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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
241

Simulation Comparison of Auto-Tuning Methods for PID Control / Jämförelse av olika automatiska trimningsmetoder för PID-regulatorer

Olsson, Markus January 2008 (has links)
Auto-tuning has become an important function in distributed control systems (DCS) and is especially appreciated in large industries that can have hundreds of controllers. In the DCS 800xA manufactured by ABB, there is an auto-tuning method implemented based on a relay experiment to determine the ultimate gain and the ultimate period, with which the PID parameters are obtained using the modified Ziegler-Nichols tuning rules. The tuning procedure can then proceed with a step identification experiment to get additional parameters for kappa-tau tuning. In the previous DCS, called Advant, there was another auto-tuning approach implemented. This method was based on dominant pole design, which included an identification of the process. The purpose of this thesis is to compare these auto-tuning methods, to investigate if the dominant pole placement method should be migrated to the 800xA system. / Automatisk trimning har blivit en viktig funktion i distribuerade styrsystem (DCS och är speciellt av intresse för stora industrier som kan ha flera hundra regulatorer. Den automatiska trimningen som idag är implementerad i ABB:s DCS 800xA är baserad på ett reläexperiment för att bestämma den ultimata förstärkningen och den ultimata periodtiden. Modifierade Ziegler-Nichols trimningsregler används sedan för att bestämma PID parametrarna. Vidare kan trimningen fortsätta med ett stegsvars-experiment för att erhålla ytterliggare parametrar och trimma med kappa-tau metoden. Den automatiska trimningsmetoden som var implementerad i tidigare DCS, Advant, var baserad på dominant polplacering med identifiering av processen. Syftet med detta examensarbete är att jämföra dessa automatiska trimningsmetoder för att undersöka om den tidigare trimningsmetoden baserad på dominant polplacering ska implementeras i 800xA systemet.
242

Multihop Concept in Cellular Systems

Rangineni, Kiran January 2008 (has links)
We are very thirsty in terms of everything to fulfil our needs in a sophisticated way, and this leads me choose the so called master thesis titled “Multihop Concept in Cellular Systems”. This thesis introduces an approach towards the integration of relaying or multihop scheme in the next generation of cellular networks. In a multihop cellular architecture, the users send their data to the base station via relay station or with direct communication to the base station. These relay stations can either be the nomadic, fixed at specific location or users’ mobile station (i.e. mobile relay station). The main objective of this paper is to compare the difference between the relaying network architecture with different channel bandwidth as well as their performance gain. For this we integrate the relay station into conventional cellular networks using IEEE 802.16j (One of the standard introduced relay station concept in WiMAX) OFDMA (Orthogonal Frequency Division Multiple Access is a transmission technique that is based on many orthogonal subchannels (set of carriers) that transmits simultaneously). The results show that under certain conditions the throughput and coverage of the system has been increased with the introduction of the relay station in to cellular base station zone.
243

