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<p>Free-space optical (FSO) communication has witnessed rapid development recently in response to ever-increasing demands for greater bandwidth. FSO links provide fiberspeed with the flexibility of wireless. Commercially available systems offer transmission speeds up to 2.5 Gbps, 5 Gbps and 10 Gbps, and demonstration systems report data rates as high as 160 Gbps. Its advantages also include license free operation, high immunity to interference, and ease of deployment. However, FSO systems are sensitive to adverse weather conditions such as fog, rain and snow.</p> <p>In order to improve the availability of FSO channels degraded by atmospheric turbulence and varying weather conditions, the effects of channel gain variations must be compensated. In this thesis, two rate-adaptive techniques, punctured low-density parity-check (LDPC) codes and Raptor codes, are studied using experimental data measured over a1.87 km terrestrial FSO link.</p> <p>Rate-adaptive performances with punctured LDPC codes and Raptor codes are evaluated in terms of outage probability and throughput. In comparison to uncoded system, rate-adaptive systems with both techniques demonstrate significant improvement of throughput and mitigation of outage probability especially in rainy weather. Due to its flexible rate-adaptation and simple hardware implementation, Raptor coded systems are judged more applicable to be implemented in field-programmable gate array (FPGA) based hardware. A dedicated decoding structure is proposed and tested, showing remarkable improvement in resource efficiency as compared to traditional Gauss-Jordan (GJ) decoding structures.</p> / Master of Applied Science (MASc)

Luby Transform Codes were the first class of universal erasure codes introduced to fully realize the concept of scalable and fault‐tolerant distribution of data over computer networks, also called Digital Fountain. Later Raptor codes, a generalization of the LT codes were introduced to trade off complexity with performance. In this work, we show that an even broader class of codes exists that are near optimal for the erasure channel and that the Raptor codes form a special case. More precisely, Raptorlike codes can be designed based on an iterative (joint) decoding schedule wherein information is transferred between the LT decoder and an outer decoder in an iterative manner. The design of these codes can be formulated as a LP problem using EXIT Charts and density evolution. In our work, we show the existence of codes, other than the Raptor codes, that perform as good as the existing ones. We extend this framework of joint decoding of the component codes to the additive white Gaussian noise channels and introduce the design of Rateless codes for these channels. Under this setting, for asymptotic lengths, it is possible to design codes that work for a class of channels defined by the signal‐to‐noise ratio. In our work, we show that good profiles can be designed using density evolution and Gaussian approximation. EXIT charts prove to be an intuitive tool and aid in formulating the code design problem as a LP problem. EXIT charts are not exact because of the inherent approximations. Therefore, we use density evolution to analyze the performance of these codes. In the Gaussian case, we show that for asymptotic lengths, a range of designs of Rateless codes exists to choose from based on the required complexity and the overhead. Moreover, under this framework, we can design incrementally redundant schemes for already existing outer codes to make the communication system more robust to channel noise variations.

Tesis por compendio / Products related with Intelligent Transportation Systems (ITS) are becoming a reality on our roads. All car manufacturers are starting to include Internet access in their vehicles and to integrate smartphones directly from the dashboard, but more and more services will be introduced in the near future. Connectivity through "vehicular networks" will become a cornerstone of every new proposal, and offering an adequate quality of service is obviously desirable. However, a lot of work is needed for vehicular networks to offer performances similar to those of the wired networks. Vehicular networks can be characterized by two main features: high variability due to mobility levels that can reach up to 250 kilometers per hour, and heterogeneity, being that various competing versions from different vendors have and will be released. Therefore, to make the deployment of efficient services possible, an extensive study must be carried out