In this dissertation, we introduce a relay protocol for multiple-relay networks called parity forwarding. The relay channel is a classic multiuser information theory problem introduced in 1971, modeling a network of three nodes: a source, a destination, and a relay node. The relay has no message of its own and assists the source to communicate to the destination. Of the two main coding techniques for the relay channel, decode-and-forward (DF) and compress-and-forward (CF), our focus is to understand the DF scheme for single- and multiple-relay channels. For the single-relay channel, we present an interpretation of the classic DF strategy from a linear-coding perspective. Identifying binning in the classic DF strategy as parity bit generation, we devise ensembles of low-density parity-check (LDPC) codes, called bilayer LDPC codes, to incorporate the parity bits generated by the relay in the decoding process at the destination. We develop code design techniques and optimize the parameters of the bilayer LDPC code structure to show that bilayer LDPC codes can approach the theoretical DF rate. Inspired by the relation between binning and parity bits, we introduce the parity forwarding protocol to improve on the achievable DF rate in a multiple-relay network. For a two-relay network, we show that the previous multihop DF protocol can be improved if the relays forward parity messages and receivers (relays or the destination)use a joint decoding scheme. Depending on the relation between relay messages and decoded messages at each relay, different parity forwarding protocols are possible. In this thesis, we present a structured characterization of a class of parity forwarding protocols for multiple-relay networks. We propose a tree structure to describe the relations between messages. Using this tree structure, we derive a closed-form expression for the parity forwarding rate in a relay network with an arbitrary number of relays. Finally, examples of new types of degraded multiple-relay networks are presented for which the parity forwarding protocol achieves capacity.

In this dissertation, we introduce a relay protocol for multiple-relay networks called parity forwarding. The relay channel is a classic multiuser information theory problem introduced in 1971, modeling a network of three nodes: a source, a destination, and a relay node. The relay has no message of its own and assists the source to communicate to the destination. Of the two main coding techniques for the relay channel, decode-and-forward (DF) and compress-and-forward (CF), our focus is to understand the DF scheme for single- and multiple-relay channels. For the single-relay channel, we present an interpretation of the classic DF strategy from a linear-coding perspective. Identifying binning in the classic DF strategy as parity bit generation, we devise ensembles of low-density parity-check (LDPC) codes, called bilayer LDPC codes, to incorporate the parity bits generated by the relay in the decoding process at the destination. We develop code design techniques and optimize the parameters of the bilayer LDPC code structure to show that bilayer LDPC codes can approach the theoretical DF rate. Inspired by the relation between binning and parity bits, we introduce the parity forwarding protocol to improve on the achievable DF rate in a multiple-relay network. For a two-relay network, we show that the previous multihop DF protocol can be improved if the relays forward parity messages and receivers (relays or the destination)use a joint decoding scheme. Depending on the relation between relay messages and decoded messages at each relay, different parity forwarding protocols are possible. In this thesis, we present a structured characterization of a class of parity forwarding protocols for multiple-relay networks. We propose a tree structure to describe the relations between messages. Using this tree structure, we derive a closed-form expression for the parity forwarding rate in a relay network with an arbitrary number of relays. Finally, examples of new types of degraded multiple-relay networks are presented for which the parity forwarding protocol achieves capacity.

In network information theory, the relay channel models a communication scenario where there is one or more relay nodes that can help the information transmission between the source and the destination. Although the capacity of the relay channel is still unknown even in the single-relay case, two fundamentally different relay schemes have been developed by (Cover and El Gamal, 1979) for such channels, which, depending on whether the relay decodes the information or not, are generally known as Decode-and-Forward (D-F) and Compress-and-Forward (C-F). In the D-F relay scheme, the relay first decodes the message sent by the source and then forwards it to the destination, and the destination decodes the message taking into account the inputs of both the source and the relay. In contrast, the C-F relay scheme is used when the relay cannot decode the message sent by the source, but still can help by compressing its observation into some compressed version, and forwarding this compression into the destination; the destination then either successively or jointly decodes the compression of the relay's observation and the original message of the source. For the single-relay case, it is known that joint compression-message decoding, although providing more freedom in choosing the compression at the relay, cannot achieve higher rates for the original message than successive decoding. This thesis addresses some fundamental issues in generalizing and unifying the above D-F and C-F relay schemes to the multiple-relay case. We first generalize the C-F scheme to multiple-relay channels, and investigate the question of whether compression-message joint decoding can improve the achievable rate compared to successive decoding in the multiple-relay case. It is demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Furthermore, it is shown that any compressions not completely decodable even with joint decoding will not provide any contribution to the decoding of the original message. We also develop a new C-F relay scheme with block-by-block backward decoding. This new scheme improves the original C-F relay scheme to achieve higher rates in the multiple-relay case as the recently proposed noisy network coding scheme. However, compared to noisy network coding which uses repetitive encoding/all blocks united decoding, our new coding scheme is not only simpler, but also reveals the essential reason for the improvement of the achievable rate, that is, delayed decoding until all the blocks have been finished. Finally, to allow each relay node the freedom of choosing either the D-F or C-F relay strategy, we propose a unified relay framework, where both the D-F and C-F strategies can be employed simultaneously in the network. This framework employs nested blocks combined with backward decoding to allow for the full incorporation of the best known D-F and C-F relay strategies. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases. It is also demonstrated through a Gaussian network example that our achievable rates are generally better than the rates obtained with existing unified schemes and with D-F or C-F alone.