Relay-assited transmission and radio resource management for wireless networks

Agustín de Dios, Adrián 01 January 2008 (has links)
La transmisión asistida por relay o transmisión cooperativa es una nueva técnica de diversidad espacial donde aparece un elemento nuevo (un relay o un usuario cooperativo) en la tradicional transmisión punto a punto (fuente a destino). Ahora en la comunicación intervienen tres enlaces: fuente-relay, relay-destino y fuente-destino. El relay, además de asistir a la fuente en la transmisión de un mensaje, permite combatir las degradaciones que puede sufrir el canal como el shadowing y el pathloss. Aunque esta técnica está basada en el trabajo realizado en los 70 por Van der Meulen, Cover y El Gamal, ha sido en los últimos años cuando se han vuelto a considerar el uso de relays. En realidad, la transmisión asistida por un relay puede verse como un sistema virtual multi-antena (virtual MIMO) donde las antenas están distribuidas en diferentes terminales. Sin embargo, al contrario de los sistemas multi-antena y debido a la limitación de la actual tecnología radio, el relay debe trabajar en modo half-duplex, ya que no puede transmitir y recibir simultáneamente en la misma banda. Este hecho, motiva que la transmisión deba realizarse en dos fases ortogonales en función del modo del relay (recibiendo datos - relay-receive phase o transmitiendo datos - relay-transmit phase). Estas fases pueden implementarse en el dominio de la frecuencia o el tiempo.Esta tesis investiga protocolos y estrategias para la transmisión asistida por relay para mejorar la eficiencia espectral y homogeneizar el servicio para todos los usuarios en un sistema de comunicación celular. La introducción del relay en la comunicación implica la redefinición de muchas técnicas y protocolos considerados en las comunicaciones punto a punto y en los sistemas multi-antena, situados en la capa física y/o superiores.En primer lugar se presentan los achievable rates obtenidos por la transmisión asistida por relay en función del rol del relay (amplifica y retransmite o decodifica y retransmite), el tipo de transmisión (siempre transmite, incremental o selectiva), los datos transmitidos por el relay (repite los símbolos recibidos o son independientes) y el tipo del protocolo half duplex. En función de los terminales activos en cada fase de la comunicación (fuente, destino o relay), existen hasta cuatro protocolos. Otro aspecto considerado es la asignación de recursos (resource allocation) para cada fase de la comunicación, la cual puede estar fijada de antemano o puede ser ajustada dinámicamente en función de los canales de los diferentes enlaces. En el caso de que todos los coeficientes del canal se conocieran perfectamente, los terminales podrían transmitir síncronamente, mejorando la comunicación gracias a la ganancia debida a técnicas de pre-codificación por medio de los autovectores del canal (con antenas distribuidas).Además dos técnicas de transmisión asistida por relay son evaluadas cuando existen múltiples relays por destino. Ambas dependen del tipo de mensajes transmitidos a cada relay (mensajes independientes o uno común). La asignación de recursos para ambas técnicas puede verse como un problema convexo.Tres escenarios resumen diferentes tipos de transmisión asistida por relay para múltiples fuentes y un solo destino: RMAC (Relay-assisted Multiple Access Channel), UC (User Cooperation) and MARC (Multiple Access Relay Channel). Su diferencia se basa en el tipo de relay half- duplex considerado. La transmisión puede hacerse síncrona o asíncronamente. Las fuentes y los relays están limitados en potencia y el acceso de ellos en cada fase de la comunicación pude hacerse por medio de TDMA (time division multiple access), FDMA (frequency division multiple access) or SC (superposition coding multiple access). La asignación de recursos puede ser formulada como un problema convexo en algunos casos y la solución óptima puede ser encontrada. Seguidamente la transmisión asistida por relay y duplexada en tiempo es aplicada a un sistema celular centralizado basado en TDMA en el downlink. Con el objetivo de mejorar la eficiencia espectral se propone el reuso espacial de un slot temporal para las transmisiones de los relays hacia sus respectivos destinos (slot de relay), generando interferencia para todos los restantes destinos activos. Un algoritmo de control de potencia basado en la teoría de juegos es propuesto para combatir la interferencia generada. Bajo esa configuración, un algoritmo de scheduling investiga las posibles ganancias debidas al multi-user gain y mide el overhead introducido.Otra forma de tratar con la interferencia es la de controlar el rate de nuestra transmisión (rate control management). Bajo ciertas condiciones es posible modelar la función de densidad de probabilidad de la potencia interferente. En ese caso, la fuente ajusta el rate para maximizar el throughput de la comunicación. Esta solución es extendida para el caso en el que cada destino es asistido por varios relays. Las dos soluciones propuestas son capaces de proporcionar mejores resultados que la transmisión directa, a pesar de la interferencia existente en el slot de relay. Finalmente, se investiga el control dinámico del enlace para la transmisión asistida por relay con dos diferentes tipos de conocimiento sobre el canal: conocimiento estadístico (statistical knowledge of the channel state) o conocimiento del canal instantáneo (actual information about the current channel state).Estos dos tipos de conocimiento derivan en diferentes estrategias a utilizar para seleccionar la modulación y el esquema de codificación (MCS). En el primer caso, los rates seleccionados no están adaptados al canal actual, por lo que el destino puede recibir erróneamente los mensajes. Los protocolos de retransmisión de mensajes (ARQ - automatic repeat request) son los encargados de asegurarse la correcta recepción y son redefinidos para la transmisión asistida por relay.. En este trabajo, se especifica los códigos espacio-tiempo distribuidos, la codificación en al fuente y el relay y la longitud de las retransmisiones. Cuando