and adequate tools must be proposed and developed. This PhD thesis addresses the service deployment problem in these networks at three different levels: (i) the physical and link layer, showing an exhaustive analysis of the physical channel and models; (ii) the network layer, proposing a forwarding protocol for IP packets; and (iii) the transport layer, where protocols are proposed to improve data delivery. First of all, the two main wireless technologies used in vehicular networks where studied and modeled, namely the 802.11 family of standards, particularly 802.11p, and the cellular networks focusing on LTE. Since 802.11p is a quite mature standard, we defined (i) a propagation and attenuation model capable of replicating the transmission range and the fading behavior of real 802.11p devices, both in line-of-sight conditions and when obstructed by small obstacles, and (ii) a visibility model able to deal with large obstacles, such as buildings and houses, in a realistic manner. Additionally, we proposed a model based on high-level performance indicators (bandwidth and delay) for LTE, which makes application validation and evaluation easier. At the network layer, a hybrid protocol called AVE is proposed for packet forwarding by switching among a set of standard routing strategies. Depending on the specific scenario, AVE selects one out of four different routing solutions: a) two-hop direct delivery, b) Dynamic MANET On-demand (DYMO), c) greedy georouting, and d) store-carry-and-forward technique, to dynamically adapt its behavior to the specific situation. At the transport layer, we proposed a content delivery protocol for reliable and bidirectional unicast communication in lossy links that improves content delivery in situations where the wireless network is the bottleneck. It has been designed, validated, optimized, and its performance has been analyzed in terms of throughput and resource efficiency. Finally, at system level, we propose an edge-assisted computing model that allows reducing the response latency of several queries by placing a computing unit at the network edge. This way, traffic traversal through the Internet is avoided when not needed. This scheme could be used in both 802.11p and cellular networks, and in this thesis we decided to focus on its evaluation using LTE networks. The platform presented in this thesis combines all the individual efforts to create a single efficient platform. This new environment could be used by any provider to improve the quality of the user experience obtainable through the proposed vehicular network-based services. / Los productos relacionados con los Sistemas Inteligentes de Transporte (ITS) se están transformando en una realidad en nuestras carreteras. Todos los fabricantes de coches comienzan a incluir acceso a internet en sus vehículos y a facilitar su integración con los teléfonos móviles, pero más y más servicios se introducirán en el futuro. La conectividad usando las "redes vehiculares" se convertirá en la piedra angular de cada nueva propuesta, y ofrecer una calidad de servicio adecuada será, obviamente, deseable. Sin embargo, se necesita una gran cantidad de trabajo para que las redes vehiculares ofrezcan un rendimiento similar al de las redes cableadas. Las redes vehiculares quedan definidas por sus dos características básicas: alto dinamismo, pues los nodos pueden alcanzar una velocidad relativa de más de 250 km/h; y heterogeneidad, por la gran cantidad de propuestas diferentes que los fabricantes están lanzando al mercado. Por ello, para hacer posible el despliegue de servicios sobre ellas, se impone la necesidad de hacer un estudio en profundidad de este entorno, y deben de proponerse y desarrollarse las herramientas adecuadas. Esta tesis ataca la problemática del despliegue de servicios en estas redes a tres niveles diferentes: (i) el nivel físico y de enlace, mostrando varios análisis en profundidad del medio físico y modelos derivados para su simulación; (ii) el nivel de red, proponiendo un protocolo de difusión de la información para los paquetes IP; y (iii) el nivel de transporte, donde otros protocolos son propuestos para mejorar el rendimiento del transporte de datos. En primer lugar, se han estudiado y modelado las dos principales tecnologías inalámbricas que se utilizan para la comunicación en redes vehiculares, la rama de estándares 802.11, en concreto 802.11p; y la comunicación celular, en particular LTE. Dado que el estándar 802.11p es un estándar bastante maduro, nos centramos en crear (i) un modelo de propagación y atenuación capaz de replicar el rango de transmisión de