Download or read book Timing Synchronization at the Relay Node in Physical Layer Network Coding written by Ashish Basireddy and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times, there has been an increased focus on the problem of information exchange between two nodes using a relay node. The introduction of physical layer network coding has improved the throughput efficiency of such an exchange. In practice, the reliability of information exchange using this scheme is reduced due to synchronization issues at the relay node. In this thesis, we deal with timing synchronization of the signals received at the relay node. The timing offsets of the signals received at the relay node are computed based on the propagation delays in the transmitted signals. However, due to the random attenuation of signals in a fading channel, the near far problem is inherent in this situation. Hence, we aim to design near far resistant delay estimators for this system. We put forth four algorithms in this regard. In all the algorithms, propagation delay of each signal is estimated using a known preamble sent by the respective node at the beginning of the data packet. In the first algorithm, we carefully construct the preamble of each data packet and apply the MUSIC algorithm to overcome the near far problem. The eigenstructure of the correlation matrix is exploited to estimate propagation delay. Secondly, the idea of interference cancellation is implemented to remove the near far problem and delay is estimated using a correlator. Thirdly, a modified decorrelating technique is presented to negate the near far problem. Using this technique we aim to obtain an estimate of the weak user's delay that is more robust to errors in the strong user's delay estimate. In the last algorithm, pilot signals with desired autocorrelation and cross correlation functions are designed and a sliding correlator is used to estimate delay. Even though this approach is not near far resistant, performance results demonstrate that for the length's of preamble considered, this algorithm performs similar to the other algorithms.

Download or read book A Primer on Physical Layer Network Coding written by Soung Liew and published by Springer Nature. This book was released on 2022-05-31 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of physical-layer network coding (PNC) was proposed in 2006 for application in wireless networks. Since then it has developed into a subfield of communications and networking with a wide following. This book is a primer on PNC. It is the outcome of a set of lecture notes for a course for beginning graduate students at The Chinese University of Hong Kong. The target audience is expected to have some prior background knowledge in communication theory and wireless communications, but not working knowledge at the research level. Indeed, a goal of this book/course is to allow the reader to gain a deeper appreciation of the various nuances of wireless communications and networking by focusing on problems arising from the study of PNC. Specifically, we introduce the tools and techniques needed to solve problems in PNC, and many of these tools and techniques are drawn from the more general disciplines of signal processing, communications, and networking: PNC is used as a pivot to learn about the fundamentals of signal processing techniques and wireless communications in general. We feel that such a problem-centric approach will give the reader a more in-depth understanding of these disciplines and allow him/her to see first-hand how the techniques of these disciplines can be applied to solve real research problems. As a primer, this book does not cover many advanced materials related to PNC. PNC is an active research field and many new results will no doubt be forthcoming in the near future. We believe that this book will provide a good contextual framework for the interpretation of these advanced results should the reader decide to probe further into the field of PNC.

Download or read book Design and Implementation of Physical Layer Network Coding Protocols written by Dumezie K. Maduike and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There has recently been growing interest in using physical layer network coding techniques to facilitate information transfer in wireless relay networks. The physical layer network coding technique takes advantage of the additive nature of wireless signals by allowing two terminals to transmit simultaneously to the relay node. This technique has several performance benefits, such as improving utilization and throughput of wireless channels and reducing delay. In this thesis, we present an algorithm for joint decoding of two unsynchronized transmitters to a modulo-2 sum of their transmitted messages. We address the problems that arise when the boundaries of the signals do not align with each other and when their phases are not identical. Our approach uses a state-based Viterbi decoding scheme that takes into account the timing offsets between the interfering signals. As a future research plan, we plan to utilize software-defined radios (SDRs) as a testbed to show the practicality of our approach and to verify its performance. Our simulation studies show that the decoder performs well with the only degrading factor being the noise level in the channel.