la fuente conoce algún parámetro del canal instantáneo puede adaptar el MCS para esa realización del canal. En ese caso se investiga la predicción del error en las transmisiones asistidas por relay, y con ello es posible diseñar el MCS para que maximice la cantidad de información transmitida para una probabilidad de pérdida de paquete o que maximice el throughput. / The relay-assisted or cooperative transmission is a relatively new class of spatial diversity technique where a new element comes up in the conventional source-destination or point-to point communication: an assisting relay or cooperating user. The relay assists to the source in transmitting a message to the destination and allows dealing with the channel impairments like shadowing and pathloss. Although the seminal works were issued in the 70's by van der Meulen, Cover and El Gamal, it has been during the last years when it has re-gained more attention by the researchers. In fact, the relay-assisted transmission can be seen as a virtual MIMO (Multiple Input Multiple Output) with distributed antennas. In contrast to MIMO systems, the transmission requires the use of additional channel resources because of the limitation of the current radio technology: the relay terminal is constrained to work in half-duplex mode, which motivates that the transmission must be carried out in two orthogonal phases (relay-receive and relay-transmit phase), duplexed in time or frequency domains.This dissertation investigates protocols and strategies for the relay-assisted transmission which improve the spectral efficiency and homogenize service in the cellular communication systems. The new element present in the communication, the relay terminal, imposes a redefinition of many techniques and protocols commonly used in the point-to-point and MIMO systems, which are placed at the physical and upper layers.First, achievable rates using the relay-assisted transmission are provided which depend on the role of the relay (amplify-and-forward or decode-and-forward), the type of the transmission (persistent transmission, incremental or selective relaying), the data transmitted by the relays (repetition or unconstrained coding) and the type of half-duplex protocol. There are up to four protocol definition depending on the activity of the terminals on each phase. An additional aspect addressed is the resource allocation for each phase, that is, either it is fixed beforehand (static) or it is adjusted dynamically (dynamic) as a function of the channel quality. For the single-user relay- assisted transmission the resources can be allocated based on the channel quality of the different links. Moreover, if there is complete channel state information about all channel coefficients, source and relay can transmit synchronously enhancing the transmission thanks to the (distributed) eigenvector precoding techniques.Two relay-assisted transmission techniques are evaluated when a destination is assisted by multiple relays. Both depend on the messages intended to each assisting relay (independent or common messaging). The resource allocation for both techniques is shown to be convex. Additionally, three different scenarios illustrate the multi-user relay-assisted transmission with a single destination and different types of half-duplex relays: RMAC (Relay-assisted Multiple Access Channel), UC (User Cooperation) and MARC (Multiple Access Relay Channel). The relay-assisted transmission can be done synchronously or asynchronously. The sources and relays are power limited and access in each phase of the communication by TDMA (time division multiple access), FDMA (frequency division multiple access) or SC (superposition coding multiple access). For those scenarios the allocation of transmitted power and time resources can be formulated as a convex problem under some circumstances, evaluating the optimal solution.Afterwards, the relay-assisted transmission duplexed in time is applied to a centralized cellular system based on TDMA in the downlink. The reuse of one time slot for the transmissions done from the relays to destinations (relay slot) is proposed to improve the spectral efficiency. This solution produces interference for all the destinations active in that time slot. A power control algorithm (at the relays) based on game theory is proposed to combat the generated interference. Under that configuration a scheduler algorithm explores the multi-user gain for the relay-assisted transmission, measuring the introduced overhead.Another way of dealing with the interference is by rate control management. Under some circumstances it is possible to model the probability density function (pdf) of the interfering power. In such a case, the source can tune the transmission rate in order to maximize the throughput. This solution is extended to the case where each destination is assisted by multiple relays. In spite of the interfering power, both proposed solutions are able to provide significant gains over the direct transmission.Finally, the dynamic link control of the relay assisted transmission is investigated under two different assumptions on the knowledge about the channel: statistical knowledge of the channel state and actual information about the current channel state. Both types of knowledge lead to different transmission strategies, in terms of selecting the modulation and coding scheme (MCS). Under the first case, the transmission rates are not adapted to the current channel realization and the destination can decode wrongly the messages. The Automatic Repeat reQuest (ARQ) protocols are redefined for the relayassisted transmission to cope with these events. In this work we specify the (distributed) space-time codes, the coding at the source and relay and the length of the retransmissions. When there is actual information about the channel state the MCS can be adapted to the current channel realization. In such a case, the link error prediction for the relay-assisted transmission is investigated, and thus the MCS can be designed for maximizing the information rate for a given probability of packet loss or maximizing the throughput.
244

