In this thesis we study Low Density Parity Check (LDPC) and LDPC like codes over non-binary fields. We extend the concepts used for non-binary LDPC codes to generalize Product Accumulate (PA) codes to non-binary fields. We present simulation results that show that PA codes over GF(4) performs considerably better than binary PA codes at smaller block lengths and slightly better at large block lengths. We also propose a trellis based decoding algorithm to decode PA codes and show that its complexity is considerably lower than the message-passing algorithm. In the second part of the thesis we study the convergence properties of non-binary PA codes and non-binary LDPC codes. We use EXIT-charts to study the convergence properties of non-binary LDPC codes with different mean column weights and show why certain irregularities are better. Although the convergence threshold predicted by EXIT-charts on non-binary LDPC codes is quite optimistic we can still use EXIT-charts for comparison between non-binary LDPC codes with different mean column weights.

Masters Research - Masters of Engineering / Mobile telephony, wireless networks and wireless telemetry systems have gone from simple single-input single-output wireless architectures with low data transmission rates to complex systems employing multiple antennas and forward error correction algorithms capable of high data transmission rates over wireless channels. Claude Shannon provided the fundamental capacity limits for a communications system and it can be shown that the capacity for a single-input single-output systems is limited in it’s capability to provide for modern wireless applications. The introduction of multiple-input multiple-output systems employing multiple antenna elements and orthogonal coding structures proved beneficial and could provide the capacities required for modern wireless applications. This thesis begins with an introduction and overview of space-time coding and the codes of Tarokh, Jafarkhani and Alamouti. Further, this thesis provides an introduction and overview to the family of forward error correction codes known as low-density parity-check (LDPC) codes. LDPC codes, when employed over Gaussian channels, provide near-Shannon limit performance and the question is posed as to their suitability for a wireless multiple-input multiple-output system employing multiple antennas and space-time coding. This question is answered by the use and demonstration of LDPC codes as outer codes to a MIMO system employing space-time block codes and a modified maximum-likelihood decoder. By modifying the space-time block-code decoder to provide a soft-information output, iterative decoders such as the sum-product algorithm can be employed to provide significant performance gains over a Rayleigh flat-fading channel. Further the use of design tools such as EXIT charts can then be used to design codes. The key to allowing the use of EXIT charts is the observation that a MIMO system employing orthogonal transmissions in a Rayleigh flat-fading channel is the equivalent to a SISO channel employing Nakagami-m fading coefficients. The seemingly complex MIMO system can now be analyzed in the form of a simpler SISO equivalent allowing the use of techniques such as EXIT charts to be employed in order to design codes with known and predictable performance haracteristics. This thesis demonstrates this technique and shows by example the performance gains that can be achieved for MIMO systems and opens some further questions for future research.

Masters Research - Masters of Engineering / Mobile telephony, wireless networks and wireless telemetry systems have gone from simple single-input single-output wireless architectures with low data transmission rates to complex systems employing multiple antennas and forward error correction algorithms capable of high data transmission rates over wireless channels. Claude Shannon provided the fundamental capacity limits for a communications system and it can be shown that the capacity for a single-input single-output systems is limited in it’s capability to provide for modern wireless applications. The introduction of multiple-input multiple-output systems employing multiple antenna elements and orthogonal coding structures proved beneficial and could provide the capacities required for modern wireless applications. This thesis begins with an introduction and overview of space-time coding and the codes of Tarokh, Jafarkhani and Alamouti. Further, this thesis provides an introduction and overview to the family of forward error correction codes known as low-density parity-check (LDPC) codes. LDPC codes, when employed over Gaussian channels, provide near-Shannon limit performance and the question is posed as to their suitability for a wireless multiple-input multiple-output system employing multiple antennas and space-time coding. This question is answered by the use and demonstration of LDPC codes as outer codes to a MIMO system employing space-time block codes and a modified maximum-likelihood decoder. By modifying the space-time block-code decoder to provide a soft-information output, iterative decoders such as the sum-product algorithm can be employed to provide significant performance gains over a Rayleigh flat-fading channel. Further the use of design tools such as EXIT charts can then be used to design codes. The key to allowing the use of EXIT charts is the observation that a MIMO system employing orthogonal transmissions in a Rayleigh flat-fading channel is the equivalent to a SISO channel employing Nakagami-m fading coefficients. The seemingly complex MIMO system can now be analyzed in the form of a simpler SISO equivalent allowing the use of techniques such as EXIT charts to be employed in order to design codes with known and predictable performance haracteristics. This thesis demonstrates this technique and shows by example the performance gains that can be achieved for MIMO systems and opens some further questions for future research.