Download or read book Parameter Estimation and Tracking in Physical Layer Network Coding written by Manish Jain and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, there has been a growing interest in improving the performance of the wireless relay networks through the use of Physical Layer Network Coding (PLNC) techniques. The physical layer network coding technique allows two terminals to transmit simultaneously to a relay node and decode the modulo-2 sum of the transmitted bits at the relay. This technique considerably improves performance over Digital Network Coding technique. In this thesis, we will present an algorithm for joint decoding of the modulo-2 sum of bits transmitted from two unsynchronized transmitters at the relay. We shall also address the problems that arise when boundaries of the signals do not align with each other and when the channel parameters are slowly varying and are unknown to the receiver at the relay node. Our approach will first jointly estimate the timing o sets and fading gains of both signals using a known pilot sequence sent by both transmitters in the beginning of the packet and then perform Maximum Likelihood detection of data using a state-based Viterbi decoding scheme that takes into account the timing o sets between the interfering signals. We shall present an algorithm for simultaneously tracking the amplitude and phase of slowly varying wireless channel that will work in conjunction our Maximum Likelihood detection algorithm. Finally, we shall provide extension of our receiver to support antenna diversity. Our results show that the proposed detection algorithm works reasonably well, even with the assumption of timing misalignment. We also demonstrate that the performance of the algorithm is not degraded by amplitude and/or phase mismatch between the users. We further show that the performance of the channel tracking algorithm is close to the ideal case i.e. when the channel estimates are perfectly known. Finally, we demonstrate the performance boost provided by the receiver antenna diversity.

Download or read book Channel Coded Physical layer Network Coding in Wireless Relay Networks written by Xiaokang Wang and published by . This book was released on 2018 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Physical Layer Network Coding for the Multi way Relay Channel written by Behnam Hashemitabar and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Wireless networks have received considerable attention recently due to the high user demand for wireless services and the emergence of new applications. This thesis focuses on the problem of information dissemination in a class of wireless networks known as the multi-way relay channel. Physical layer network coding is considered to increase the throughput in these networks. First, an algorithm is proposed that increases the full data exchange throughput by 33% compared to traditional routing. This gain arises from providing common knowledge to users and exploiting this knowledge to restrain some users from transmitting. Second, for complex field network coding, a transmission scheme is designed that ensures the receipt of a QAM constellation at the relay. This requires precoding the user symbols to make all possible combinations distinguishable at the relay. Using this approach, the throughput of data exchange is 1/2 symbol per user per channel use. The error performance of both schemes is derived analytically for AWGN channels.

Download or read book Coding Schemes for Physical Layer Network Coding Over a Two Way Relay Channel written by Brett Michael Hern and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a two-way relay channel in which two transmitters want to exchange information through a central relay. The relay observes a superposition of the trans- mitted signals from which a function of the transmitted messages is computed for broadcast. We consider the design of codebooks which permit the recovery of a function at the relay and derive information-theoretic bounds on the rates for reliable decoding at the relay. In the spirit of compute-and-forward, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be decoded is chosen at the relay depending on the channel realization. We define such a class of reliably computable functions for the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme permits substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields. Our numerical results indicate that it is favorable to allow the relay to attempt both compute-and-forward and decode-and-forward decoding. Indeed, either method considered separately is suboptimal for computation over general channels. However, we obtain a converse result when the transmitters are restricted to using identical binary linear codebooks generated uniformly at random. We show that it is impossible for this code ensemble to achieve any rate higher than the maximum of the rates achieved using compute-and-forward and decode-and-forward decoding. Finally, we turn our attention to the design of low density parity check (LDPC) ensembles which can practically achieve these information rates with joint-compute- and-forward message passing decoding. To this end, we construct a class of two-way erasure multiple access channels for which we can exactly characterize the performance of joint-compute-and-forward message passing decoding. We derive the processing rules and a density evolution like analysis for several classes of LDPC ensembles. Utilizing the universally optimal performance of spatially coupled LDPC ensembles with message passing decoding, we show that a single encoder and de- coder with puncturing can achieve the optimal rate region for a range of channel parameters. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151149

