Different Relay Combinations Let p̂ = ET (q(K)) be the execution of the estimation via Algorithm 1 with the resulting estimated relay errors p̂ and the threshold T . There,q(K) = {qKK ,K1 } ∪ {qK j ,K j+1 | j ∈ {1, 2, . . . , K}}(3.7)

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Estimated relay errors in iterations
0.2

BER of the destination−110

p1 = 0.17
p2 = 0.19
p3 = 0.03
p4 = 0.19
p5 = 0.13
p6 = 0.02
p7 = 0.06

0.1

10−2

0
2

4

6

8

10−3

10

2

4

Iteration index

6

8

10

Iteration index

Figure 3.2: Example of singular estimation for p̂6 → 0 and resulting BER. K = 7 with correct error probabilities in the legend and estimated values in the diagram. As the p̂6 → 0, the BER at the destination
tends to the BER of this particular relay.

qK7 ,K1
qK1 ,K2
SK1

qK2 ,K3
SK2

qK3 ,K4
SK3

qK4 ,K5
SK4

qK5 ,K6
SK5

qK6 ,K7
SK6

SK7

Figure 3.3: Illustration of selection of pairwise error probabilities.
describes the pairwise error probabilities between the relay pairs indexed in the vector K, where K j denotes the jthelement of K. The process of selecting the qi j is illustrated in Figure 3.3 where Su denotes LLR of the uth relay. The
estimation of the relay errors of the proposed algorithm in [HZA+13] is therefore given by p̂ = ET (q([1, 2, . . . , K])).
Hence, the proposed estimator only considers one combination of pairwise error probabilities of the relays toestimate the relay errors.
In order to reduce the estimation variance with the help of the law of large numbers, the estimated relay errors canbe calculated as the mean of estimated errors for different permutations of pairwise error probabilities. Hence, an
improved estimate p̂i is given by
p̂i =

1 PK
∑ ET (q(Pp ({1, 2, . . . , K}))),
PK p=1(3.8)

where PK denotes the number of permutations of K elements, given by PK = K! and Pp (K ) denotes the pth permutation of the set K . The performance improvement of this technique greatly depends on the number available
permutations and hence on the number of relays in the network.
Least-Squares Solution of Over-Determined System From the pairwise error probabilities qi j , the proposed
algorithm in [HZA+13] solves the following equation system to calculate the relay errors p̂i with a non-negative
constrained least squares solution:

q12 = p̂1 + p̂2 − 2 p̂1 p̂2

q23 = p̂2 + p̂3 − 2 p̂2 p̂3..
.

qK,1 = p̂K + p̂1 − 2 p̂K p̂1(3.9)(3.10)(3.11)(3.12)

Hence, to calculate K relay errors, K equations
and K pairwise estimated errors are considered. However, accordingto the handshake problem [BK04], K2 different pairwise errors can be estimated and hence be used as input forPage 23 (54)RESCUE

D2.1.1 Version 1.0

Algorithm 1 to estimate the relay errors p̂. With this approach the estimation accuracy can be increased since aleast squares solution is found which utilizes the complete information of the system and not only a subset.
3.1.3

Novel Approaches for Pairwise Estimators

This section presents some novel pairwise error probability estimators that are studied with the hope of improving
the estimation accuracy compared to the state-of-the-art estimator (3.3). Here, two correlated sequences of LLRs
are compared packet-by-packet to estimate the probability of error between the two sequences. Since the decoding
process produces error bursts rather than scattered errors, in reality the number of errors between blocks may vary
greatly. Thus, the number of samples to use is always limited to the code block length N.

3.1.3.1

Model-Based Unbiased Estimator

Let the estimator input be two sequences of LLRs: L1 (n) and L2 (n), n = 1, 2, ..., N, where N is the code block length
in terms of data bits. When obtained directly via Gaussian channel and assuming binary modulation ui ∈ {±1},the corresponding LLRs can be written as√(3.13)Li (n) = 2γi ui (n) + 2 γi zi (n), i = 1, 2
where γi is the per-bit SNR for sequence i, and zi (n) is a real unit-variance zero-mean Gaussian random variable.
Here, the data amplitude or mean is 2γi , and the variance of the noise is 4γi . The mean and the variance areconnected by the consistency relation mean = variance/2 [Bri01]. We assume that this consistency holds also forpost-decoding LLRs, and utilize it in the estimation of q. It is also assumed that γi is constant (flat) over eachestimation period (code block).
We calculate the powers of and the cross-product between the LLR sequences as
Pi ,

1 N
∑ |Li (n)|2 ,
N n=1

C,

1 N
∑ L1 (n)L2 (n),N n=1

i = 1, 2(3.14)(3.15)and obtain the statistical properties
E[Pi ] = 4(γi2 + γi ),i = 1, 2

E[C] = 4(1 − 2q)γ1 γ2 ,(3.16)(3.17)

where the pairwise error probability q , Pr(u1 (n) 6= u2 (n)). Now, estimates of the sequence-specific SNRs and of
the error probability q can be solved as
1 pγˆi = ( Pi + 1 − 1), i = 1, 2
(3.18)
2
1
C).
(3.19)q̂ = (1 −2
4γˆ1 γˆ2
These estimates are unbiased asymptotically, i.e., when N grows large. It can also be seen that the SNR estimates
are always non-negative. However, q̂ may get negative values as well. The negative values can easily be avoided
by truncating negative values to zero.
The model-based estimation is sensitive to the assumptions. If the a-posteriori LLRs from the decoder output turnout not be not consistent, or if the channel (SNR) over the code block is not flat, the estimator performance will
degrade.

3.1.3.2

Heuristic Estimators

The simplest pairwise error probability estimator one can think of is ”hard” BER counting, where we just calculate
how many times L1 (n) and L2 (n) have different signs. At low observation SNR, this kind of estimator is poor due

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to the high rate of decision errors in the observed sequences. In this case, the estimator is counting the bit errors
caused by the relay-destination channels instead of the underlying errors that were made at the relay. When SNR
grows, BER counting will produce accurate results.
As a refinement to the hard BER counting, we introduce ”soft” BER counting defined as1∑Nn=1 L1 (n)L2 (n)
.
1− N
q̂ =
2
∑n=1 |L1 (n)L2 (n)|(3.20)

Here, the uncertain samples with low magnitudes get lower weighting in the estimation, while the certain samples
with high magnitudes are weighted more. Soft BER is consistent with hard BER in the sense that if all samples
have equal magnitude, the two estimators are equal. Furthermore, both hard and soft BER counts get values only
between 0 and 1.
3.1.4
3.1.4.1

Numerical Results of Proposed Estimators
Reference Scenario and State-of-The-Art Performance

To investigate the decoding and estimation performance with the proposed estimation algorithms, we consider the
CEO system model described in Section 2.2.2 and Figure 2.6 with K = 7 relays, where the error probabilities of
the BSCs are given by the values in Table 3.1. Each block contains of N = 1000 payload bits. Figure 3.4 shows the
decoding performance at the destination. There, an AWGN channel is considered, where each channel between
the relay and the destination has the provided SNR. Figure 3.4 shows both the decoding performance with known
correlation and with the correlation estimated by the SoTA algorithm provided, where T = 2. With higher SNR(SNR> −2.5dB), the correlation estimation becomes unbiased, but at lower SNR the estimation performance isvery inaccurate. Hence, according to the figure, both the waterfall region and error floor can be improved with
better correlation knowledge. Accordingly, the waterfall region can be shifted to the left by 1.4dB.
Table 3.1: Bit flipping probabilities for the considered scenario.
k
pk

1
0.17

2
0.19

3
0.03

4
0.19

5
0.13

6
0.02

7
0.06

The standard deviation of the estimator over several runs is illustrated in Figure 3.5a. As visible, the standard
deviation is relatively high compared to the magnitude of the relay errors and hence it is very likely that one relay
error is estimated to 0. It is worth to note, that the deviation does not decrease with a higher SNR, instead it seems
to be an inherent property of the underlying estimator. The error floor with estimated p̂k is above the optimal error
floor with known correlation. Compared to perfect correlation knowledge, by using a more accurate estimator theerror floor can hence be reduced to one third in the presented scenario.

3.1.4.2

Performance of Modified Estimators

This section summarizes the decoding and estimation performance of the algorithm modifications described in
sections 3.1.2.1 and 3.1.2.2, based on the pairwise estimator (3.3), in the above scenario. The look-up table for theconsidered scenario providing the optimal T for the pairwise error estimation is provided in Figure 3.5b. As canbe seen, the optimal threshold tends to consider all LLRs for estimation in high SNR regions, but considers only
reliable LLRs in worse channel conditions to provide better error estimates. The resulting decoding and estimation
performance with the optimized T is shown in Figure 3.6. Compared to Figure 3.4, with the optimized T the error
probabilities can be already estimated in lower SNR regimes. Accordingly, the waterfall region of the decoder isshifted to the left, leaving a gap of only 0.4dB compared to the ideal curve. However, the error floor remains highand far above the achievable error floor with perfect correlation knowledge.
In order to remove the error floor, singular estimation, i.e. one relay is estimated to have zero error, needs to becombated. This can be done by providing a more accurate solution to the estimation performance, meaning thatthe estimator’s variance is reduced. The standard deviation of the improved estimation algorithms using several

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D2.1.1 Version 1.0
Estimated error per relay with reference algorithm

BER at the destination

0.2

pk known
pk estimated, T = 2
10−1
BER

p̂k

0.15

0.1

1.4dB

10−2

·3

5 · 10−2
10−3

0
−8

−6

−4

−2

0

2

4

SNR dB

−8

−6

−4

−2

0

2

4

SNR dB

Figure 3.4: Relay error estimation and decoding performance at the destination with reference correlation
estimation algorithm and perfect correlation knowledge.