New methodology for transmission line relay testing and evaluation using advanced tools

Ristanovic, Dragan 30 September 2004 (has links)
Protective relays are important parts of the power system. The protection guards valuable equipment, and protective relays play a vital role in performing the task. The relay detects fault conditions within an assigned area, opens and closes output contacts to cause the operation of other devices under its control. The relay acts to operate the appropriate circuit breakers to prevent damage to personnel and property. To ensure consistent reliability and proper operation, protective relay equipment must be evaluated and tested. The importance of the relay evaluation issue is linked to capability to test the relays and relaying systems using very accurate waveform representation of a fault event. The purpose of testing protective relays is to ensure correct operation of the relay for all possible power system conditions and disturbances. To fulfill this purpose, relay testing in varying network configurations and with different fault types is required. There are a variety of options that have different performance potentials and implementation constraints. Use of digital simulators to test protective relays has proven to be an invaluable mean to evaluate relay performance under realistic conditions. This thesis describes a new methodology that attempts to improve the existing practices in testing relays by using advanced digital simulator hardware, different software packages for network modeling, and new software tools for generating and replaying test waveforms. Various types of microprocessor relays are tested and evaluated through the set of scenarios. New methodology that combines different software packages to facilitate particular testing objectives is applied.
245

Cooperative Protocols for Relay and Interference Channels with Half-Duplex Constraint

Bagheri, Hossein January 2010 (has links)
Enabling cooperation among nodes of a wireless network can significantly reduce the required transmit power as well as the induced intra-network interference. Due to the practical half-duplexity constraint of the cooperating nodes, they are prohibited to simultaneously transmit and receive data at the same time-frequency resource. The purpose of this dissertation is to illustrate the value of cooperation in such an environment. To understand how to cooperate efficiently, information theory is employed as a useful tool, which not only determines the fundamental limits of communication (i.e., capacity) over the considered network, but also provides insights into the design of a proper transmission scheme for that network. In this thesis, two simple but yet important types of wireless networks, namely Relay Channel, and Interference Channel are studied. In fact, these models constitute building blocks for larger networks. The first considered channel is a diamond-shaped relay channel consisting of a source, a destination, and two parallel relays. The second analyzed channel is an interference channel composed of two transmitter-receiver pairs with out-of-band transmitter cooperation, also referred to as conferencing encoders. While characterizing the capacity of these channels are difficult, a simpler and a more common approach is to find an achievable scheme for each channel that ensures a small gap from the capacity for all channel parameters. In chapter 2, the diamond relay channel is investigated in detail. Because of the half-duplex nature of the relays, each relay is either in transmit or receive mode, making four modes possible for the two-relay combination, specifically, 1) broadcast mode (both relays receive) 2,3) routing modes (one relay transmits, another receives) 4) multiple-access mode (both relays transmit). An appropriate scheduling ( i.e., timing over the modes) and transmission scheme based on the decode-and-forward strategy are proposed and shown to be able to achieve either the capacity for certain channel conditions or at most 3.6 bits below the capacity for general channel conditions. Particularly, by assuming each transmitter has a constant power constraint over all modes, a parameter Δ is defined, which captures some important features of the channel. It is proven that for Δ=0 the capacity of the channel can be attained by successive relaying, i.e., using modes 2 and 3 defined above in a successive manner. This strategy may have an infinite gap from the capacity of the channel when Δ≠0. To achieve rates as close as 0.71 bits to the capacity, it is shown that the cases of Δ>0 and Δ<0 should be treated differently. Using new upper bounds based on the dual problem of the linear program associated with the cut-set bounds, it is proven that the successive relaying strategy needs to be enhanced by an additional broadcast mode (mode 1), or multiple access mode (mode 4), for the cases of Δ<0 and Δ>0, respectively. Furthermore, it is established that under average power constraints the aforementioned strategies achieve rates as close as 3.6 bits to the capacity of the channel. In chapter 3, a two-user Gaussian Interference Channel (GIC) is considered, in which encoders are connected through noiseless links with finite capacities. The setup can be motivated by downlink cellular systems, where base stations are connected via infrastructure backhaul networks. In this setting, prior to each transmission block the encoders communicate with each other over the cooperative links. The capacity region and the sum-capacity of the channel are characterized within some constant number of bits for some special classes of symmetric and Z interference channels. It is also established that properly sharing the total limited cooperation capacity between the cooperative links may enhance the achievable region, even when compared to the case of unidirectional transmitter cooperation with infinite cooperation capacity. To obtain the results, genie-aided upper bounds on the sum-capacity and cut-set bounds on the individual rates are compared with the achievable rate region. The achievable scheme enjoys a simple type of Han-Kobayashi signaling, together with the zero-forcing, and basic relaying techniques.
246