dispositivos 802.11p reales, en condiciones de visión directa y obstrucción por pequeños obstáculos, y (ii) un modelo de visibilidad capaz de simular el efecto de grandes obstáculos, como son los edifcios, de una manera realista. Además, proponemos un modelo basado en indicadores de rendimiento de alto nivel (ancho de banda y retardo) para LTE, que facilita la validación y evaluación de aplicaciones. En el plano de red, se propone un protocolo híbrido, llamado AVE, para el encaminamiento y reenvío de paquetes usando un conjunto de estrategias estándar de enrutamiento. Dependiendo del escenario, AVE elige entre cuatro estrategias diferentes: a) entrega directa a dos saltos, b) Dynamic MANET On-demand (DYMO) c) georouting voraz, y d) una técnica store-carry-and- forward, para adaptar su comportamiento dinámicamente a cada situación. En el plano de transporte, se propone un protocolo bidireccional de distribución de contenidos en canales con pérdidas que mejora la entrega de contenidos en situaciones en las que la red es un cuello de botella, como las redes inalámbricas. Ha sido diseñado, validado, optimizado, y su rendimiento ha sido analizado en términos de productividad y eficiencia en la utilización de recursos. Finalmente, a nivel de sistema, proponemos un modelo de computación asistida que permite reducir la latencia en la respuesta a muchas consultas colocando una unidad de computación en el borde de la red, i.e., la red de acceso. Este esquema podría ser usado en redes basadas en 802.11p y en redes celulares, si bien en esta tesis decidimos centrarnos en su evaluación usando redes LTE. La plataforma presentada en esta tesis combina todos los esfuerzos individuales para crear una plataforma única y eficiente. Este nuevo entorno puede ser usado por cualquier proveedor para mejorar la calidad de la experiencia de usuario en los servicios desplegados sobre redes vehiculares. / Els productes relacionats amb els sistemes intel · ligents de transport (ITS) s'estan transformant en una realitat en les nostres carreteres. Tots els fabri- cants de cotxes comencen a incloure accés a internet en els vehicles i a facilitar- ne la integració amb els telèfons mòbils, però en el futur més i més serveis s'hi introduiran. La connectivitat usant les xarxes vehicular esdevindrà la pedra angular de cada nova proposta, i oferir una qualitat de servei adequada serà, òbviament, desitjable. No obstant això, es necessita una gran quantitat de treball perquè les xarxes vehiculars oferisquen un rendiment similar al de les xarxes cablejades. Les xarxes vehiculars queden definides per dues característiques bàsiques: alt dinamisme, ja que els nodes poden arribar a una velocitat relativa de més de 250 km/h; i heterogeneïtat, per la gran quantitat de propostes diferents que els fabricants estan llançant al mercat. Per això, per a fer possible el desplegament de serveis sobre aquestes xarxes, s'imposa la necessitat de fer un estudi en profunditat d'aquest entorn, i cal proposar i desenvolupar les eines adequades. Aquesta tesi ataca la problemàtica del desplegament de serveis en aquestes xarxes a tres nivells diferents: (i) el nivell físic i d'enllaç , mostrant diverses anàlisis en profunditat del medi físic i models derivats per simular-lo; (ii) el nivell de xarxa, proposant un protocol de difusió de la informació per als paquets IP; i (iii) el nivell de transport, on es proposen altres protocols per a millorar el rendiment del transport de dades. En primer lloc, s'han estudiat i modelat les dues principals tecnologies sense fils que s'utilitzen per a la comunicació en xarxes vehiculars, la branca d'estàndards 802.11, en concret 802.11p; i la comunicació cel · lular, en partic- ular LTE. Atès que l'estàndard 802.11p és un estàndard bastant madur, ens centrem a crear (i) un model de propagació i atenuació capaç de replicar el rang de transmissió de dispositius 802.11p reals, en condicions de visió directa i obstrucció per petits obstacles, i (ii) un model de visibilitat capaç de simular l'efecte de grans obstacles, com són els edificis, d'una manera realista. A més, proposem un model basat en indicadors de rendiment d'alt nivell (ample de banda i retard) per a LTE, que facilita la validació i l'avaluació d'aplicacions. En el pla de xarxa, es proposa un protocol híbrid, anomenat AVE, per a l'encaminament i el reenviament de paquets usant un conjunt d'estratègies estàndard d'encaminament. Depenent de l'escenari , AVE tria entre quatre estratègies diferents: a) lliurament directe a dos salts, b) Dynamic MANET On-demand (DYMO) c) georouting voraç, i d) una tècnica store-carry-and- forward, per