The future wireless communication systems are required to meet the growing demands of reliability, bandwidth capacity, and mobility. However, as corruptions such as fading effects, thermal noise, are present in the channel, the occurrence of errors is unavoidable. Motivated by this, the work in this dissertation attempts to improve the system performance by way of exploiting schemes which statistically reduce the error rate, and in turn boost the system throughput. The network can be studied using a simplified model, the two-way relay channel, where two parties exchange messages via the assistance of a relay in between. In such scenarios, this dissertation performs theoretical analysis of the system, and derives closed-form and upper bound expressions of the error probability. These theoretical measurements are potentially helpful references for the practical system design. Additionally, several novel transmission methods including block relaying, permutation modulations for the physical-layer network coding, are proposed and discussed. Numerical simulation results are presented to support the validity of the conclusions.

Given the exponentially increasing number of connected devices to the network which will lead to a larger number of installed celluar towers and base stations that are in closer proximity to one another when compared to the current cellular network setup, and the increasing demand of higher data rates by end users, it becomes essential to investigate new methods that will more effectively mitigate the larger interference introduced by the more packed celluar grid and that result in higher data rates. This paper investigates using Device-to-Device communication where neighboring users can cooperate to mitigate the correlated interference they both receive, where one user acts as a relay and the other as the intended destination of a broadcast message sent by the source base station. The setup studied utalizes a non-orthogonal multiple access (NOMA) scheme and a combined decode-forward and compress-forward relaying scheme. We show that this combined scheme outperforms the individual schemes for some channels and network setups, or reduces to either scheme when the combination does not offer any achievable rate gains. The performance of each scheme is measured with respect to the locations of the base station and the two devices, and to the capacity of the digital link between the users.

Demand for high data rates is increasing rapidly for future wireless systems.This trend is due to the increase in the number of mobile subscribers that need bandwidth hungry multimedia applications anywhere, anytime. Fourth generation cellular systems like IMT-advanced are being developed to meet these requirements. The unreliable nature of the wireless medium is one of the main hinderance in providing high data rates. Cooperative communication in cellular networks is emerging as a new paradigm to deal with the channel impairments. User cooperation via fixed relays in cellular systems form multiple access relay channels (MARCs) and provide an effective and cost efficient solution to achieve spatial diversity gains. Network resources can be utilized efficiently by using network coding at cooperating nodes. A lot of research work has focused on highlighting the gains achieved by using network coding in MARCs. However, there are certain areas that are not fully explored yet. For instance, the kind of the detection scheme used at the base station receiver and its impact on the link performance has not been addressed. In most cases, the outage probability has been used as a performance measure of MARCs. However, it is well known that the outage probability gives information about the signal availability, but it does not give the complete picture about the reliability of the link and the achieved quality of service. This thesis work looks at the link performance, in terms of symbol error probability, of multiple access relay channels that employ network coding at the relay node. Different types of detection schemes are considered and their performance is compared under different link conditions. Analytical expressions for the average symbol error probability of the cooperating users are derived. Focusing on the uplink of cellular systems, certain rules are devised on how to group users at relay node to ensure mutual benefit for the cooperating users. As a way of improving the link performance of multiple access relay channels and their robustness, the thesis considers constellation selection for the different branches. This method takes advantage of the redundancy between the transmitted symbols created by network coding and the augmented signal space obtained at the base station receiver. The obtained results show that, with a proper selection of the constellation sets, the link performance of MARCs can be improved. The thesis further looks at the interaction between the channel coding schemes of the cooperating users and network coding. It is shown that joint channel-network coding in MARCs can be seen as a product code. This new representation provides considerable flexibility in selecting efficient decoding algorithms at the base station receiver and gives the possibility to use more powerful network coding schemes for MARCs. / QC 20101118 / Sino-Swedish Cooperative Program: IMT-Advanced and Beyond

Motivated by current applications in multihop transmission and ad hoc networks, the classical three-node relay channel consisting of a source-destination pair and a relay has received significant attention. One of the crucial aspects of the relay channel is the design of proper relaying protocols, i.e., how the relay should take part into transmission. The thesis addresses this problem and provides a partial answer to that. In this thesis, we propose and study two novel relaying protocols. The first one is based on constellation rearrangement (CR) and is suitable for higher-order modulation schemes. With CR, the relay uses a bit-symbol mapping that is different from the one used by the source. We find the optimal bit-symbol mappings for both the source and the relay and the associated optimal detectors, and show that the improvement over conventional relaying with Gray mapping at the source and the relay can amount to a power gain of several dB. This performance improvement comes at no additional power or bandwidth expense, and at virtually no increase in complexity. The second one is a half-duplex decode-and-forward (DF) relaying scheme based on partial repetition (PR) coding at the relay. With PR, if the relay decodes the received message successfully, it re-encodes the message using the same channel code as the one used at the source, but retransmits only a fraction of the codeword. We analyze the proposed scheme and optimize the cooperation level (i.e., the fraction of the message that the relay should transmit). We compare our scheme with conventional repetition in which the relay retransmits the entire decoded message, and with parallel coding, and additionally with dynamic DF. The finite SNR analysis reveals that the proposed partial repetition can provide a gain of several dB over conventional repetition. Surprisingly, the proposed scheme is able to achieve the same performance as that of parallel coding for some relay network configurations, but at a much lower complexity. Additionally, the thesis treats the problem of resource allocation for collaborative transmit diversity using DF protocols with different type of CSI feedback at the source. One interesting observation that emerges is that the joint powerbandwidth allocation only provides marginal gain over the relaying protocols with optimal bandwidth allocation. / QC 20101119

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

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