2Tp̂k ± sk

0.2

0.1

0
−6

1

0
−4

−2

0

2

4

SNR [dB]

−8

−6

−4

−2

0

2

4

SNR [dB](a) Standard deviation of the estimation performance of (b) Look-up table of the optimal T calculated by Algothe reference estimator [HZA+13] for selected relays
rithm 2.
with constant T = 2.

Figure 3.5: Standard deviation and optimal threshold.
permutations or an overdetermined equation system is shown in Figure 3.7 and numerical values for the resulting
standard deviation are shown in Table 3.2, where the standard deviation is averaged over the denoted Eb /N0
range. Obviously, the estimation performance can be significantly improved by using all available informationin the estimator. Furthermore, solving the over-determined system outperforms the permutation approach by 33%
reduced standard deviation.
Table 3.2: Standard deviation of modified estimators.
Eb /N0 ∈ [−5dB, 4dB]s̄p̂

Estimator in [HZA+13]
1.3 · 10−2

Permutations
0.34 · 10−2

Over-Determination
0.19 · 10−2

The decoding performance at the destination with the correlation estimator which exploits the over-determinationof the system is shown in Figure 3.8. The waterfall region is remarkably close to the optimal performance and theerror floor is equal to optimal performance. This shows that the improved estimators have significantly improved
the overall decoding performance at the destination.

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Decoder performance

Estimated error per relay with optimal threshold
0.2
10
BER

p̂k

0.15
0.1

p̂k , T = 2
p̂k = pkp̂k , T optimized

−1

0.4dB

10−2

5 · 10−2
−8

−6

−4

−2

0

2

10−3

4

−8

SNR dB

−6

−4

−2

0

2

4

SNR dB(a)(b)

Figure 3.6: Decoding and error estimation performance when using the optimized threshold.

Performance with mean of relay permutations.

Performance with overdetermined system.
0.2p̂k ± skp̂k ± sk

0.2

0.1

0
−6

−4

−2

0

2

0.1

0
−6

4

SNR dB

−4

−2

0

2

4

SNR dB

Figure 3.7: Error estimation performance with reduced variance and using optimized threshold.

Decoder performance

BER

10

p̂k , T = 2
p̂k = pkp̂k , Overdet.

−1

10−2
10−3

−8

−6

−4

−2

0

2

4

SNR dB

Figure 3.8: Decoding performance at the destination with improved estimator using the overdetermined
equation system and optimized threshold.

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3.1.4.3

D2.1.1 Version 1.0
Performance of Novel Pairwise Estimators

The novel pairwise error probability estimators – model-based unbiased, soft BER, and hard BER – presented
in Section 3.1.3 were experimented by generating two flat LLR sequences drawn from Gaussian distributions as
defined in (3.13). Error probability q was estimated over 10000 randomly generated blocks by different estimators,
and the mean and mean-squared-error (MSE) of the estimators was calculated. In addition, a genie-aided nearly
optimal threshold setting for the sample selection was experimented. The criterion for the threshold setting was tominimize MSE.
Pairwise error probability estimation, q = 0.12, N = 1000

Pairwise error probability estimation, q = 0.12, N = 1000

0.5

0.4

Unbiased
Soft BER (no T)
Soft BER (optim T)
Hard BER (no T)
Hard BER (optim T)
Reference (no T)
Reference (optim T)

0.45

0.4

0.3

0.35

MSE

0.25

0.3

0.2

√

Mean

Unbiased
Soft BER (no T)
Soft BER (optim T)
Hard BER (no T)
Hard BER (optim T)
Reference (no T)
Reference (optim T)

0.35

0.25

0.15

0.2

0.1

0.15

0.05

0.1
−6

−4

−2

0

2

4

6

8

10

0
−6

12

−4

−2

0

SNR [dB]

Figure 3.9: Mean and
N = 1000.

2

4

6

8

10

12

SNR [dB]√
MSE of pairwise error probability estimation as function of LLR-SNR, q = 0.12,

Pairwise error probability estimation, SNR = 0dB, N = 1000

Pairwise error probability estimation, SNR = 0dB, N = 1000

0.5

0.35

Unbiased
Soft BER (no T)
Soft BER (optim T)
Hard BER (no T)
Hard BER (optim T)
Reference (no T)
Reference (optim T)

0.45
0.3

0.4

0.25

0.35

MSE

0.25

0.2

√

Mean

0.3

0.15

0.2

Unbiased
Soft BER (no T)
Soft BER (optim T)
Hard BER (no T)
Hard BER (optim T)
Reference (no T)
Reference (optim T)

0.15

0.1

0.05

0.1

0.05

0

0

0

0.05

0.1

0.15

0.2

q (pairwise error probability)

0.25

0.3

0.35

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

q (pairwise error probability)√
Figure 3.10: Mean and MSE of pairwise error probability estimation as function of error probability q,
SNR=0dB, N = 1000.
The results are shown in Figures 3.9, 3.10, and 3.11. As can be seen, both soft and hard BER perform better
than the reference method. Furthermore, the threshold setting reduces bias for all (biased) methods. Adaptive
thresholding is also able to benefit from the increasing block length.
The model-based estimator is very accurate and asymptotically unbiased. It relies on the consistency property of
the LLRs, and it also assumes that the SNR over each code block is constant (flat). This estimator does not needsample selection or threshold setting: all samples are good samples. The model-based estimator may be sensitive
to the breach of the underlying assumptions.

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Pairwise error probability estimation, q = 0.12, SNR = 0dB

Pairwise error probability estimation, q = 0.12, SNR = 0dB

0.45

0.4
0.25

Unbiased
Soft BER (no T)
Soft BER (optim T)
Hard BER (no T)
Hard BER (optim T)
Reference (no T)
Reference (optim T)

0.25

MSE

Mean

0.3

Unbiased
Soft BER (no T)
Soft BER (optim T)
Hard BER (no T)
Hard BER (optim T)
Reference (no T)
Reference (optim T)

0.2

0.15

√

0.35

0.1

0.2

0.05

0.15

0.1

0
2

10

3

10

N (number of bits per packet)

4

10

2

10

3

10

4

10

N (number of bits per packet)√
Figure 3.11: Mean and MSE of pairwise error probability estimation as function of code block length N,
q = 0.12, SNR=0dB.
Soft BER counting is not based on any assumptions of the LLR distribution. It is a heuristic refinement to thestraightforward hard BER counting. Like the reference method, both soft and hard BER counting schemes can be
combined with sample selection to further improve the estimation accuracy.
To investigate the final decoding performance with the novel estimation algorithms, we again simulated the Chief
Executive Officer (CEO) system model described in Section 2.2.2 and Figure 2.6 with K = 7 relays, where theerror probabilities of the Binary Symmetric Channel (BSC)s are given by the values in Table 3.1. The reference
least-squares estimator for resolving the underlying BSC error probabilities from the pairwise error probability
estimates was used. It turned out that the best decoding performance is obtained when all the LLR samples areused, and thus results only without sample selection are shown here.
Figure 3.12 depicts the decoding performance as a function of the per-link SNR. The results are surprising in thesense that the best performance is achieved by using the simple hard BER counter instead of the more advanced
estimators. The model-based unbiased estimator performs clearly worst. There are multiple candidate explanations
to this phenomenon. The first is that the distribution of the post-decoding LLRs does not follow the ”consistency
condition”, which renders the unbiased estimator almost useless. The second is that the least-squares estimator ismore robust when the pairwise error probabilities have been over-estimated, which helps to avoid getting zeros for
BER-estimates. The third explanation is that also the iterative decoder actually benefits from over-estimated bit
error probabilities, especially in the beginning of the iteration. Clearly, further investigations are needed.
Finally, Figure 3.13 shows a comparison between the SoTA estimator with fixed (T = 2) and adaptive thresholdsetting, over-determined least-squares estimator, and hard BER counting (no sample selection, reference leastsquares). As can be seen, even the hard BER counting outperforms the SoTA estimator with fixed T. Due to its
reasonable performance and extreme simplicity, hard BER is a potential candidate for implementation.

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100

Decoding performance with novel pairwise BER estimators

Unbiased
10

Soft BER−1BER

Hard BER

10

10

−2

−3

−8

−6

−4

−2
SNR [dB]0

24Figure 3.12: Decoding performance with novel pairwise BER estimators, no sample selection (T = 0).