a adaptar-ne el comportament dinàmicament a cada situació. En el pla de transport, es proposa un protocol bidireccional de distribució de continguts en canals amb pèrdues que millora el lliurament de continguts en situacions en què la xarxa és un coll de botella, com les xarxes sense fils. Ha sigut dissenyat, validat, optimitzat, i el seu rendiment ha sigut analitzat en termes de productivitat i eficiència en la utilització de recursos. Finalment, a nivell de sistema, proposem un model de computació assistida que permet reduir la latència en la resposta a moltes consultes col · locant una unitat de computació a la vora de la xarxa, és a dir, la xarxa d'accés. Aquest esquema podria ser usat en xarxes basades en 802.11p i en xarxes cel · lulars, si bé en aquesta tesi decidim centrar-nos en la seua avaluació usant xarxes LTE. La plataforma presentada en aquesta tesi combina tots els esforços indi- viduals per a crear una plataforma única i eficient. Aquest nou entorn pot ser usat per qualsevol proveïdor per a millorar la qualitat de l'experiència d'usuari en els serveis desplegats sobre xarxes vehiculars. / Báguena Albaladejo, M. (2017). Design and implementation of simulation tools, protocols and architectures to support service platforms on vehicular networks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/85333 / Compendio

[pt] Esta dissertação aborda o estudo de códigos fontanais (códigos LT e códigos Raptor) que são uma classe de códigos criados para a transmissão de dados de maneira confiável e eficiente através de canais os quais podem ser modelados como canais com apagamento. Os códigos LT e códigos Raptor são denominados códigos fontanais, devido a que eles são uma boa aproximação para o conceito de fontanas digitais. Além disso, eles são classificados como códigos de taxa versátil, no sentido que o número de símbolos codificados que podem ser gerados a partir dos dados de entrada é potencialmente ilimitado. Códigos LT são capazes de recuperar, com probabilidade maior do que (1 − delta), um conjunto de k símbolos de entrada a partir de quaisquer k + O((raiz quadrada de k)(ln(2))(k/delta)) símbolos codificados recebidos, com uma média de O(k ln(k/delta)) operações XOR. Os códigos Raptor são uma extensão de códigos LT, na qual o processo de codificação é composto de duas etapas: um código de bloco de comprimento fixo (denominado pré- código) e um código LT com uma distribuição de graus apropriada. Investigou-se o desempenho dos códigos LT usando duas novas distribuições de graus (Sóliton Robusta Melhorada e Sóliton Robusta Truncada) e foi proposto um modelo de códigos LT Bidimensionais, na qual os símbolos de entrada são agrupados em forma de matriz. Neste esquema os blocos correspondentes às linhas da matriz são codificados usando um código LT e, em seguida, a matriz resultante tem suas colunas também codificadas usando um código LT. Ainda que a complexidade do esquema tenha sido dobrada o desempenho alcançado pelos códigos LT Bidimensionais superou o desempenho dos códigos LT convencionais para situações em que a qualidade do canal BEC é elevada. / [en] Fountain Codes (LT Codes and Raptor Codes) are a class of codes proposed to efficient and reliably transmit data through Erasure Channels. LT Codes and Raptor Codes are a good approximation to the concept of digital fountain and as such are named as fountain codes. They are said to be rateless codes in the sense that the number of symbols produced by the encoder could grow, potentially, to infinite. With probability of success larger than (1&#8722;delta), a decoder of an LT code based scheme can recover the k transmitted symbols from any received block of k + O((square root k)(ln(2))(k/delta)) correct symbols with an average of O(k ln(k/delta)) XOR operations. Raptor codes are an extension of the LT codes idea, with a tandem scheme where a fixed length block code (namely a pre- code) is followed by an LT code that uses a properly chosen degree distribution. In this dissertation the performance of LT codes with two recently proposed degree distributions, the Improved Robust Soliton and the Truncated Soliton Robust Distribution were investigated. A new scheme called Bidimensional LT Codes, has been proposed. In this scheme the input symbols are structured in a matrix form and afterwards the blocks corresponding to the lines of the matrix are encoded with an LT code. The columns of the new matrix so obtained are next encoded with a similar LT code. The complexity of the new scheme is doubled and yet its performance only just surpasses that of the conventional LT scheme for high quality BEC.