Abstract This thesis seeks to develop a robust semi-analytical performance prediction method for an advanced iterative receiver that processes spatially multiplexed signals that have propagated through frequency-selective receive correlated multiple-input multiple-output (MIMO) wireless communication channels. In a change of perspective, the proposed performance prediction methods are applied at the transmitter, which seeks to attain a target frame error rate (FER) either by adaptive power control or by adaptive modulation and coding (AMC). The performance prediction scheme utilises the statistical properties of the channel—namely noise variance, number of separable propagation paths and the eigenvalues of the receive correlation matrix—to predict the signal-to-interference-plus-noise ratio (SINR) at the output of a frequency domain soft interference cancellation minimum mean square error equaliser. The SINR distribution is used to derive the distribution of the variance of the log-likelihood ratios (LLRs) at the output of a soft symbol-to-bit demapper. Mutual information transfer charts establish a bijective relationship between the variance of the LLRs and mutual information. A 3rd Generation Partnership Project compliant turbo code is assumed. Since the decoder operates independently from the channel, its extrinsic information transfer (EXIT) charts can be simulated in advance. By utilising the approximate LLR variance distribution of the demapped equaliser output, it is possible to evaluate the probability of an intersection between an equaliser chart associated with a random channel realisation and a fixed decoder chart. This probability provides the FER. Since the proposed performance prediction method does not require any instantaneous channel state information, it can be applied at the transmitter side as a robust link adaptation scheme. In adaptive transmission power control, the modulation order and code rate are fixed. By iteratively adjusting transmission power, the transmitter attempts to find an equaliser output LLR variance distribution that reaches a specified target FER. In AMC, transmission power is fixed. The equaliser output's LLR variance distribution is determined by the modulation order, while the decoder chart's position is determined by the code rate. The transmitter iteratively adjusts the code rate and attempts to find a modulation order and code rate pairing that reaches the target FER. For vertically encoded spatially multiplexed systems, the adaptive transmission power control and AMC schemes are complemented by adaptive repeat redundancy and incremental redundancy hybrid automatic repeat request (HARQ) techniques, respectively. / Tiivistelmä Työn tavoitteena on kehittää luotettava semianalyyttinen suorituskyvyn ennustusmenetelmä tehokkaalle iteratiiviselle vastaanottimelle, joka käsittelee taajuusselektiivisen, vastaanotinpäässä tilakorreloituneen moniantennikanavan kautta kulkeneita tilakanavoituja signaaleja. Toisessa vaiheessa esitettyjä ennustusmenetelmiä hyödynnetään mukauttamalla lähetystehoa tai modulaatioastetta ja koodisuhdetta (adaptive modulation and coding [AMC]), samalla säilyttäen tavoitteeksi asetetun kehysvirhesuhteen (frame error rate [FER]). Suorituskyvyn ennustusmenetelmä hyödyntää kanavan tilastollisia ominaisuuksia – kohinan varianssia, eroteltavien etenemispolkujen lukumäärää sekä vastaanottimen korrelaatiomatriisin ominaisarvoja – ennustaakseen signaali–kohina-plus-interferenssisuhteen (signal-to-interference-plus-noise ratio [SINR]) jakauman taajuustasossa toimivan, häiriötä poistavan pienimmän keskineliösumman kanavakorjaimen lähdössä. SINR-jakaumasta johdetaan pehmän symboleista biteiksi -muunnoksen jälkeisten logaritmisten bittitodennäköisyyksien suhdelukujen (log-likelihood ratio [LLR]) jakauma. Keskinäisinformaation siirroskartat perustuvat LLR:ien varianssin sekä keskinäisinformaation väliseen bijektiivisyyteen. Informaatio on kanavakoodattu 3rd Generation Partnership Project -standardin mukaisella turbokoodilla. Turbodekooderin toiminta on kanavasta riippumatonta, joten dekooderin lisäinformaation siirroskartat (extrinsic information transfer [EXIT] charts) voidaan simuloida itsenäisesti. Hyödyntämällä kanavakorjaimen lähdön pehmeiden bittipäätösten LLR:ien varianssin jakaumaa, on mahdollista arvioida millä todennäköisyydellä korjaimen satunnaisen kanavarealisaation siirroskartta leikkaa dekooderin siirroskartan. Tämä todennäköisyys voidaan tulkita kehysvirhesuhteeksi. Koska suorituskyvyn ennustusmenetelmä ei vaadi hetkellistä tietoa kanavan tilasta, sitä voidaan hyödyntää lähetyksen mukautuksessa. Mukautuvassa tehonsäädössä modulaatio ja koodisuhde eivät muutu. Lähetin pyrkii iteratiivisella tehonsäädöllä löytämään korjaimen lähdölle LLR-jakauman, joka tuottaa halutun kehysvirhesuhteen. Mukautuvassa modulaation ja koodisuhteen valinnassa lähetysteho säilyy vakiona. Modulaatioaste vaikuttaa korjaimen lähdön LLR-jakaumaan ja koodisuhde dekooderin siirroskartan muotoon. Iteratiivisesti koodisuhdetta säätämällä lähetin pyrkii löytämään modulaation ja koodisuhteen yhdistelmän, joka saavuttaa tavoitellun kehysvirhesuhteen. Vertikaalisesti tilakanavoiduissa järjestelmissä mukautuvaa tehonsäätöä täydennetään lähetystehoa mukauttavilla uudellenlähetyksillä, kun taas mukautuvaa modulaation ja koodisuhteen valintaa täydennetään puolestaan koodisuhdetta pienentävillä automattisilla uudelleenlähetyspyynnöillä (hybrid automatic repeat request [HARQ]).

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.

L’estimation de canal joue un rôle important dans les communications mobiles sans fil et en particulier dans les systèmes multi-antennes MIMO. Contrairement aux techniques classiques d’estimation de canal basées sur des séquences d’apprentissage ou des symboles pilotes, les techniques aveugles ne nécessitent aucune insertion de symboles d'apprentissage et permettent d'augmenter le débit utile. Les principales difficultés des techniques aveugles résident dans l’ambiguïté présente sur les estimées. Les techniques d’estimation semi-aveugles, basées sur les mêmes méthodes que l’estimation aveugle, sont plus robustes. Elles exploitent l’information aveugle ainsi que l’information provenant d’un nombre réduit de symboles d’apprentissage. Cette estimation du canal de communication est très utile dans les systèmes MIMO et permet de précoder le signal MIMO-OFDM en lui appliquant un pré-mélange permettant d'améliorer les performances. De nombreux types de précodeurs existent et leurs performances varient en fonction des critères d'optimisation retenus (Water-Filling, MMSE, Equal Error, max-SNR, max-d min …), mais aussi avec la qualité de l'estimation du canal de communication. Nous étudions dans cette thèse l’impact de l’utilisation de l’information du canal (CSI) provenant des méthodes d’estimation aveugle et semi-aveugle, dans l’application des précodeurs linéaires MIMO. Nous présentons également une étude statistique de l’erreur d’estimation provenant de ces méthodes. L’optimisation de ces précodeurs nous mène par la suite à exploiter un autre procédé permettant l’amélioration des performances : les codes correcteurs d’erreur. Nous nous intéressons particulièrement aux codes LDPC non-binaires et leur association avec les précodeurs linéaires MIMO. Nous montrons qu’une adaptation est possible et s’avère bénéfique dans certains cas. L’optimisation de cette association nous a permis de proposer un nouveau précodeur basé sur la maximisation de l’information mutuelle, robuste et plus performant. / Channel estimation plays an important role in wireless mobile communications, especially in MIMO systems. Unlike conventional channel estimation techniques based on training sequences or pilot symbols, blind techniques does not require the insertion of training symbols and allow higher throughput. The main problems of the blind lies in the ambiguity over the estimated channel. Based on the same methods as the blind estimation, the