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In wireless communication, multipath fading distorts the phase and the amplitude of received signals and increases error rate, which degrades causes communication quality. Multiple-input-multiple-output (MIMO) techniques can be adopted to achieve diversity gain and reduce error rate. However, MIMO is hard to be implemented in mobile devices due to size limitation. With this regard, cooperative communications are proposed to allow users to cooperate each other¡¦s and then achieve diversity without equipping multiple antennas. On the other hand, if source and relays adopt fixed-rate transmission under time-varying wireless channels, it requires timely feedback about channel-information for transmitters to adjust the rate of channel encoder. To reduce overhead required for aforementioned scheme, we adopt rateless fountain codes in cooperative networks. In recent year, most related studies focus on information-theoretical aspect, but it lacks discussion of practical coding. In our work, we use fountain codes in dual-hop cooperative communication and analyse transmission rate in terms of transmitting time. Fountain code was first proposed as Luby transform codes(LTC) for erasure channels. We combine low-density parity-check code( LDPC code) and LTC in cooperative communication networks, and analyze required transmission time under different cooperative protocols.

Network coding (NC) is an optimal data dissemination technique where intermediate nodes linearly combine incoming packets. To recover a network-coded message, a sink must use a Gaussian elimination decoder, but this high-complexity decoder may not be acceptable in resource-constrained applications like sensor networks. A good alternative to Gaussian elimination is for the sink to apply the well-known belief propagation (BP) algorithm; however, the performance and complexity of BP decoding is dependent on the statistics of the linearly-combined packets. In this work, we propose two protocols that address this issue by applying fountain coding paradigms to network codes. For a two-source, single-relay, and single-sink network, named the Y-network, if the relay can network-code incoming packets while maintaining the key properties of the fountain code, then BP decoding can be applied efficiently to recover the original message. Particularly, the sink should see a Soliton-like degree distribution for efficient BP decoding. The first protocol, named Soliton-like rateless coding (SLRC), recognizes that certain encoded packets are essential for BP decoding to perform well. Therefore, the relay protects these important packets by immediately forwarding them to the sink. It can be shown analytically that the proposed scheme is resilient to nodes leaving the transmission session. Through simulations, the SLRC scheme is shown to perform better than buffer-and-forwarding, and the Distributed LT code. Although SLRC achieves good performance, the degree distribution seen by the sink is non-optimal and assumes that a large number of packets can be buffered, which may not always be possible. Extending SLRC, we propose the Improved Soliton-like Rateless Coding (ISLRC) protocol. Assuming a resource-constrained relay, the available resources at the relay are effciently utilized by performing distribution shaping; packets are intelligently linearly combined. The aggregate degree distribution for the worst case is derived and used in performing an asymptotic error analysis using an AND-OR tree analysis. Simulation results show that even under the worst case scenario of ISLRC, better performance can be achieved compared to SLRC and other existing schemes. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2011-10-07 21:13:03.862

This thesis investigates four FEC (forward error correction) coding schemes for their suitability for a broadcast system where there is one energy-rich transmitter and many energy-constrained receivers with a variety of channel conditions. The four coding schemes are: repetition codes (the baseline scheme); Reed-Solomon (RS) codes; Luby-Transform (LT) codes; and a type of RS and LT concatenated codes. The schemes were tested in terms of their ability to achieve both high average data reception success probability and short data reception time at the receivers (due to limited energy). The code rate (Rc) is fixed to either 1/2 or 1/3. Two statistical channel models were employed: the memoryless channel and the Gilbert-Elliott channel. The investigation considered only the data-link layer behaviour of the schemes. During the course of the investigation, an improvement to the original LT encoding process was made, the name LTAM (LT codes with Added Memory) was given to this improved coding method. LTAM codes reduce the overhead needed for decoding short-length messages. The improvement can be seen for decoding up to 10000 number of user packets. The maximum overhead reduction is as much as 10% over the original LT codes. The LT-type codes were found to have the property that can both achieve high success data reception performance and flexible switch off time for the receivers. They are also adaptable to different channel characteristics. Therefore it is a prototype of the ideal coding scheme that this project is looking for. This scheme was then further developed by applying an RS code as an inner code to further improve the success probability of packet reception. The results show that LT&RS code has a significant improvement in the channel error tolerance over that of the LT codes without an RS code applied. The trade-off is slightly more reception time needed and more decoding complexity. This LT&RS code is then determined to be the best scheme that fulfils the aim in the context of this project which is to find a coding scheme that both has a high overall data reception probability and short overall data reception time. Comparing the LT&RS code with the baseline repetition code, the improvement is in three aspects. Firstly, the LT&RS code can keep full success rate over channels have approximately two orders of magnitude more errors than the repetition code. This is for the two channel models and two code rates tested. Secondly, the LT&RS code shows an exceptionally good performance under burst error channels. It is able to maintain more than 70% success rate under the long burst error channels where both the repetition code and the RS code have almost zero success probability. Thirdly, while the success rates are improved, the data reception time, measured in terms of number of packets needed to be received at the receiver, of the LT&RS codes can reach a maximum of 58% reduction for Rc = 1=2 and 158% reduction for Rc = 1=3 compared with both the repetition code and the RS code at the worst channel error rate that the LT&RS code maintains almost 100% success probability.