The area of cooperative communications has received tremendous research interest in recent years. This interest is not unwarranted, since cooperative communications promises the ever-so-sought after diversity and multiplexing gains typically associated with multiple-input multiple-output (MIMO) communications, without actually employing multiple antennas. In this dissertation, we consider several cooperative communication channels, and for each one of them, we develop information theoretic coding schemes and derive their corresponding performance limits. We next develop and design practical coding strategies which perform very close to the information theoretic limits. The cooperative communication channels we consider are: (a) The Gaussian relay channel, (b) the quasi-static fading relay channel, (c) cooperative multiple-access channel (MAC), and (d) the cognitive radio channel (CRC). For the Gaussian relay channel, we propose a compress-forward (CF) coding strategy based on Wyner-Ziv coding, and derive the achievable rates specifically with BPSK modulation. The CF strategy is implemented with low-density parity-check (LDPC) and irregular repeataccumulate codes and is found to operate within 0.34 dB of the theoretical limit. For the quasi-static fading relay channel, we assume that no channel state information (CSI) is available at the transmitters and propose a rateless coded protocol which uses rateless coded versions of the CF and the decode-forward (DF) strategy. We implement the protocol with carefully designed Raptor codes and show that the implementation suffers a loss of less than 10 percent from the information theoretical limit. For the MAC, we assume quasi-static fading, and consider cooperation in the low-power regime with the assumption that no CSI is available at the transmitters. We develop cooperation methods based on multiplexed coding in conjunction with rateless codes and find the achievable rates and in particular the minimum energy per bit to achieve a certain outage probability. We then develop practical coding methods using Raptor codes, which performs within 1.1 dB of the performance limit. Finally, we consider a CRC and develop a practical multi-level dirty-paper coding strategy using LDPC codes for channel coding and trellis-coded quantization for source coding. The designed scheme is found to operate within 0.78 dB of the theoretical limit. By developing practical coding strategies for several cooperative communication channels which exhibit performance close to the information theoretic limits, we show that cooperative communications not only provide great benefits in theory, but can possibly promise the same benefits when put into practice. Thus, our work can be considered a useful and necessary step towards the commercial realization of cooperative communications.

Fountain codes have demonstrated great results for the binary erasure channel and have already been incorporated into several international standards to recover lost packets at the application layer. These include multimedia broadcast/multicast sessions and digital video broadcasting on global internet-protocol. The rateless property of Fountain codes holds great promise for noisy channels. These are more sophisticated mathematical models representing errors on communications links rather than only erasures. The practical implementation of Fountain codes for these channels, however, is hampered by high decoding cost and delay. In this work we study trapping sets in Fountain codes over noisy channels and their effect on the decoding process. While trapping sets have received much attention for low-density parity-check (LDPC) codes, to our knowledge they have never been fully explored for Fountain codes. Our study takes into account the different code structure and the dynamic nature of Fountain codes. We show that 'error-free' trapping sets exist for Fountain codes. When the decoder is caught in an error-free trapping set it actually has the correct message estimate, but is unable to detect this is the case. Thus, the decoding process continues, increasing the decoding cost and delay for naught. The decoding process for rateless codes consists of one or more decoding attempts. We show that trapping sets may reappear as part of other trapping sets on subsequent decoding attempts or be defeated by the reception of more symbols. Based on our observations we propose early termination methods that use trapping set detection to obtain improvements in realized rate, latency, and decoding cost for Fountain codes. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2009-10-29 14:33:06.548

Reliable and energy-efficient delivery of multimedia to mobile terminals in dynamic networks is a very challenging problem. In this thesis, we focus on a cooperative extension to the Digital Video Broadcasting – Handheld (DVB-H) standard, forming a cooperative broadcast network whereby terminal-to-terminal cooperation creates a distributed form of multi-input-multi-output (MIMO) that supplements existing fixed network infrastructure. First, we develop a novel and computationally-efficient hierarchical Markov model that is able to accurately perform a cross-layer packet error mapping between the physical and transport layers of the DVB-H/IPDC (IP DataCast) protocol stack. We then construct a discrete-event simulator in MATLAB® that incorporates all of the necessary modules to conduct dynamic multiterminal network simulations. Next, the convergence of cooperative wireless communication, Raptor application layer forward error correction (AL-FEC) and Network Coding (NC) is examined. Originally proposed for broadcasting over the Internet, the application of Raptor codes to wireless cooperative communications networks has been limited to date, but they have been mandated for use in DVB-H. Network coding is used to reduce energy consumption by opportunistically recombining and rebroadcasting required combinations of packets. Two novel coding-enabled cooperative relaying protocols are developed for multicast and multiple unicast file distribution scenarios that are transparent, fully distributed, and backwards compatible with today's systems. Our protocols are able to exploit several different forms of diversity inherent to modern wireless networks, including spatial diversity, radio interface diversity, and symbol diversity. Extensive simulations show that our protocols simultaneously achieve breakthroughs in network energy efficiency and reliability for different terminal classes and densities, allowing greatly improved user experiences. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2010-08-03 19:45:54.943