semi-blind estimation techniques are more robust. They exploit the blind information along with information provided by a small number of training symbols. The channel estimation is useful in MIMO systems and allows the precoding of the MIMO-OFDM signal by applying a pre-mixture in order to improve performance. Many types of precoders exist and their performance varies depending not only on the optimization criteria (Water-Filling, MMSE, Equal Error, max-SNR, max-d min ...), but also on the estimated channel. In this thesis we study the impact of using the channel information (CSI) from the blind and semi-blind estimation techniques to apply MIMO linear precoders. We also present a statistical study of the estimation error of these methods. The optimization of these precoders leads eventually to use another process allowing more performance improvement: the error correcting codes. We are particularly interested in non-binary LDPC codes and their association with linear MIMO precoders. We show that a matching is possible, and is beneficial in some cases. The optimization of this combination has allowed us to propose a new robust and more efficient precoder based on the maximization of mutual information.

The objective of this thesis is to improve the performance of real-time communication overa wireless channel, by means of specifically tailored channel coding. The deadlinedependent coding (DDC) communication protocol presented here lets the timeliness and thereliability of the delivered information constitute quality of service (QoS) parametersrequested by the application. The values of these QoS parameters are transformed intoactions taken by the link layer protocol in terms of adaptive coding strategies.Incremental redundancy hybrid automatic repeat request (IR-HARQ) schemes usingrate compatible punctured codes are appealing since no repetition of previously transmittedbits is made. Typically, IR-HARQ schemes treat the packet lengths as fixed and maximizethe throughput by optimizing the puncturing pattern, i.e. the order in which the coded bitsare transmitted. In contrast, we define an IR strategy as the maximum number of allowedtransmissions and the number of code bits to include in each transmission. An approach isthen suggested to find the optimal IR strategy that maximizes the average code rate, i.e., theoptimal partitioning of n-kparity bits over at most M transmissions, assuming a givenpuncturing pattern. Concatenated coding used in IR-HARQ schemes provides a new arrayof possibilities for adaptability in terms of decoding complexity and communication timeversus reliability. Hence, critical reliability and timing constraints can be readily evaluatedas a function of available system resources. This in turn enables quantifiable QoS and thusnegotiable QoS. Multiple concatenated single parity check codes are chosen as examplecodes due to their very low decoding complexity. Specific puncturing patterns for thesecomponent codes are obtained using union bounds based on uniform interleavers. Thepuncturing pattern that has the best performance in terms of frame error rate (FER) at a lowsignal-to-noise ratio (SNR) is chosen. Further, using extrinsic information transfer (EXIT)analysis, rate compatible puncturing ratios for the constituent component code are found.The puncturing ratios are chosen to minimize the SNR required for convergence.The applications targeted in this thesis are not necessarily replacement of cables inexisting wired systems. Instead the motivation lies in the new services that wireless real-time communication enables. Hence, communication within and between cooperatingembedded systems is typically the focus. The resulting IR-HARQ-DDC protocol presentedhere is an efficient and fault tolerant link layer protocol foundation using adaptiveconcatenated coding intended specifically for wireless real-time communications. / Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, 2198, Technical report. D, 29,