Fountain codes were introduced to provide higher reliability, lower complexities, and more scalability for networks such as the Internet. In this thesis, we study Luby- Transform (LT) codes which are the realization of Fountain codes. In the LT codes, a sparse random factor graph is dynamically generated on both the encoder and decoder sides of the communications channel. The graph is generated from an ensemble degree distribution. The LT codes are also known as rateless codes, in the sense that they can generate potentially limitless codeword symbols from original data and self-adjust to channels with different erasure probabilities. LT Codes also have a very low encoding and decoding complexities when comparing with some traditional block codes, e.g., Reed Solomon (RS) codes and Low-Density-Parity-Check (LDPC) codes. Therefore, LT Codes are suitable for many different kinds of applications such as broadcast transmission. LT codes achieve the capacity of the Binary Erasure Channel (BEC) asymptotically and universally. For finite lengths, the search is continued to nd codes closer to the capacity limits at even lower encoding and decoding complexities. Most previous work on single-layer Fountain coding targets the design via the right degree distribution. The left degree distribution of an LT code is left as Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, we focus on the design of better codes for the BEC and noisy channels as well at practical lengths. We propose two encoding schemes for BEC and noisy channels by shaping the left degree distribution. Our left degree shaping provides codes outperforming regular LT code and all other competing schemes in the literature. For instance, at a bit error rate of 10_{-7} and k = 256, our scheme provides a realized rate of 0.6 which is 23.5% higher than Sorensen et al.'s scheme over BEC. In addition, over noisy channels our proposed scheme achieves an improvement of 14% in the released rates at k = 100 and 30 Belief Propagation (BP) iterations. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2013-08-22 19:40:59.885

Random linear network coding is widely proposed as the solution for practical network coding applications due to the robustness to random packet loss, packet delays as well as network topology and capacity changes. In order to implement random linear network coding in practical scenarios where the encoding and decoding methods perform efficiently, the computational complex coding algorithms associated with random linear network coding must be overcome. This research contributes to the field of practical random linear network coding by presenting new, low complexity coding algorithms with low decoding delay. In this thesis we contribute to this research field by building on the current solutions available in the literature through the utilisation of familiar coding schemes combined with methods from other research areas, as well as developing innovative coding methods. We show that by transmitting source symbols in predetermined and constrained patterns from the source node, the causality of the random linear network coding network can be used to create structure at the receiver nodes. This structure enables us to introduce an innovative decoding scheme of low decoding delay. This decoding method also proves to be resilient to the effects of packet loss on the structure of the received packets. This decoding method shows a low decoding delay and resilience to packet erasures, that makes it an attractive option for use in multimedia multicasting. We show that fountain codes can be implemented in RLNC networks without changing the complete coding structure of RLNC networks. By implementing an adapted encoding algorithm at strategic intermediate nodes in the network, the receiver nodes can obtain encoded packets that approximate the degree distribution of encoded packets required for successful belief propagation decoding. Previous work done showed that the redundant packets generated by RLNC networks can be used for error detection at the receiver nodes. This error detection method can be implemented without implementing an outer code; thus, it does not require any additional network resources. We analyse this method and show that this method is only effective for single error detection, not correction. In this thesis the current body of knowledge and technology in practical random linear network coding is extended through the contribution of effective decoding techniques in practical network coding networks. We present both analytical and simulation results to show that the developed techniques can render low complexity coding algorithms with low decoding delay in RLNC networks. / Thesis (PhD (Computer Engineering))--North-West University, Potchefstroom Campus, 2013