SoTA, T = 2
SoTA, T opt.
SoTA, T opt.+Overdet.
Hard BER countp known

BER

10−1

10−2

10−3

−8

−6

−4

−2

0

2

4

SNR dB

Figure 3.13: Comparison of decoding performance of the proposed estimators.

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3.2

D2.1.1 Version 1.0

Source Correlation Estimation at Relays

In this section, a complexity reduced error-propagation mitigation algorithm is proposed by exploiting limited
channel feed-forward from the relay node to the destination node. The proposed idea employs limited channel
feed-forward bits as the source-relay correlation information indicator and uses it for the iterative decoding at
the destination node. Comparing with the state-of-the-art schemes (i.e. see [AM12a; HZA+13]), the proposed
algorithm omits the threshold-based iterative estimation process, and thus the computational complexity at thedestination node can be reduced. Also, with limited channel feed-forward, the spectral efficiency of the system
can be improved by comparing with the soft-information forwarding scheme. It is shown in the simulations thatthe proposed algorithm based on limited channel feed-forward can provide a similar performance as the thresholdbased estimation algorithm. Moreover, the results also show that the proposed algorithm by exploiting the sourcerelay correlation information outperforms the conventional selective decode-and-forward (S-DF) relaying up to 1
dB gain by introducing extra decoding process at the destination node.
3.2.1

System Model

The block diagram of the considered single-relay system model is shown in Figure 3.14.
bs

ENC s

xs

L( y sd )ChannelL( y sr )Lbes
Lbas,updatef (L, ρ )Channel

DECr

b̂ s

DEC s

f (L, ρ )Lbar, update

br

ENCr

xr

ChannelL( yrd )

DECr

Lber

Figure 3.14: The block diagram of the system model.

As shown in the figure, at the source node, the data sequence bs is firstly encoded by the channel encoders ENCs
using turbo principle, and then modulated by binary phase shift keying (BPSK) to obtain the modulated sequencexs . After that, xs is transmitted to the relay node and the destination node in time-slot 1. As follows, the recovered
binary sequence br at the relay node is encoded by the turbo encoders ENCr and modulated by BPSK to generate
the signal sequence xr . xr is then forwarded to the destination node during time-slot 2. After receiving the signals from the source node and the relay node, the destination node performs joint turbo decoding by exploiting
the correlation information to retrieve the original data sequences from the source node. Here, the message br
which is obtained by the relay node is the erroneous version of the original data sequences bs . Thus, the binary
data sequences emitted from the source node and the relay node are correlated with each other. The correlation
information can be expressed as [AM12a]ρ = 1 − 2pe ,(3.21)
where pe = Pr(bs 6= br ) is the error probability of the corresponding bit between the source node and the relay
node, and it is in a range of [0, 0.5].
3.2.2

The Source-Relay (S-R) Correlation Knowledge Estimation

As mentioned in Sec. 3.2.1, the destination node performs joint turbo decoding by exploiting the correlation
information to retrieve the original data sequences from the source node. Such decoding process can be found in[AM12a]. It was shown in [AM12a], when pe is unknown at the destination node, the threshold-based estimation
method (i.e. see [GZ05]) can be implemented to obtain the pe value. Here, the threshold is imposed to limit the
number of log likelihood ratio (LLR) values for calculation to guarantee the estimation reliability. The estimation
accuracy mainly depends on the threshold set-up. If the threshold is set up to a very big value, few LLR values
can meet the requirement and N will approach to 0. If the threshold is set up to a very small value, a lot of
unreliable LLR values will be included in the estimation process and the accuracy of pe estimation cannot be

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guaranteed. Thus, the main drawback of the threshold-based estimation method is that biased estimation results
may be produced when different threshold values are applied.
Motivated by the above observation, a novel scheme to exploit the channel state information (CSI) of S-R linkto obtain the correlation information pe (also ρ) is proposed. As we know, the pe value is an indication of thechannel quality of S-R link. When transmission over quasi-statistic fading channels, the block-wise constantfading coefficient and the power of additive white gaussian noise (AWGN) determine the received signal-to-noise
ratio (SNR) for each transmitted block, which can be used to link with the pe value at the relay node. According tothis, a look-up table then can be built up in order to link different SNRs with different pe values. Such look-up tableneeds to be shared by both the relay node and the destination node before data transmission. Then, at the relay
node, after obtaining its estimated SNR value, it can search the look-up table to find the corresponding pe value
and then forward the corresponding index to the destination node. With such procedure, at the destination node,
the pe value can be obtained based on the feed-forward index bits, and thus, the pe estimation can be omitted.
Table 3.3: Look-up table for pe with channel information, where the SNR thresholds are corresponding to
the pe obtained through S-R link training.
SNR range
pe level SNR range
pe level(-∞ , -14.5]
0.463(-4.5,-3.5]
0.167(-14.5, -10.5]
0.432(-3.5,-2.5]
0.117(-10.5,-9.5]
0.328(-2.5,-1.5]
0.0429(-9.5, -8.5]
0.308(-1.5, -0.5]
0.00821(-8.5, -7.5]
0.287(-0.5,0.5]
0.000282(-7.5,-6.5]
0.263(0.5,1.5]0.00000123(-6.5,-5.5]
0.236(1.5, +∞)
0.000(-5.5, -4.5]
0.205
Table 3.3 gives an example of different SNR ranges corresponding to different average pe values. The look-up
table pre-stores the average pe values for different CSI ranges, and an indicator symbol is used to represent the
SNR ranges with their corresponding average pe values, e.g., a 4-bit symbol to present 16 SNR ranges and theircorresponding average pe values. In order to formulate the different average pe values for different SNR rangesof S-R link, an off-line training is designed by employing the low complexty decoding algorithm at the relay nodethrough the non-fading AWGN channel. It is worthwhile to note that, if a relatively strong code is used and theblock-length is long, the threshold-based estimated results converge to the average error probability, especially ata high SNR range. Thus, the channel information is able to provide a relatively accurate estimation on pe .
3.2.3

Performance Analysis

3.2.3.1

Convergence Property

Figure 3.15 and Figure 3.16 compare the proposed pe estimation scheme with the threshold-based pe estimation
scheme in terms of the pe performance and the mean square error (MSE) performance, respectively. Assume that
the SNR of S-R link is fixed to -2 dB, hence, for the proposed pe estimation scheme, based on the above look-up
table 3.3, the estimated average pe value in this case is equal to 0.0429. For the threshold-based pe estimation
scheme, different thresholds are set up for the pe estimation. Turbo-like codes are used for encoding/decoding
process, where each encoder at both source node and relay node is an non-recursive convolutional code with agenerator polynomial G = ([6, 13])8 , the decoding process at the relay node is only with 2 horizontal iterations,and the decoding precess at the destination node is with 5 horizontal iterations and 5 vertical iterations. As shownin Figure 3.15, the estimated pe values of the threshold-based pe estimation scheme decreases as the SNR ofsource-destination (S-D) link increases, and finally they are converged to the estimated average pe value of the
proposed pe estimation scheme when the SNR of S-D link is above 0 dB. In Figure 3.16, the MSE performanceof the threshold-based pe estimation scheme also converges to the ones of the proposed pe estimation scheme as
the SNR of S-D link increases. Furthermore, the convergence rate of the threshold-based pe estimation scheme
depends on the value of the threshold set-up, since the threshold affects the number of samples and the reliabilityof the pe estimation. It is shown that, as the reliability of the decoding process increases (e.g. the SNR value of
S-D link increases), the estimation accuracy of the threshold-based pe estimation scheme increases. In contrast,

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0.22

0.18

Threshold 1.0
Threshold 2.0
Threshold 3.0
Threshold 4.0
Proposed (pe=0.0429)

0.2

0.18

0.14

Mean Square Error

0.16

pe

0.14

0.12

0.1

0.12

0.1

0.08

0.06

0.08

0.04

0.06

0.02

0.04
−5

−4

−3

−2

−1

0

1

2

3

Threshold 1.0
Threshold 2.0
Threshold 3.0
Threshold 4.0
Proposed (pe=0.0429)

0.16

0
−5

4

−4

−3

−2

SNR of S−D link (dB)

−1

0

1

2

3

4

SNR of S−D link (dB)Figure 3.15: The threshold-based estimation of pe Figure 3.16: MSE of estimation pe with various threshold set-ups and blockwith various threshold set-ups andlength=1000.
block-length=1000.
−1

−1

10

10

−2

−2

10

10

−3

−3

BER

10

BER

10

−4

−4

10

10

Threshold−based S−DF A
DF without vertical iterations A
Threshold−based A
CSI−based A
Known pe A

−5

10

−6

10

0

Threshold−based S−DF B
DF without vertical iterations B
Threshold−based B
CSI−based B
Known pe B

−5

10

−6

2

4

6

8

10

12

Average SNR (dB)

14

16

18

20

10

0

2

4

6

8

10

12

14

16

18

20

Average SNR (dB)Figure 3.17: BER performance in block Rayleigh fading channels and block-length=1000.
for the proposed channel feed-forward scheme, the correlation information can be accurately obtained regardlessof the channel quality of S-D link and the threshold set-up.