Download or read book Physical layer Network Coding in Multi way Relay Channels written by Hao Li and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Physical-layer network coding (PNC) is an attractive approach to increasing the network throughput by exploiting the broadcast nature of wireless channels. This thesis focuses on the application of PNC in a class of wireless networks known as multi-way relay channels (MRWC), where multiple users share information through a single relay. The primary objective of the thesis is to develop new uplink and downlink schemes for PNC in MWRC, with the main focus on signal detection and power allocation. First, we propose a novel signal detection scheme for PNC in MWRC from the perspective of sequential multi-user detection. The extraction of the network codes from the superimposed user signals at the relay node is formulated as an under-determined linear system. To solve this problem with low decoding complexity, the proposed method combines successive interference cancellation (SIC) with Babai estimation for regularized integer least squares (ILS). We develop a power allocation scheme to enhance the performance of both SIC and ILS steps, and discuss an optimal user pairing strategy based on the average decoding error probability. The performance of the proposed method improves the relay's capability of extracting network codes from multiple superimposed user signals, as demonstrated by the numerical results. Next, we address the design of power allocation schemes for PNC in downlink MWRC. The power allocation is formulated as a constrained optimization problem, where the aim is to maximize the probability of successfully decoding a chain of network codes, so-called success probability, under a total power constraint when using Babai estimation for signal detection. Three aggregate measures of success probability are considered over the participating user terminals, i.e., arithmetic mean, geometric mean, and maximin, and the solutions are obtained based on the concavity of the related problems. Results demonstrate the effectiveness of the proposed schemes in improving the success probability in the reception of a chain of network codes. Finally, we propose a new power allocation scheme based on the success probability of SIC detection for PNC in uplink MWRC. We develop a generalized expression for the closed-form success probability of the SIC detection at the relay in the case of pulse-amplitude modulation (PAM). A constraint optimization is formulated over this probability subject to the transmit power constraints at the user terminals. We develop an evolutionary particle swarm optimization (PSO) algorithm to solve the problem, whose cost function is relatively complex and not necessarily concave. Results show that the proposed method can improve the quality of network code extraction at the relay"--

Download or read book Data Rate Optimization for Two way Relay Channel with Physical layer Network Coding written by Shanshan Huang and published by . This book was released on 2013 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Proceedings of the 28th Conference of Spacecraft TT C Technology in China written by Rongjun Shen and published by Springer. This book was released on 2017-07-25 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects selected papers from the 28th Conference of Spacecraft TT&C Technology in China held on November 8-10, 2016. The book features state-of-the-art studies on spacecraft TT&C in China with the theme of “Openness, Integration and Intelligent Interconnection”. To meet requirements of new space endeavors, development of spacecraft instrumentation systems have to follow an open concept and approach in China. An open spacecraft instrumentation system encompasses integrated development of different types of services, integration of disciplines and specialties, intelligent links, and more scientific and intelligent information interface technology. Researchers and engineers in the field of aerospace engineering and communication engineering can benefit from the book.

Download or read book Intelligent Computing and Internet of Things written by Kang Li and published by Springer. This book was released on 2018-09-03 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set CCIS 923, CCIS 924, and CCIS 925 constitutes the thoroughly refereed proceedings of the First International Conference on Intelligent Manufacturing and Internet of Things, and of the 5th International Conference on Intelligent Computing for Sustainable Energy and Environment, ICSEE 2018, held in Chongqing, China, in September 2018. The 135 revised full papers presented were carefully reviewed and selected from over 385 submissions.The papers of this volume are organized in topical sections on: digital manufacturing; industrial product design; logistics, production and operation management; manufacturing material; manufacturing optimization; manufacturing process; mechanical transmission system; robotics.

Download or read book Coding for Relay Networks with Parallel Gaussian Channels written by Yu-Chih Huang and published by . This book was released on 2013 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information forwarding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a network. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/149620

Download or read book Space time Coding for Asynchronous Cooperative Relay Networks written by Zheng Li and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Space-time coding (STC) is a promising technique to achieve transmit diversity in Multiple-Input-Multiple-Output (MIMO) systems. Recently, space-time coding in a distributed fashion (DSTC) for cooperative relay networks attracts a lot of research interests. The design of space-time coding for cooperative relay networks has some new challenges which are different from the design of space-time coding for MIMO systems. The synchronization issue is one of the most important problems in the design of distributed space-time coding for cooperative communication systems since the cooperative systems are asynchronous in nature, e.g., there may exist timing errors and multiple frequency offsets in the cooperative systems. In this dissertation, we will discuss and study several designs of space-time coding for cooperative systems with different system models and in different asynchronous scenarios. In the first topic, we attempt to design very simple space-time coding schemes for cooperative systems with timing errors in Amplify-and-Forward (AF) mode. One of the major purposes is to make the relay nodes as simple as possible so that the relay nodes only need to implement very simple operations with a very low complexity. Another major purpose is to achieve full diversity and fast Maximum-Likelihood (ML) decoding at the receiver despite the existence of the timing errors. Except for the timing errors, the problem of multiple frequency offsets is another kind of asynchronous error which should be solved as well. In the second topic, we investigate the scenario that the timing errors and the multiple frequency offsets are existed simultaneously in the Decode-and-Forward (DF) cooperative systems. We adopt OFDM to combat the timing errors and propose an intercarrier interference (ICI) Self-Cancellation scheme to suppress the ICI caused by multiple frequency offsets. In the third topic, we consider the physical layer security issue in cooperative systems with timing errors. In order to avoid illegal interception of the eavesdropper in a cooperative system, we propose a distributed differential encoding/decoding scheme combined with deliberate signal randomization to achieve Low Probability of Interception (LPI) as well as to obtain full diversity regardless of the timing errors.