One of the most important technologies used in modern communication systems is channel coding. Channel coding dates back to a paper published by Shannon in 1948 [1] entitled “A Mathematical Theory of Communication”. The basic idea behind channel coding is to send redundant information (parity) together with a message to make the transmission more error resistant. There are different types of codes that can be used to generate the parity required, including block, convolutional and concatenated codes. A special subclass of codes consisting of the codes mentioned in the previous paragraph, is sparse graph codes. The structure of sparse graph codes can be depicted via a graphical representation: the factor graph which has sparse connections between its elements. Codes belonging to this subclass include Low-Density-Parity-Check (LDPC) codes, Repeat Accumulate (RA), Turbo and fountain codes. These codes can be decoded by using the belief propagation algorithm, an iterative algorithm where probabilistic information is passed to the nodes of the graph. This dissertation focuses on noisy decoding of fountain codes using belief propagation decoding. Fountain codes were originally developed for erasure channels, but since any factor graph can be decoded using belief propagation, noisy decoding of fountain codes can easily be accomplished. Three fountain codes namely Tornado, Luby Transform (LT) and Raptor codes were investigated during this dissertation. The following results were obtained: <ol> <li>The Tornado graph structure is unsuitable for noisy decoding since the code structure protects the first layer of parity instead of the original message bits (a Tornado graph consists of more than one layer).</li> <li> The successful decoding of systematic LT codes were verified.</li> <li>A systematic Raptor code was introduced and successfully decoded. The simulation results show that the Raptor graph structure can improve on its constituent codes (a Raptor code consists of more than one code).</li></ol> Lastly an LT code was used to replace the convolutional incremental redundancy scheme used by the 2G mobile standard Enhanced Data Rates for GSM Evolution (EDGE). The results show that a fountain incremental redundancy scheme outperforms a convolutional approach if the frame lengths are long enough. For the EDGE platform the results also showed that the fountain incremental redundancy scheme outperforms the convolutional approach after the second transmission is received. Although EDGE is an older technology, it still remains a good platform for testing different incremental redundancy schemes, since it was one of the first platforms to use incremental redundancy. / Dissertation (MEng)--University of Pretoria, 2008. / Electrical, Electronic and Computer Engineering / MEng / unrestricted

This thesis investigates both theoretical and practical aspects of the design and analysis of modern error-control coding schemes, namely low-density parity-check (LDPC) codes and rateless codes for unequal error protection (UEP). It also studies the application of modern error-control codes in efficient data dissemination in wireless ad-hoc and sensor networks. Two methodologies for the design and analysis of UEP-LDPC codes are proposed. For these proposed ensembles, density evolution formulas over the binary erasure channel are derived and used to optimize the degree distribution of the codes. Furthermore, for the first time, rateless codes that can provide UEP are developed. In addition to providing UEP, the proposed codes can be used in applications for which unequal recovery time is desirable, i.e., when more important parts of data are required to be recovered faster than less important parts. Asymptotic behavior of the UEP-rateless codes under the iterative decoding is investigated. In addition, the performance of the proposed codes is examined under the maximum-likelihood decoding, when the codes have short to moderate lengths. Results show that UEP-rateless codes are able to provide very low error rates for more important bits with only a subtle loss in the performance of less important bits. Moreover, it is shown that given a target bit error rate, different parts of the information symbols can be decoded after receiving different numbers of encoded symbols. This implies that information can be recovered in a progressive manner, which is of interest in many practical applications such as media-on-demand systems. This work also explores fundamental research problems related to applying error-control coding such as rateless coding to the problem of reliable and energy-efficient broadcasting in multihop wireless ad-hoc sensor networks. The proposed research touches on the four very large fields of wireless networking, coding theory, graph theory, and percolation theory. Based on the level of information that each node has about the network topology, several reliable and energy-efficient schemes are proposed, all of which are distributed and have low complexity of implementation. The first protocol does not require any information about the network topology. Another protocol, which is more energy efficient, assumes each node has local information about the network topology. In addition, this work proposes a distributed scheme for finding low-cost broadcast trees in wireless networks. This scheme takes into account various parameters such as distances between nodes and link losses. This protocol is then extended to find low-cost multicast trees. Several schemes are extensively simulated and are compared.