3.2.3.2

BER Performance

Figure 3.17 illustrates the bit-error-rate (BER) performance of the schemes exploiting correlation informationcompared with conventional S-DF relaying. For the S-DF relaying, two methods are used to control the error
propagation. One is using a cyclic redundancy check (CRC) at the relay node, where the relay node remains
silence if the CRC fails. The other one is SNR threshold-based check, where the relay node only operates when the
SNR of S-R link exceeds a predetermined value. In this experiment, the same turbo-like code as last experimentis used, the block-length is set up to 1000 bits, and 10000 blocks are transmitted from the source node. For thethreshold-based S-DF relaying, an 1-dB SNR threshold is employed to control the error propagation at the relay
node. The relay node is placed in two positions: A) in the middle of the S-D link, which results a 6 dB SNR gain for
S-R link and relay-destination (R-D) link comparing to the S-D link; B) in the position where the distance of S-R
and R-D links are the same as that of S-D link. To demonstrate the performance gain achieved by exploiting the SR link correlation, the BER curves of conventional S-DF relaying are provided as the benchmark. The performance

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D2.1.1 Version 1.0of threshold-based pe estimation at the destination scheme is also presented, where the threshold is set to 2.0. The
ideal scenario with known pe at the destination node is used as the upper bound for comparison. It can be observedthat the proposed scheme exploiting CSI-based correlation information at the relay node can achieve 1 dB gain
over the conventional S-DF relaying schemes at BER of 10−4 . Moreover, it is also found that the BER curve of the
proposed scheme is very close to that of the ideal situation using actual pe and the threshold-based pe estimation
scheme, which means that the complicated iterative pe estimation process at the destination node can be replacedby the limited channel feed-forward at the relay node, thus, the computational complexity at the destination node
can be significantly reduced.
3.2.4

Summary

In this section, a novel strategy for iterative decoding exploiting correlation information with limited channel feedforward at the relay node has been presented. The proposed algorithm aims to mitigate the error propagation at
the destination node through the limited channel feed-forward of S-R link correlation information from the relay
node. Here, a look-up table is used to provide the S-R link channel correlation information. It is shown that the
proposed scheme can outperform the conventional S-DF relaying scheme. Moreover, without the pe estimation
process at the destination node, the proposed scheme can achieve close BER performance as the scheme that thepe is estimated at the destination node.

3.3

Summary and Discussion

In order to optimally decode received messages, the proposed joint decoder requires the knowledge of correlation
information between the relays. However, if all relays experience some errors, the joint decoder will always have a
decoding error floor since it can happen that all relays have made an error for the same bit. To acquire knowledge
about the correlation, the decoder can estimate the bit errors at the destination by considering the decoded LLRs.
The estimation is carried out in three phases: 1) The LLR samples that are used for estimation are selected. Thiscan either be done by thresholding or using the some percentile of the most reliable LLRs. 2) Pairwise bit errors
between relays are estimated. 3) The pairwise bit errors are used to resolve the actual transmitter-specific BER.
In this chapter new methods for all three phases were presented. It is worth mentioning that in order resolve thetransmitter-specific BERs at the destination – based on just the pairwise estimates – at least three transmitters, orat least three different packet copies, need to be received.
In the estimation, each received code block (packet) is treated separately, which takes into account the fading stateof the channel and the decoding success per block. For each packet, the correlation between messages is newly
analyzed to get most accurate results. Hence, the estimation complexity needs to be considered in the overallsystem complexity. Therefore, in comparison to the conventional estimator, a new promising low-complexity
pairwise BER estimator based on the hard BER count was presented. It showed slightly worse performancecompared to the higher complexity estimators based on threshold adaptation that were proposed in this chapter.
An alternative approach to obtain the correlation knowledge for the destination is to estimate the BER already at
the relays by measuring the channel state of the source-relay link. The BER information can then be forwarded tothe destination, however here quantization noise and signaling overhead appears. The BER estimation at the relays
is especially useful, when there are error-free relays. Error-free relays can hardly be estimated at the destination
as a wrong singular estimation can significantly influence the decoder error floor. In addition, CRC checks at therelays can help in finding the zero BER packet copies. Forwarding the CRC pass or fail information would only
require one bit signaling overhead but can potentially improve performance significantly. One more estimation
strategy could be to consider the decoded LLRs at the relays. This approach would provide soft information of thedecoding success of each packet separately, whereas the CRC check can only resolve whether the packet is totallyerror-free or not.
It is worth noting that most of the studied estimators assume that SNR per link can be accurately estimated to
calculate the BER or to adjust the sample selection threshold. This assumption is not restrictive as channel stateand noise variance information is necessary also for running the iterative turbo decoding process itself. Finally,
as estimates are always in practice inaccurate, the estimates provided by the relays could be further improvedby utilizing pairwise BER estimation methods at the destination in conjunction with the iterative decoder. It is

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certainly a future design challenge to find a protocol that provides the best trade-off between decoding performance,
estimation complexity, and signaling overhead.

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D2.1.1 Version 1.0

Advanced Topologies and Access Methods

In this chapter, complex communication network structures such as multi-route relaying with more than two hops,
and relaying with multiple source transmitters are addressed. The specific problems are described, coding anddecoding solutions presented, and performance results shown. Furthermore, the concept of IDMA is motivatedand explained, the related additional functionality at the receiver is described, and numerical results are shown.

4.1

Interleave-Division Multiple-Access (IDMA)

In our previous work, orthogonal transmission is assumed to be used for multiple relays when transmitting messages to the common destination. In order to keep the transmissions orthogonal, different time slots are requiredfor different relays. Interleave-division multiple-access (IDMA) technique [FOO00; LVW+06] can be applied
here for the transmissions of relays to reduce the number of required time slots while still maintaining good system
performance. IDMA technique is somewhat similar to code-division multiple-access (CDMA) technique, and thetwo system models are shown in Fig. 4.1. IDMA uses different interleavers to separate the users, while CDMA
uses spreading codes. The key idea of IDMA is that the interleaver plays a role of user identification without
using spreading, and hence, we can allocate the entire bandwidth expansion to coding by using very low-rate codeswith the aim of achieving the optimal multiple access channel (MAC) capacity and maximizing the coding gain
[VS99]. Hence, designing very low-rate codes is a crucial problem in IDMA systems in order to maximize thecoding gain.
In order to approach the MAC capacity, multi-user detection (MUD) should be performed at the receiver. A
sub-optimal but simpler approach is to employ single-user detection (SUD), and accept some reduction in theachievable rates. In this section, we review the code design, SUD, MUD as well as the BER performance evaluationof the IDMA technique [WAM14].
4.1.1

Code design

The motivation of using concatenated single parity check and irregular repetition (SPC-IrR) codes together withextended mapping (EM) in IDMA systems is threefold: 1) very low-rate can be achieved using SPC-IrR codes,
as stated above, designing low-rate codes is a very important issue in IDMA; 2) the code design is flexible using
EXIT-constrained binary switching algorithm (EBSA) [FOT+12]; 3) EM gains additional degree-of-freedom inthe system design since the labeling pattern in EM can be easily adjusted.
Fig. 4.2 shows the proposed coding/decoding scheme for IDMA. The information sequence uk =[uk (i), uk (2), · · · , uk (n)] generated by k-th user is first encoded by the SPC-IrR code with coding parameter dc ,dv and a. A simple example of SPC-IrR code is depicted in Fig. 4.3. The coded sequence ck is then permutated byinterleaver Πk and doped-accumulated by ACC with doping ratio pd . Finally, the output sequence dk from ACC ismodulated by EM and transmitted to the destination through MAC. Hence, the received signal r at the destination

ACC

Mapper

ACC

Mapper

ACC

MapperIDMA+

Spreading

MapperSpreading

MapperSpreading

Mapper+CDMA

Figure 4.1: A comparison of system models of IDMA and CDMA.

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SPC-IrR

ACC

EM
+
+

SPC-IrR

ACC

-

-

-

EM

+

Globaliteration
Soft symbol
generator+

Only for MUD

Figure 4.2: System model of the proposed coding scheme and detection algorithm.
Example: 𝑑𝑑𝑐𝑐 = 5, 𝑑𝑑𝑣𝑣 = 2, 3 , 𝑎𝑎 = [0.2, 0.8]
Information sequence: 1101

Append a parity check bit toevery
𝑑𝑑𝑐𝑐 − 1 = 4 bits.

SPC coded sequence: 1101 1

0.2 0.8
1 10112

3

20% and 80% of
the SPC coded
sequence arerepeated 2 and 3
times,
respectively.