Download or read book Cross layer Design for Multi hop Two way Relay Network written by Haoyuan Zhang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Physical layer network coding (PNC) was proposed under the two-way relay hannel (TWRC) scenario, where two sources exchange information aided by a relay. PNC allows the two sources to transmit to the relay simultaneously, where superimposed signals at the relay can be mapped to network-coded symbols and then be broadcast to both sources instead of being treated as interference. Concurrent transmissions using PNC achieve a higher spectrum efficiency compared to time division and network coding solutions. Existing research mainly focused on the symmetric PNC designs, where the same channel coding and modulation configurations are applied by both sources. When the channel conditions of the two source-relay links are asymmetric or unequal amount of data are exchanged, heterogeneous modulation PNC designs are necessary. In additional, the design and optimization of multi-hop PNC, where multiple relays forming a multi-hop path between the two sources, remains an open issue. The above issues motivate the study of this dissertation.This dissertation investigates the design of heterogeneous modulation physicallayer network coding (HePNC), the integration of channel error control coding into HePNC, the combination of HePNC with hierarchical modulation, and the design and generalization of multi-hop PNC. The contributions of this dissertation are four-fold.First, under the asymmetric TWRC scenario, where the channel conditions ofthe two source-relay links are asymmetric, we designed a HePNC protocol, including the optimization of the adaptive mapping functions and the bit-symbol labeling, to minimize the end-to-end BER. In addition, we developed an analytical framework to derive the BER of HePNC. HePNC can substantially enhance the throughput compared to the existing symmetric PNC under the asymmetric TWRC scenario.Second, we investigated channel coded HePNC and integrated the channel errorcontrol coding into HePNC in a link-to-link coding, where the relay tries to decode the superimposed codewords in the multi-access stage. A full-state sum-product decoding algorithm is proposed at the relay based on the repeat-accumulate codes to guarantee reliable end-to-end communication.Third, we proposed hierarchical modulation PNC (H-PNC) under asymmetric TWRC, where additional data exchange between the relay and the source with the relatively better channel condition is achieved in addition to that between the two end sources, benefiting from superimposing the additional data flow on the PNC transmission. When the relay also has the data exchange requirement with the source with a better source-relay channel, H-PNC outperforms HePNC and PNC in terms of the system sum throughput.Fourth, we designed and generalized multi-hop PNC, where multiple relays located in a linear topology are scheduled to support the data exchange between two end sources. The impact of error propagation and mutual interference among the nodes are addressed and optimized. The proposed designs outperform the existing ones in terms of end-to-end BER and end-to-end throughout.

Download or read book Cross Layer Coding Schemes for Broadcasting and Relaying written by Makesh Pravin John Wilson and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is divided into two main topics. In the first topic, we study the joint source-channel coding problem of transmitting an analog source over a Gaussian channel in two cases - (i) the presence of interference known only to the transmitter and (ii) in the presence of side information about the source known only to the receiver. We introduce hybrid digital analog forms of the Costa and Wyner-Ziv coding schemes. We present random coding based schemes in contrast to lattice based schemes proposed by Kochman and Zamir. We also discuss superimposed digital and analog schemes for the above problems which show that there are infinitely many schemes for achieving the optimal distortion for these problems. This provides an extension of the schemes proposed by Bross and others to the interference/source side information case. The result of this study shows that the proposed hybrid digital analog schemes are more robust to a mismatch in channel signal-to-noise ratio (SNR), than pure separate source coding followed by channel coding solutions. We then discuss applications of the hybrid digital analog schemes for transmitting under a channel SNR mismatch and for broadcasting a Gaussian source with bandwidth compression. We also study applications of joint source-channel coding schemes for a cognitive setup and also for the setup of transmitting an analog Gaussian source over a Gaussian channel, in the presence of an eavesdropper. In the next topic, we consider joint physical layer coding and network coding solutions for bi-directional relaying. We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter and relay nodes exchange data over synchronized, average power constrained additive white Gaussian noise channels. We propose structured coding schemes using lattices for this problem. We study two decoding approaches, namely lattice decoding and minimum angle decoding. Both the decoding schemes can be shown to achieve the upper bound at high SNRs. The proposed scheme can be thought of as a joint physical layer, network layer code which outperforms other recently proposed analog network coding schemes. We also study extensions of the bi-directional relay for the case with asymmetric channel links and also for the multi-hop case. The result of this study shows that structured coding schemes using lattices perform close to the upper bound for the above communication system models.