On the use of hierarchical modulation for resource allocation in OFDMA-based networks

Jdidi, Anis 03 November 2011 (has links) (PDF)
We investigate, in this thesis, the use of Hierarchical Modulation (HM), a physical layer technique that enables to exploit multiuser diversity, for resource allocation in OFDMA-based systems with and without use of relaying, so as to improve the system capacity. HM allows the sharing of the resources, namely subcarriers and power, between users of different radio conditions by sending an additional stream to a user with good radio conditions on a subcarrier that was initially allocated to carry an original stream to a user with lower radio conditions. And this, without affecting the original user's rate nor the total amount of power assigned to the shared subcarrier. In the literature, most of the works that consider the use of HM focus solely on the physical layer performance, notably in terms of the bit error rate. And this for a static user scenario,i.e., with a fixed number of users in the system, each with an infinite service duration. This configuration however does not reflect the real system behavior where the number of users is dynamic, i.e., the users come to the system at random time epochs and leave it after a finite duration, corresponding to the completion of their services. The study of the system at the flow-level, as opposed to the packet level, for a dynamic user configuration, enables us to investigate the realistic relationship between capacity and demand and to quantify several system-level performance metrics, such as mean transfer times and blocking rates, which are meaningful both to the user and the network operator/provider.
247

Relinės apsaugos nuo įžemėjimo atrankumo tyrimas / Selectivity investigation of relay protection from earth fault

Sakalauskas, Tomas 16 August 2007 (has links)
Darbe atliktas relinės apsaugos nuo įžemėjimo atrankamo tyrimas, išnagrinėti neutralės įžeminimo režimai ir jų įtaka įžemėjimo atrankumui. Išanalizuotas apsaugų skirstymas pagal kontroliuojamą elementą. Atlikta Akcinės bendrovės „VST“ Šiaulių regione naudojamų relinės apsaugos įrenginių analizė ir funkcijų palyginimas. Ištirtos keturių tipų neteisingos relinės apsaugos nuo įžemėjimo suveiktys. Nustačius, kad įžemėjimo pažaidos metu nulinės sekos srovėje atsiranda aukštesnės eilės harmonikų atliktas bandymas, kurio metu išanalizuotas aukštesnių dažnių įtaka nulinės sekos transformatorių paklaidoms. Nustatyti dėsningumai susiję tarp dažnio ir paklaidos. Tyrimo metu išaiškintos priežastys lemiančios atrankumą įžemėjimo pažaidos metu. / The selectivity research of link protection of grounding has been done and the grounding modes of neutrality and their influence to grounding selectivity have been analyzed. Moreover, the distribution of protection under a controlling element has been studied. The research of the equipment of link protection used in the Stock Company “VST” Šiauliai region has been implemented and compared its functions. There have also been analyzed four types of effect due to wrong link protection of grounding. It was estimated that during the period of disturbance of grounding a higher line of harmonic appears in the current of null string. The experiment was implemented which estimated bias of transformers of null string by the influence of higher rates. Regularity related between rates and bias has been estimated. In addition the research explained the reasons which determines selectivity during the period of the grounding disturbance.
248