IrR coded sequence: 11 111000111111

Figure 4.3: A simple example of SPC-IrR code.
is expressed as
K

r= ∑
k=1

p

Pk · xk + w,

(4.1)

where Pk and w denote the power allocated to the k-th user and the zero mean AWGN sequence with variance
σw2 , respectively. The source information is then reconstructed from r based on SUD or MUD we proposed. The
details of SUD and MUD is shown in below subsections.
4.1.2

Single-User Detection (SUD)

In SUD, the signals of other users is treated as noise when the k-th user’s signal is detected, i.e., the global iteration
shown in Fig. 4.2 is not activated. Hence, (4.1) can be rewritten aspr = Pk · xk + ζk ,
(4.2)
with
K

ζk =

∑

g=1,g6=kp
Pg · xg + w,

(4.3)

where ζk indicates the multiple access interference (MAI) from the other users plus AWGN. It is assumed that
ζk in (4.2) can be approximated as a Gaussian random variable according to the central limit theorem. Thus, thePage 37 (54)RESCUE

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2 , is expressed as
variance of interference plus noise, experienced by the k-th user, σk,ζ
K
2
=
σk,ζ

∑ Pg + σw2 ,(4.4)

g=1,g6=kwhere we assume E[|xg,i |2 ] = 1 with xg,i is the i-th element of xg . The performance of the SUD reception is
2 remains non-zero even if σ 2 is reduced to zero.
interference limited since σk,ζw
The extrinsic information exchange between EM−1 and decoder is performed iteratively, at the receiver side,
adhering the turbo principle. The extrinsic LLR output from the EM−1 is fed into the decoder ACC−1 to generatepthe a posteriori LLR Ldk and the a priori LLR Ledk . Then the extrinsic LLR Ledk is deinterleaved and result in apriori LLR Lack , which is input to the decoder SPC-IrR−1 . The extrinsic LLR Leck output from the decoder SPCIrR−1 is then interleaved and fed back to both ACC−1 and EM−1 . This process is performed iteratively until nomore relevant gain in mutual information can be achieved. Finally, the estimation ûk is obtained based on harddecision of the a posteriori LLR of the decoder.
4.1.3

Multi-User Detection (MUD)

The major difference between SUD and MUD is that soft successive interference cancellation (SSIC) [CCC00] is
performed in MUD to cancel the interference from the other users. In order to perform SSIC, the global iteration
shown in Figure 4.2 is activated in MUD.
The received signal r is expressed by (4.1)–(4.3) in the same way as in SUD. However, for cancelling out theinterference from the other users when we detect the k-th user’s signal by SSIC, the received signal ri is subtracted
from the mean value of ζk,i asr̂k,i = ri − E[ζk,i ],(4.5)

with i representing the symbol index. Now the major task of the ”Soft symbol generator” box shown in Fig. 4.2 isto compute the second term of (4.5) to perform SSIC in each global iteration. As stated above, since we assume
that ζk,i follows Gaussian distribution, the mean and the variance of ζk,i is expresses asKE[ζk,i ] = E[p∑g=1,g6=k=p∑

g=1,g6=k

Pg · xg,i + wi ]Pg · E[xg,i ],(4.6)

where E[xg,i ] represents the mean value of g-th user’s i-th soft symbol. E[xg,i ] can be calculated in each globalppp
iteration based on the a posteriori LLR sequence Lk = Lck + Ldk fed back from the decoder, as`

E[xk,i ] = ∑ s ∏ P(dk,ϖ = W ),
s∈S

(4.7)

ϖ=1

with

p

P(dk,ϖ = W ) =exp(−dk,ϖ Lk,ϖ )p

1 + exp(Lk,ϖ )

,

(4.8)

where W ∈ {0, 1} and ϖ is bit index of i-th EM symbol. S is a set of constellation points with s representing its
element. However, for initialization, the mean E[xg,i ] is set to 0.
2 of ζ
−1 to calculate theSince SSIC is performed, the variance σk,ζk,i is also updated by (4.9) and used in EMiextrinsic LLR in each iteration.
K

2
σk,ζ
=
i

2
+ σw2 ,∑ Pg · σg,x
i

(4.9)

g=1,g6=k

with
2
σg,x
= E[|xg,i − E[xg,i ]|2 ].
i(4.10)

2 is set to 1 to activate the global iteration. The process of SSIC and decoding is iteratively
The initial value of σg,xi
performed until the required iteration times are reached.

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0

10

−1

10

−2

BER

10

MUD with equal
power allocation

SUD

−3

10

−4

10

−5

10

BER (6 users with SUD)
Shannon Limit
BER (2 users with MUD)
Shannon Limit

0.95 dB

0.52 dB

−6

10
−10

−9

−8

−7

−6
−5
SINR (dB)

−4

−3

−2

Figure 4.4: BER performance of IDMA-SUD and IDMA-MUD with equal power allocation. The coding parameters are: dc = 5, dv = [2, 5, 20, 21, 100], a = [0.0721, 0.2441, 0.4767, 0.1610, 0.0461], pd = 10 for
SUD, and dc = 5, dv = [2, 6, 7, 23, 24], a = [0.2542, 0.2479, 0.436, 0.0109, 0.0511], pd = 20 for MUD.
The coding rates are 0.0424 and 0.1226 for SUD and MUD, respectively [WAM14].

4.1.4

Numerical Results

With the proposed coding/decoding scheme in IDMA system, good BER performance versus SINR can be achieved
with SUD, where the SINR of k-th user SINRk is defined as
SINRk =

Pk.
K
∑g=1,g6=k Pg + σw2(4.11)The BER performance with SUD is shown in Fig. 4.4. It can be found that the BER at 10−5 range is only around0.95 dB away from the Shannon limit. However, when the number of users increases, BER versus each user’s
SINR, degrades due to the multiple access interference from the other simultaneous users. Therefore, to achieve
better performance, a technique to reduce or to ultimately eliminate the interference, such as SSIC, is needed.
The BER performances with MUD is also shown in Fig. 4.4. With our proposed technique, the BER threshold isvery sharp and no error-floor is visible in the BER range. Due to the exactly matched EXIT curves combined withthe soft cancellation technique, very near-capacity performance, only {0.52} dB away from the corresponding
limit, is achieved.
However, the BER performance is degraded when equal power is allocated to users in MUD. We can further
improve the system performance by using unequal power allocation scheme, which is shown in [WAM14].

4.2

Coding and Decoding for Multi-Hop Relaying

In our previous work, we assume that the signal of single hop relays can cover the distance between the source
and the destination. However, if the destination and the source is far away, we should also establish effective lossy
forwarding techniques for this case. This motivates us work on multi-hop relaying system using lossy forwarding
relays. Recently, multi-hop relaying networks have been recognized as an effective technique to increase thecoverage of signals. In a multi-hop network, a source and a destination exchange information through a set ofrelays which are located in different hops, and hence, the source can transmit its information to the destination

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...

...

SourceDestination
1st hop
Relays

2nd hop
RelaysFigure 4.5: A schematic diagram of a two-hop relaying system with cross-link transmission.

+

+

...

...

Source++
1st hop
RelaysACC

BPSK

2nd hop
RelaysFigure 4.6: The proposed coding scheme for the two-hop relaying network.
via different routes connected by relays. In [SLW+09], authors proposed and analyzed several novel solutions
including separation of control and data, effective SINR-based routing as well as cooperative relay schemes inorder to improve both the system capacity and coverage. A suboptimal path selection based on using amplify-andforward (AF) protocol at relays was proposed in [YLR+12], with the target of achieving outage probability close tothat of the optimal routing scheme. The outage probability of using maximum distance separable code at link-level
cooperative multi-hop relaying network was evaluated in [SIT10]. However, in this section, we study a multi-hop
relaying network using decode-and-forward (DF) protocol at relays and evaluate the BER performance.
4.2.1

System Model: Coding and Decoding

We consider a two-hop relaying system where a schematic diagram is shown in Fig. 4.5 to examine the lossy
forwarding technique we proposed.
Figure 4.6 shows the proposed coding scheme for a two-hop relaying network to be analyzed. A binary i.i.d. sourceu = [u(1), u(2), · · · , u(i), · · · , u(n)] is transmitted to multiple relays at the first hop, where i is the time index andn represents the block length. For simplicity, we assumed the channels between the source and the relays at thefirst hop are simply BSCs. The received message uk of k-th relay is then a corrupted version of u by the binary
error sequence ek with Pr (ek (n) = 1) = pk , where k = 1, 2, · · · , K indicates the index of relays. Consequently, themessages at relays are correlated with each other since they have the common input u of the independent BSCs. The
k-th relay encodes the message uk by an encoder C and then interleaves the encoder output by Π1,k . The interleaved
information is then doped and accumulated by the ACC. Finally, the output of the ACC is modulated by BPSK andtransmitted to all the relays at the second hop over AWGN channels. We currently assume that the transmissions
are orthogonal with each other to ensure interference-free reception. In order to guarantee orthogonal transmission,different time slots are allocated to the transmission. However, we can use IDMA technique for non-orthogonaltransmission to reduce the number of time slots, which is left as future work in our next stage.