Random linear network coding is widely proposed as the solution for practical network coding applications due to the robustness to random packet loss, packet delays as well as network topology and capacity changes. In order to implement random linear network coding in practical scenarios where the encoding and decoding methods perform efficiently, the computational complex coding algorithms associated with random linear network coding must be overcome. This research contributes to the field of practical random linear network coding by presenting new, low complexity coding algorithms with low decoding delay. In this thesis we contribute to this research field by building on the current solutions available in the literature through the utilisation of familiar coding schemes combined with methods from other research areas, as well as developing innovative coding methods. We show that by transmitting source symbols in predetermined and constrained patterns from the source node, the causality of the random linear network coding network can be used to create structure at the receiver nodes. This structure enables us to introduce an innovative decoding scheme of low decoding delay. This decoding method also proves to be resilient to the effects of packet loss on the structure of the received packets. This decoding method shows a low decoding delay and resilience to packet erasures, that makes it an attractive option for use in multimedia multicasting. We show that fountain codes can be implemented in RLNC networks without changing the complete coding structure of RLNC networks. By implementing an adapted encoding algorithm at strategic intermediate nodes in the network, the receiver nodes can obtain encoded packets that approximate the degree distribution of encoded packets required for successful belief propagation decoding. Previous work done showed that the redundant packets generated by RLNC networks can be used for error detection at the receiver nodes. This error detection method can be implemented without implementing an outer code; thus, it does not require any additional network resources. We analyse this method and show that this method is only effective for single error detection, not correction. In this thesis the current body of knowledge and technology in practical random linear network coding is extended through the contribution of effective decoding techniques in practical network coding networks. We present both analytical and simulation results to show that the developed techniques can render low complexity coding algorithms with low decoding delay in RLNC networks. / Thesis (PhD (Computer Engineering))--North-West University, Potchefstroom Campus, 2013

[pt] A construção de novos códigos através de modificações (alongamento, puncionamento, etc) de um código conhecido é uma prática comum quando se lida com códigos clássicos. Neste trabalho é mostrado que bons códigos podem ser obtidos com algumas dessas técnicas, aparentemente não efetivas aos códigos fontanais. Os Códigos LT (Luby Transform) Sistemáticos Alongados são apresentados e, a partir de simulações realizadas em programa desenvolvido para tal, mostra-se um melhor desempenho em relação aos seus códigos-mãe correspondentes, sob uma mesma condição de redundância. A técnica de alongamento pode ser bastante útil, minimizando a necessidade de trabalhar-se com blocos de informação grandes, caracterizada nos códigos fontanais e, por conseqüência, nos códigos LT. / [en] Construction of new codes by modifying (extending,puncturing,etc) a known code is common practice when dealing with classical codes.We have shown in this thesis that good codes can be obtained with these techniques,apparently not effective for fountain codes.Lengthened Systematic Luby Transform Codes have being demonstrated ,through simulation ,to perform better when compared to the mother codes, under the same redundancy condition.Lengthening might be a useful technique which alleviates the need for large frame requirements posed by the fountain codes.