Scheduling in omnidirectional relay wireless networks

Wang, Shuning January 2013 (has links)
The capacity of multiuser wireless network, unclear for many years, has always been a hot research topic. Many different operation schemes and coding techniques have been proposed to enlarge the achievable rate region. And omnidirectional relay scheme is one of them. This thesis mainly works on the achievable region of the all-source all-cast network with omnidirectional relay scheme. In order to better understand this problem, we first describe the half-duplex model on the one-dimensional and two-dimensional regular networks. And we present an optimal operation scheme for them to have the maximum achievable rate. For the one-dimensional general network, we proposed an achievable region that indicates valued improvement compared to the previous results. In the full-duplex model of the one-dimensional general network, the maximum achievable rate is presented with a simpler proof in comparison with the previous results. In this thesis, we also show some discussions on more general networks.
249

Joint Source Channel Coding in Broadcast and Relay Channels: A Non-Asymptotic End-to-End Distortion Approach

Ho, James January 2013 (has links)
The paradigm of separate source-channel coding is inspired by Shannon's separation result, which implies the asymptotic optimality of designing source and channel coding independently from each other. The result exploits the fact that channel error probabilities can be made arbitrarily small, as long as the block length of the channel code can be made arbitrarily large. However, this is not possible in practice, where the block length is either fixed or restricted to a range of finite values. As a result, the optimality of source and channel coding separation becomes unknown, leading researchers to consider joint source-channel coding (JSCC) to further improve the performance of practical systems that must operate in the finite block length regime. With this motivation, this thesis investigates the application of JSCC principles for multimedia communications over point-to-point, broadcast, and relay channels. All analyses are conducted from the perspective of end-to-end distortion (EED) for results that are applicable to channel codes with finite block lengths in pursuing insights into practical design. The thesis first revisits the fundamental open problem of the separation of source and channel coding in the finite block length regime. Derived formulations and numerical analyses for a source-channel coding system reveal many scenarios where the EED reduction is positive when pairing the channel-optimized source quantizer (COSQ) with an optimal channel code, hence establishing the invalidity of the separation theorem in the finite block length regime. With this, further improvements to JSCC systems are considered by augmenting error detection codes with the COSQ. Closed-form EED expressions for such system are derived, from which necessary optimality conditions are identified and used in proposed algorithms for system design. Results for both the point-to-point and broadcast channels demonstrate significant reductions to the EED without sacrificing bandwidth when considering a tradeoff between quantization and error detection coding rates. Lastly, the JSCC system is considered under relay channels, for which a computable measure of the EED is derived for any relay channel conditions with nonzero channel error probabilities. To emphasize the importance of analyzing JSCC systems under finite block lengths, the large sub-optimality in performance is demonstrated when solving the power allocation configuration problem according to capacity-based formulations that disregard channel errors, as opposed to those based on the EED. Although this thesis only considers one JSCC setup of many, it is concluded that consideration of JSCC systems from a non-asymptotic perspective not only is more meaningful, but also reveals more relevant insight into practical system design. This thesis accomplishes such by maintaining the EED as a measure of system performance in each of the considered point-to-point, broadcast, and relay cases.
250

Coding Schemes for Physical Layer Network Coding Over a Two-Way Relay Channel

Hern, Brett Michael 16 December 2013 (has links)
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.

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