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010

K = 4 (2 Hops, Estimated Correlation)
K = 4 (2 Hops, Known Correlation)
Error Floor K= 4(Approximated)
K = 7 (2 Hops, Known Correlation)
Error Floor K= 7(Approximated)

−1

10

−2

10

−3

BER

10

−4

10

−5

10

−6

10

−7

10
−14

−12

−10
−8
−6
−4
−2
per−link (Relay to Destination) SNR (dB)02

Figure 4.7: The BER performance of our proposed scheme.
The k-th relay at the second hop first decodes the signal received from each relay at the first hop with a few
iterations L. The estimate ûk , which is generated based on the hard decision for the summation of the posteriorip
LLRs Luk , is first interleaved by an random interlaver Πk and then encoded by using the same coding chain asthat using by the relays at the first hop. After that, the modulated signal is transmitted to the destination overindependent AWGN channel.
The proposed decoding algorithm at the destination is shown in Figure 2.7, which is the same as we have proposedin [HZA+13] for the binary data gathering WSN, and hence, we have not provided the detail description of thedecoding algorithm used in this section.
4.2.2

Results and Discussion

The BER performances are evaluated by running a series of simulations. The obtained results are shown in Figure 4.7 with different numbers of relays K at each hop as a parameter. The parameters were set as follows:• Block length n = 10000 bits.
• Interleavers: random.
• Encoder C: rate Rck = 12 nonrecursive systematic convolutional code with generator polynomial G = [03, 02]8 .
• Doping ratio of the ACC: 1.
• Crossover probability of BSCs: 0.01.
• The number of iterations at the second hop: 1.
• Decoding algorithm for D and ACC−1 : log-maximum a posteriori (MAP).
• The number of iterations at the destination: 25 times of GI and LI.
• SNRrr representing the per-link SNR from relays to relays was set larger than SNRrd representing the per-link

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SNR from relays to the destination by δ (dB). We set δ = 8 for K = 4 and δ = 15 for K = 7.
From the simulation results from Figure 4.7, it is found that the BER of the two-hop relaying network can also
have a very sharp turbo cliff and the same level of error floor as in the single hop relaying network. It should be
noted here that the errors in the information sequence obtained at the second hop relays after hard decision are
correlated with each other. This is the key reason that we can not get better error floor in multi-hop relaying systemthan the single-hop relaying system. Furthermore, the power allocation is extremely important to achieve such
good performance in this two-hop relaying network. If the power of the relays at the first hop is too low, the BER
performance may degrade a lot since the correlation among the signals received at the destination becomes verysmall. Therefore, in the simulations, we set the SNRrr larger than SNRrd , however, this is not the optimal allocationof power. In our future work, the optimal power allocation and/or rate allocation in multi-hop relaying networks inorder to achieve minimal BER performance will be carried out by using convex optimization tools.

4.3

Joint Adaptive Network and Channel Coding for Orthogonal Multiple Access Relay Channel

4.3.1

System Model

Figure 4.8 illustrates a basic model of the orthogonal multiple access relay channel (MARC) system allowing
intra-link errors (MARC-IE), where there are two source nodes A and B, a single relay R, and one common
destination D. The N-bit length i.i.d. binary information sequences generated from nodes A and B are denoted as
uA = {uA (k)}Nn=1 and uB = {uB (k)}Nn=1 , respectively. The signaling scheme used at the source node is denoted as
ES (·), which consists of a serial concatenation of channel encoding and modulation.
1st time slot

A

A

A
D

D
B

3rd time slot

2nd time slot

B

D
B

Figure 4.8: Orthogonal MARC-IE system model, where there are three time slots in a transmission cycle[LZM14].

There are three time slots in one transmission cycle. In the first two time slots, nodes A and B respectively broadcastM
their M-bit length coded sequences xA = ES (uA ) = {xA (m)}M
m=1 and xB = ES (uB ) = {xB (m)}m=1 to R and D, andtheir corresponding received signals obtained at R and D are respectively written as
yiR = hiR · xi + niR

yiD = hiD · xi + niD ,i ∈ {A, B}(4.12)

where hiR and hiD indicate the channel coefficients of iR and iD links with the source node i, respectively. niR andniD indicate the vectors of independent zero-mean complex additive white Gaussian noise (AWGN) of the iR and2 = σ 2 = σ 2 per dimension. The iR and iD links are also referred to as theiD links, respectively, with variance σiRiDintra and direct links, respectively, in this section.
The receiver applied at the relay R is denoted as DR (·), composed of signal detection and decoding, which correei = DR (yiR ) of ui obtained at R may contain errors due tosponds to the inverse structure of ES (·). The estimates u
the variation of the iR link. The error probability of the iR link is represented byei ) =
pi = B(ui , u∑Nn=1 |ui (n) − uei (n)|, i ∈ {A, B}.
N(4.13)

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In the orthogonal MARC system with selective decode-and-forward relaying strategy (MARC-SDF) [IH11], if theei is found to contain errors, it will be discarded at the relay. However, in the proposed MARC-IE systemestimates ueA and ueB , are always joint network-channel coded at R regardless of whether they are correctmodel, the estimates u
or not, aseB ) = {xR (m)}M
xR = ER (uR ) = ER (euA ⊕ um=1 ,(4.14)yRD = hRD · xR + nRD ,(4.15)

where the notation ⊕ denotes a binary exclusive-OR (XOR) operation and ER (·) represents the signaling scheme
applied at R, including channel encoding and modulation. In the second time slot, the destination D receives thesignal vector yRD of xR sent via the relay-destination (RD) link as
2 = σ 2 of the RD link,
where hRD and nRD indicate the channel coefficient and AWGN vector with variance σRD
respectively. The estimates of uR obtained at the destination is denoted as ûR , and the error rate of the RD link is

pR = B(uR , ûR ). Finally, to obtain the estimates ûA and ûB of the information sequences uA and uB , respectively,
at the destination, decoding of JNCC is performed on the received signal vectors yAD and yBD with the help of thesignal vector yRD .
Following the block Rayleigh fading assumption, hiR , hiD and hRD are assumed to be constant over one coded
sequence but vary independently transmission-by-transmission and link-by-link. Without loss of generality, we
assume that E[|hiR |2 ] = E[|hiD |2 ] = E[|hRD |2 ] = 1. The error probabilities pi and pR , thus, vary in each transmission
cycle. The instantaneous SNRs γiR , γiD and γRD of the links are then given by
γiR = |hiR |2 · ΓiR ,γiD = |hiD |2 · ΓiD ,γRD = |hRD |2 · ΓRD ,(4.16)

where ΓiR , ΓiD and ΓRD represent the average SNRs of the intra, direct and RD links, respectively.

4.3.1.1

Network Correlation

The errors occurring in the two SR links can be described by the bit-flipping model with flipping probability
pi , i ∈ {A, B}. Then, since XOR-network coding is always performed at the relay in the proposed MARC-IE
system, we found a new bit-flipping probability pnc between the two sequences: one is the forwarded XOR-codedeA ⊕ ueB , and the other is their corresponding XOR-ed information
sequence uR generated at the relay (i.e., uR = u
sequences u⊕ (i.e., u⊕ = uA ⊕ uB ). Hence, the probability pnc between original two XORed information u⊕ anduR can be calculated as

pnc = Pr(uR 6= u⊕ )eB ) 6= (uA ⊕ uB ))= Pr((euA ⊕ u= 1 − (1 − pA )(1 − pB ) − pA pB= pA + pB − 2 · pA pB .

(4.17)We refer the probability pnc as network correlation. Note that although pnc is assumed to be known to the destination in this section, pnc can also be estimated at the destination using the estimation methods presented in
Section 3.1. In the following subsection, we will show how the network correlation pnc can be utilized in the joint
decoding process at the destination to help recover the original information sequences uA and uB .
4.3.2
4.3.2.1

Coding and Decoding Scheme
Coding Structure at The Source and Relay NodeseA and ueB to obtain uR , andThe key idea with MARC-IE system is that the relay always performs XOR coding on uthen the interleavered version of uR is encoded and modulated with ER (·). In summary, the coding structures at the

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Figure 4.9: Coding structures at the source and relay nodes for proposed MARC-IE.

source and relay nodes are illustrated in Figure 4.9.
We use the same coding chain for both ES and ER , which is a serial concatenation of a half-rate recursive convolutional code (RSC) with generator polynomial (07, 05)8 and a accumulator (ACC), followed by BPSK modulation.
As a consequence, the spectrum efficiency of both ES and ER are 1/2. All the interleavers used are random interleavers. Note the receiver DR at the relay simply extracts the original information by performing hard-decision on
the output from the differential detection. This greatly reduces the computational complexity at the relay becauseof its simplicity.

4.3.2.2

Joint Network-Channel Decoding Structure

Figure 4.10: Joint network/channel decoding structure for proposed MARC-IE.