Wireless Sensor Networks (WSNs) that use tiny wireless devices capable of communicating, processing, and sensing promise to have applications in virtually all fields. Smart homes and smart cities are just few of the examples that WSNs can enable. Despite their potential, WSNs suffer from reliability and energy limitations. In this study, we address the problem of designing Distributed Data Storage Systems (DDSSs) for WSNs using decentralized erasure codes. A unique aspect of WSNs is that their data is inherently decentralized. This calls for a decentralized mechanism for encoding and decoding. We propose a distributed data storage framework to increase data survivability in WSNs. The framework utilizes Decentralized Erasure Codes for Data Survivability (DEC-DS) which allow for determining the amount of redundancy required in both hardware and data to allow sensed data to survive failures in the network. To address the energy limitations, we show two approaches to implement the proposed solution in an energy efficient manner. The two approaches employ Random Linear Network Coding (RLNC) to exploit coding opportunities in order to save energy and in turn prolong network life. A routing based scheme, called DEC Encode-and-Forward (DEC-EaF), applies to networks with routing capability, while the second, DEC Encode-and-Disseminate (DEC-EaD), uses a variation of random walk to build the target code in a decentralized fashion. We also introduce a new decentralized approach to implement Luby Transform (LT)-Codes based DDSSs. The scheme is called Decentralized Robust Soliton Storage (DRSS) and it operates in a decentralized fashion and requires no coordination between sensor nodes. The schemes are tested through extensive simulations to evaluate their performance. We also compare the proposed schemes to similar schemes in the literature. The comparison considers energy efficiency as well as coding related aspects. Using the proposed schemes can greatly improve the reliability of WSNs especially under harsh working conditions. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2013-09-30 22:43:04.509

Thesis (MScEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The discovery of sparse graph codes, used in forward error correction strate- gies, has had an unrivaled impact on Information theory over the past decade. A recent advancement in this field, called Fountain codes, have gained much attention due to its intelligent rate adaptivity, and lend itself to applications such as multicasting and broadcasting networks. These particular properties can be considered valuable in a wireless sensor network setting as it is capable of providing forward error correction, and the added conceptual network protocol related extensions. A wireless sensor network testbed in France, called SensLAB, provides an experimental facility for researchers to develop and evaluate sensor network protocols, aside from a simulation environment. Tremendous value can be added to the SensLAB community if an appropriate forward error correction design, such as Fountain codes, is deemed feasible for use on such a platform. This thesis investigates the use of Fountain codes, in a binary erasure channel environment, as a forward error correction strategy for the distribution of reliable data content over the SensLAB platform. A short message length LT code using two different decoding mechanisms were developed and evaluated for possible implementation. Furthermore, a short message length Raptor code was developed by using supplementary theory and optimisation techniques that permit scalability in terms of the message size. The results favoured the Raptor code design as it performs close to near optimal while still satisfying the rateless- and universality property, at low computational complexity. / AFRIKAANSE OPSOMMING: Die ontdekking van yl-grafiekkodes, van toepassing op foutkorreksie strategieë, het onlangs 'n ongeewenaarde impak op Informasieteorie gehad. In 'n onlangse vooruitgang in hierdie veld, genoem Fonteinkodes, word daar meer fokus geplaas op die intelligente tempo aanpassingsvermoë van hierdie kodes, wat nuttige toepassing kan inhou in multi-saai- en uitsaai netwerke. Hierdie eienskappe kan moontlik as waardevol beskou word in draadlose sensor netwerke weens die fout regstellingsvermoë en die bykomende konseptuele netwerk protokol verwante uitbreidings. 'n Draadlose sensor netwerk toetsplatvorm in Frankryk, genoem die SensLAB, bied navorsers die geleentheid om eksperimentele sensor netwerk protokolle te ontwikkel en te toets buite 'n tipiese simulasie-omgewing. Groot waarde kan bygevoeg word aan die SensLAB gemeenskap indien 'n geskikte foutkorreksie strategie ontwikkel word, soos Fonteinkodes, en as geskik beskou kan word vir hierdie platvorm. In hierdie tesis word Fonteinkodes saam met die SensLAB platvorm ondersoek, binne die raamwerk van 'n binêre verlieskanaal, om vir foutkorreksie oor die verspreiding van betroubare data in SensLAB op te tree. 'n Kort boodskap LT kode word voorgestel deur van twee verskillende dekoderings meganismes gebruik te maak. 'n Alternatief, genaamd Raptorkode, was ook ondersoek. 'n Raptorkode. 'n Kort boodskap Raptor kode, wat ontwikkel is met bykomende teorie en optimeringstegnieke, word ook voorgestel. Die bykomende tegnieke bied 'n skaleerbare boodskap lengte terwyl dit tempoloos en universeel bly, en lae kompleksiteit bied.