Download or read book Network Coding Applications written by Christina Fragouli and published by Now Publishers Inc. This book was released on 2008-01-08 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network Coding Applications looks at how ideas from network coding can have an impact on a number of new applications. It explains what network coding is, explores what its benefits are, and how much it costs to design and operate networks implementing network coding

Download or read book Distributed Coding for Wireless Cooperative Networks written by Atoosa Hatefi and published by . This book was released on 2012 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the rapid growth of wireless technologies, devices and mobile applications, the quest of high throughput and ubiquitous connectivity in wireless communications increases rapidly as well. Relaying is undoubtedly a key concept to provide coverage extension and capacity increase in wireless networks. Network coding, which allows the intermediate nodes to share their computation capabilities in addition to their resource and their power, has grabbed a significant research attention since its inception in information theory. It has become an attractive candidate to bring promising performance improvement, especially in terms of throughput, in relay-based cellular networks. Substantial research efforts are currently focused on theoretical analysis, implementation and evaluation of network coding from a physical layer perspective. The question is, what is the most efficient and practical way to use network coding in wireless relay-based networks, and whether it is beneficial to exploit the broadcast and multiple-access properties of the wireless medium to perform network coding. It is in such a context, that this thesis proceeds. In the first part of the thesis, the problem of Joint Network-Channel Coding (JNCC) for a Multiple Access Relay Channel (MARC) is investigated in the presence of multiple access interferences and for both of the relay operating modes, namely, half-duplex and full-duplex. To this end, three new classes of MARC, referred to as Half-Duplex Semi-Orthogonal MARC (HD-SOMARC), Half-Duplex Non-Orthogonal MARC (HD-NOMARC), and Full-Duplex Non-Orthogonal MARC (FD-NOMARC) have been introduced and studied. The relaying function in all of the classes is based on a Selective Decode-and-Forward (SDF) strategy, which is individually implemented for each source, i.e, the relay forwards only a deterministic function of the error-free decoded messages. For each class, an information-theoretic analysis is conducted, and practical coding and decoding techniques are proposed. The proposed coding schemes, perform very close to the outage limit for both cases of HD-SOMARC and HD-NOMARC. Besides, in the case of HD-NOMARC, the optimal allocation of the transmission time to the relay is considered. It is also verified that exploiting multiple access interferences, either partially or totally, results in considerable gains for MARC compared to the existing interference-avoiding structures, even in the case of single receive antenna. In the second part of the thesis, the network model is extended by considering multiple relays which help multiple sources to communicate with a destination. A new class of Multiple Access Multiple Relay Channel (MAMRC), referred to as Half-Duplex Semi-Orthogonal MAMRC (HD-SOMAMRC) is then proposed and analyzed from both information theoretic and code design perspective. New practical JNCC schemes are proposed, in which binary channel coding and non binary network coding are combined, and they are shown to perform very close to the outage limit. Moreover, the optimal allocation of the transmission time to the sources and relays is considered. Finally, in the third part of the thesis, different ways of implementing cooperation, including practical relaying protocols are investigated for the half-duplex MARC with semi-orthogonal transmission protocol and in the case of JNCC. The hard SDF approach is compared with two Soft Decode and Forward (SoDF) relaying functions: one based on log a posterior probability ratios (LAPPRs) and the other based on Mean Square Error (MSE) estimate. It is then shown that SDF works well in most of the configurations and just in some extreme cases, soft relaying functions (based on LAPPR or MSE estimate) can slightly outperform the hard selective one.