The block diagram of the joint network/channel decoding algorithm for the proposed MARC-IE system is shownin Figure 4.10. To utilize the network correlation pnc , the LLR-updating function fc (·) shown in Equation (2.4) isused in the decoding scheme.
The received signal vectors yiD from the two source nodes are respectively demodulated at D to obtain the corre-

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sponding soft channel values, as
L(yiD |xi ) =2· ℜ {yiD · h∗iD } ,σ2i ∈ {A, B},(4.18)

where the notations L(·) and ℜ(·) denote LLR vector and a function that takes the real part of its argument elementwisely, respectively, and ∗ indicates complex conjugation. The computation from received vector yRD to L(yRD |xR )also applies (4.18). Given these soft channel value vectors, the extrinsic LLR vector Le (ui ) and Le (uR ) are calculated by the soft-in-soft-out (SISO) decoder ES−1 (·) and ER−1 (·), respectively, using the Log-MAP algorithm. Then,since XOR-network-coding is performed at the relay, the extrinsic LLR vector Le (u⊕ ) before the function fc (·) isobtained by performing the “box-plus” operation [HOP96] bit-wisely on Le (uA ) and Le (uB ), asLe (u⊕ ) = Le (uA )  Le (uB ) = ln

exp(Le (uA )) + exp(Le (uB )).
1 + exp(Le (uA ) + Le (uB ))(4.19)We then use the function fc (·) with the knowledge of pnc to obtain the a priori LLR values for uR by modifying
Le (u⊕ ), asLa (uR ) = fc (ΠR [Le (u⊕ )] , pnc ) ,(4.20)

where ΠR [ · ] denotes interleaving by ΠR . Similarly, we extract Le (uA ) and Le (uB ) from Le (uR ) generated from
ER−1 (·) with the bit-wise “box-plus” operation, and modify them by taking into account the network correlation
pnc to obtain a priori LLR values for uA and uB as
La (uA ) = fc (Π−1
R [Le (uR )], pnc )  Le (uB ),(4.21)La (uB ) = fc (Π−1
R [Le (uR )], pnc )  Le (uA ),(4.22)

andrespectively, where Π−1
R [ · ] indicates de-interleaving from ΠR .
4.3.3

Numerical Results

In this subsection, we show the FER performance of the proposed MARC-IE, where all the links in MARC are
assumed to suffer from block Rayleigh fading. Two different scenarios are considered: in Symmetric case, thedistances from B to R and D are the same with that from A to R and D, respectively; in Asymmetric case, B
is further away form R and D than A. The average SNRs of all the links in both scenarios are summarized inTable 4.1, where X represents the average SNR of the AD link in dB; ∆ and L denoting additional gain and loss
due to the shorter and longer distance, respectively, and are set to 3 dB and 10 dB. In the simulations, the length of
information sequence is set at N = 2048 bits. The local decoding of ES−1 is performed 10 iterations, followed by 1
iteration of decoding between ES−1 and ER−1 , and in total the whole process is repeated 10 times.
Results of the FER performances of the proposed MARC-IE in Symmetric and Asymmetric scenarios are demonstrated in Figure 4.11, where the FER performances of MARC-SDF using the same coding structure are also
provided for comparisons. Here FER is defined as follows: number of the transmission cycles where either one orboth of the information sequences sent from the nodes A and B cannot successfully recovered at D even with thehelp of R, divided by the total number of transmission cycles.

Table 4.1: Settings of symmetric and asymmetric scenarios.
ScenarioΓAD ΓBD
ΓAR
ΓBR
ΓRD
Symmetric
X
X
X+∆
X+∆
X+∆
AsymmetricX
X-L X+∆ X+∆-L X+∆

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0

0

10

10

−1

−1

10

FER / Outage

FER / Outage

10

−2

−2

10

10

Outage, MARC−IE
FER, MARC−IE
FER, MARC−SDF
Without relay

Outage, MARC−IE
FER, MARC−IE
FER, MARC−SDF
Without relay

−3

10
−10

−3

−5

0

5

10

15

Average SNR of AD link, Γ

AD

20

10
−10

25

−5

[dB]

0

5

10

15

Average SNR of AD link, ΓAD(a) Symmetric scenario

20

25

[dB]

(b) Asymmetric scenario

Figure 4.11: FER performances of proposed MARC-IE in Symmetric and Asymmetric scenarios, where alllinks in MARC suffer from block Rayleigh fading [LZM14].

It can be observed in Figure 4.11 that in Symmetric and Asymmetric scenarios, the proposed MARC-IE respecei
tively obtains 0.7 dB and 2.2 dB gain from the MARC-SDF. This indicates that even though the estimates u
contains errors, the erroneous estimates received at the relay, instead of being discarded, can still be efficiently
utilized in the proposed MARC-IE system for reconstructing the information sequences ui , sent via the iD link, atthe destination.
The outage probabilities of MARC-IE in both scenarios are also included in Figure 4.11 for reference, which are
obtained in [LZM14]. It can be observed from Figure 4.11 that the FER performances of the proposed MARC-IE
are roughly 6 dB and 5 dB away from the limits, respectively. It is expected the gap can be narrowed by using
capacity-achieving codes and better decoding strategy at the relay.
010MARC−IE (S)MARC−SDF (S)without relay (S)MARC−IE (A)MARC−SDF (A)without relay (A)

−1

BER

10

−2

10

−3

10

−5

0

5

10

15

20

25

Average SNR of AD link, ΓAD [dB]

Figure 4.12: BER performances of the proposed MARC-IE, where all links in MARC suffer from block
Rayleigh fading.

The BER performances of the proposed MARC-IE and the MARC-SDF systems are demonstrated in Figure 4.12.
Compared with the FER performance shown in Figure 4.11, the proposed MARC-IE is more advantageous in BER
performance, and provides roughly 2.3 dB and 3.8 dB gain over MARC-SDF at BER = 10−3 in Symmetric andAsymmetric scenarios, respectively. This is because with the less amount of mutual information, caused by larger
value of pnc , is still possible to correct several error bits, even though it is not enough to correct all the error bits.

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D2.1.1 Version 1.0

Support for System Design

This chapter discusses the options for multi-rate coding for the RESCUE system, and the preliminary code design
choices for the SDR implementation are disclosed. The basic interfaces between the higher layer protocols and thephysical layer coding/decoding are also described. For the purpose of system level simulations, a novel abstract”black box” simulation tool is outlined.

5.1

Multi-Rate Coding

The ability to adjust transmission rate in response to the communication application requirements or wirelesschannel capacity, is typically realized via multi-rate coding and modulation. To this end, for each supported
transmission rate, the code, modulation constellation, and modulation mapping are to be designed.
In the context of turbo codes, a design tool called ”EXIT-Constrained Binary Switching Algorithm” (EBSA) has
been proposed in [FOT+12]. It is used for finding a good match in terms of EXIT curves between concatenatedsingle parity check and irregular repetition (SPC-IrR) codes and extended mapping (EM). As a result, a wide
range of rates can be flexibly supported. The BER performance for various code rates when employing 16QAM
modulation are shown in Figure 5.1. It can be seen that excellent BER performance in terms of very sharp turbo
cliff can always be achieved.
0

10

−1

10

−2

10

−3

BER

10

−4

10

−5

10

0.48 dB

0.65 dB

1.19 dB

−6

10

−7

10

1

2

3

4

5
SNRbldB)

6

7

8

9

d =b5,bd =b[2b3b4b12],ba=[0.1715b0.7276b0.0102b0.0907],bP =b90,bSpec−effb=b1.3133bbits/symbolcvddc =b5,bdv =b[2b3b4b5],ba=[0.4986b0.2000b0.2358b0.0656],bPd =b90,bSpec−effb=b1.9687bbits/symbol
d =b5,bd =b[2b3],ba=[0.6798b0.3202],bP =b40,bSpec−effb=b2.5343bbits/symbolcvdFigure 5.1: The BER performance of the SPC-IrR codes with optimized code parameters and labeling patterns. Spec-eff represents spectrum efficiency.

For the SDR implementation, the emphasis of the multi-rate code design, however, is in simplicity. Our choicefor the component code is a rate 1/2 systematic non-recursive convolutional code concatenated with a doped accumulator. The multi-rate functionality is realized via selecting between QPSK and 16QAM modulation schemes.
Simple Gray mapping for the modulation is used. This coding scheme is a safe choice as it is known to perform
well in the context of multi-rate relaying. However, the choice lacks in flexibility when compared to the approachwith SPC-IrR codes and EBSA.

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5.2

D2.1.1 Version 1.0

Interaction with Higher Layers

This section summarizes how the code and decoder design carried out in WP2 interfaces with the work of WP3 and
WP4. Section 5.2.1 presents the functional block diagram of the chosen encoding and decoding chain at a relay
node. Furthermore, the parameters that need to be signalled or known by the higher layers are shown. In Section
5.2.2, a new abstraction of the physical layer coding functionality, for the purpose of simulating the higher layer
protocols such as ARQ and MAC, is proposed.
5.2.1

Functional Block Diagram and Interfaces

The basic functional blocks of the physical layer coding/decoding, and the interfaces towards the higher layer
protocols are exemplified in Figure 5.2, where a simplified model of the relay node is depicted. As can be seen,
the coding and modulation parameters (modulation and coding set, MCS) for both the received and for the corresponding transmitted packet copy need to be exchanged with higher layers. Most importantly, the interleaving (IL)patterns are different for different transmitting nodes, even if all the other parameters are relatively fixed.
It is recognized that the robust and flexible approach for appropriately signaling the code parameters is to attach aphysical frame header carrying the MCS and IL indexes to each of the packet copies at the transmitter side. Thisway, any receiving node – relay or destination – is able to decode the packet and restore the original payload data.
In addition to the code parameters, the header will carry a unique message identifier that enables the receiver to
identify which packet copies are to be iteratively combined. However, while it is tolerated that decoding results forthe data may be incomplete and include errors, the physical frame headers must always be received without error.
Otherwise the decoding process of the data cannot be started. Thus, the physical frame header needs to be well
protected by a strong code and/or adequate transmit energy.

MCS
index

MOD/MAP
index
a

Code
index
d

DEC

DEMAP
b,c

Doping
ratio

f

IL-1

Doping Coderatio index

IL index(TX)

IL index
(RX)

g

h

IL

ENC

MOD/MAP
index

i

MAP

j

e
Iterative processing
Equivalent to source transmitter

CRC
CI

OK/NOK

Confidence
indicator

Figure 5.2: Block diagram of the relay functionality.

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5.2.2

D2.1.1 Version 1.0
Simulation Abstraction for Higher Layers

In the system level, and for the higher layer functionalities such as multi-rate control, power control, ARQ, andMAC, it is desirable to be able to run simulations without the need to implement all the details of the physicallayer. For cellular systems, it is a common practice to apply link quality metric tools such as Exponential Effective
SNR Mapping (EESM) or Mutual Information (MI) based mapping [TS03; WTA06; YZW+14]. In essence, basedon the knowledge of the SNR level, and the (time or frequency selective) fading channel coefficients, the metricattempts to describe the link quality with just one scalar parameter that is the effective SINR or MI. The total MI
is the average of the MIs per subchannel, and the assumption is that at certain averaged MI level, the decoding
performance is the same regardless of how MI is divided into subchannels. The MI metric itself is independent of
the FEC coding scheme, but can be formulated as dependent on the modulation constellation such as QPSK and
16QAM. The metric can be used
• in simulations, to predict or approximate the block error probability (BLER) without running the actual
coding and decoding processes, or• in multi-rate control, to choose the appropriate modulation and coding parameters.
In order to create the mapping from SINR or MI to BLER, coding and decoding simulations are usually run for
example in the AWGN channel. Thus, code design and decoder implementation dependent performance mapping
is obtained. Each modulation and coding scheme as well as code block length may be simulated separately in orderto get an accurate mapping.
The MI-based metric suits well the RESCUE system model where multiple parallel links with the same data
are received. However, a RESCUE-specific problem remains: how to deal with the decoding errors at relaytransmitters. To address this issue, one can employ the information theoretic outage probability analysis derived
for the case of single-relay lossy forwarding in [ZCH+14]. The analysis is based on the theory of source codingwith side information.
WP2 proposes to create a quality mapping that predicts the BER distribution at a receiver that combines multiple
packet copies. The purpose is to facilitate fast and flexible simulations of the higher layers in terms of multi-rate
control, power control, ARQ, and MAC.
A simplified version of the ”admissible rate region” from [ZCH+14] is shown in Figure 5.3. 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 is unable to decode correctly, and the resulting BER at
the relay is p. The axes R1 and R2 represent the normalized channel constellation constrained capacities (mutual
information) of the source-to-destination link and the relay-to-destination link, respectively. Theoretically, if therate pair falls into the admissible 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 can assume
that the source data has full entropy, i.e., H(U1 ) = 1, and that the data transmitted by the relay also has full entropy
so that H(U2 ) = 1.
The bound of the admissible rate region consists of the straight line a
R1 + (1 − Hb (pi )) = 1(5.1)

and the curve b. In order to simplify the model, we approximate the curve by the straight c as
R1 + (1 − Hb (pi )) R2 = 1.

(5.2)

By combining the two lines, we get an expression for the approximated admissible rate region as
R1 + min{1 − Hb (pi ), (1 − Hb (pi ))R2 } ≥ 1(5.3)

We further propose to generalize the combining of MI over any number of parallel incoming links so thatM = ∑ Mi

(5.4)

i


Mi =

Ri ,
min{(1 − Hb (pi ))Ri , 1 − Hb (pi )},pi = 0pi > 0(5.5)

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R2aAchievable
Rate Region

H(U2)

b

Hb(p)

R1

H(U1)

Figure 5.3: Rate region for black boxes.
In theory, when MI per bit is unity, it is perfect. Note that if there are errors in the transmitter, corresponding MI
remains always below unity. Otherwise, MI can get larger values.
By employing the Shannon’s source-channel separation theorem, the distortion (BER) at the output of the receivercan be lower bounded by the inverse of the binary entropy function [ZCH+14] as
pe = Hb−1 (1 − M),(5.6)

which equals to zero when M ≥ 1. We call the mapping from the link-specific SNRs and transmitter BERs into the
MI and receiver BER as ”black box #1” as shown in Figure 5.4. It employs a very simple deterministic mapping thatis independent of the coding and decoding scheme, and requires no simulations. It predicts optimistic performancethat corresponds to infinite packet sizes and perfect codes.
modulation
order

code block
length (L)

code
rate

number ofparallel links (N)

p1
:
pN

:

SINR1
:
SINRN

MI

black box #1:

MIp (BER)

black box #2

BER perpacket (p)Figure 5.4: Black boxes 1 and 2.
In order to obtain code, decoder, and packet length dependent BER performance results, we propose to concatenate
black box #1 with black box #2 that employs a mapping obtained via simulations in the AWGN channel. The idea
is to obtain the random packet-by-packet decoding performance in terms BER.
The composite black box model is capable of providing BER performance per simulated packet, which depends
on the code rate and the SNRs of the parallel links. The black box model shall be used by WP3 to characterize theperformance of their proposed MAC, ARQ, and routing protocols, based on the simulated BER.

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D2.1.1 Version 1.0

Conclusion

This deliverable provided initial results and descriptions of the coding/decoding and source-correlation estimation
algorithms considered in the RESCUE project. First, the state-of-the-art in the case of a simple network model
consisting of a single source, a set of parallel relay nodes, and one destination node was summarized. Then, newsource-correlation estimation methods and signaling protocols that aim to improve the joint decoding performanceor to reduce the estimation complexity were proposed. Furthermore, more general system models were considered,including non-orthogonal multiple access for the relay transmissions, multi-hop networks where the destination ismore than two hops away from the source, and multiple-access relaying where two sources utilize a single relay
node. Finally, a preliminary description of the new simulation abstraction concept, called ”black box”, that aims
to support system level development and simulations, was given. Also, some code design choices for the SDR
implementation and demonstration were discussed.
For the simple ”toy scenarios” addressed in Chapter 2, no major performance improvements by code design canbe found since the performance of the state-of-the-art codes is already close to the theoretical limit. The remaining
challenge and the main novel contribution of this deliverable lie in more practical aspects: how to estimate or signal
the correlation between the relayed data sequences to the destination. Several novel ideas concerning this problem
were proposed in Chapter 3. In the usual scenario where the data packets are accompanied by CRC fields, it makes
sense for the relays to check it, and to signal the result to the destination along with the forwarded data. Similarly, it
is beneficial for the destination to know if one of the transmitters is actually the source: this way the joint decoder
can rely on hard facts about the transmitted sequence. However, when the CRC check fails at the relay, morerefined estimates of the BER of the decoded data packet can be obtained by estimating the SNR of the incoming
channel, or by calculating the confidence indicator (CI) based on the post-decoding LLRs. Finally, as estimates arealways in practice inaccurate, the estimates provided by the relays could be further improved by utilizing pairwise
BER estimation methods at the destination in conjunction with the iterative decoder. It is certainly a future design
challenge to find a protocol that provides the best trade-off between decoding performance, estimation complexity,
and signaling overhead.
When the network model is extended to cover more than two hops between the source and the relay, the multi-route
coding and decoding problem gets more challenging. For example, the decoding strategy at the relays needs to be
selected. If complexity is not an issue, the relays may carry out the same type iterative multi-packet combining as
the destination does. On the other hand, at the destination, the errors in the received packet copies may becomecorrelated, when the same errors are transmitted by the parallel relays of the second stage. However, as shownin Section 4.2, the cross-link problem does not seem to be severe, at least when the error probabilities remain
relatively low. Multi-hop relaying and more general topologies as well as communication scenarios are in thecentral focus of WP2 in the near future.
So far, WP2 has evaluated the performance in simplified models only, and mainly in terms of BER/FER as afunction of link-level SNRs. This approach is not completely fair in terms of the total transmit energy consumption
and spectral efficiency. It is recognized that the multi-route coding gain needs to compensate for the bandwidth
expansion caused by the parallel relays that reserve orthogonal time slots. One efficient way of avoiding the
bandwidth expansion is IDMA, where the relays are allowed to transmit at the same time in a non-orthogonalmanner. IDMA is studied in more details in WP1. Finally, the real test of the links-on-the-fly concept is carriedout when system level protocols such as ARQ and MAC are integrated with the coding strategy. The preliminary
descriptions of the higher layer protocols will be disclosed in another RESCUE deliverable D3.1 [D31].

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