Submitted by Carmen Torres (carmensct@globo.com) on 2018-02-09T18:11:30Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_MapeamentoBitsAdaptacao.pdf: 986310 bytes, checksum: 6e1b30f6ca34fc67df43f3141680c73a (MD5) / Approved for entry into archive by Edisangela Bastos (edisangela@ufpa.br) on 2018-02-16T16:12:49Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_MapeamentoBitsAdaptacao.pdf: 986310 bytes, checksum: 6e1b30f6ca34fc67df43f3141680c73a (MD5) / Made available in DSpace on 2018-02-16T16:12:49Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_MapeamentoBitsAdaptacao.pdf: 986310 bytes, checksum: 6e1b30f6ca34fc67df43f3141680c73a (MD5) Previous issue date: 2017-09-29 / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / Os codigos com matriz de vericação de paridade de baixa densidade (LDPC) tem sido adotados como estrategia de correção de erros em diversos padrões de sistemas de comunicação, como nos sistemas G.hn (padrão que unifica as redes domesticas) e IEEE 802.11n (padrão para redes sem o locais). Nestes sistemas com modulação de amplitude em quadratura (QAM) codicados com LDPC, mapear propriamente os bits codificados para os diferentes sub-canais, considerando o fato de os sub-canais terem diferentes qualidades, garante uma melhora no desempenho geral do sistema. Nesse sentido, esta Tese apresenta uma nova técnica de mapeamento de bits, baseada na suposição de que bits transmitidos em sub-canais \bons" ajudam bits transmitidos em sub-canais \ruins". Isto e possível através de algumas restrições impostas ao grafo de Tanner associado, semelhantes aos códigos Root-LDPC. A otimização deste mapeamento de bits utilizando curvas de transferência de informação extrínseca (EXIT charts) também e apresentada. Observa-se que esse mapeamento tem a vantagem de um espaço de busca de otimização reduzido quando aplicado ao sistema com modo de transmissão de portadora única. Além disso, em situações nas quais o espaço de busca não e tão reduzido, como em aplicações baseadas em multiplexação por divisão de frequência ortogonal (OFDM), chegou-se a uma simples regra pratica associada as restrições do mapeamento de bits que praticamente elimina a necessidade de uma otimização. Por fim, um estudo do impacto do nível de desequilíbrio de contabilidade através dos sub-canais sobre o desempenho do mapeamento de bits e apresentado. Os resultados das simulações mostram que a estratégia de mapeamento de bits melhora o desempenho do sistema, e que, na presença de variações do canal, o sistema pode, adaptativamente, aplicar um novo mapeamento de bits sem a necessidade de recorrer a uma otimização complexa, podendo ser muito útil em sistemas práticos. / Low-Density parity-check (LDPC) codes are being adopted as the error correction strategy in di erent system standards, such as the G.hn (home networking standard) and the IEEE 802.11n (wireless local standard). In these LDPC-coded quadrature amplitude modulation (QAM) systems, mapping the LDPC coded bits properly to the di erent sub-channels considering the fact that sub-channels have di erent qualities ensures an improved overall system performance. Accordingly, this thesis presents a new bit mapping technique based on the assumption that bits transmitted in \good" sub-channels, help bits transmitted in \bad" sub-channels. This can be made possible through some restrictions to be imposed on the associated Tanner graph, akin to Root-LDPC codes. An optimization of the root-like bit mapping through extrinsic information transfer (EXIT) charts analysis is also presented. We show that this mapping has the advantage of a reduced optimization search space when applied to single-carrier based systems. Moreover, in situations where the search space is not só reduced, such as in orthogonal frequency division multiplexing (OFDM)-based applications, we arrive at a rule of thumb associated with the bit mapping constraints that practically eliminates the need for an optimization. Finally, a study of the impact of the level of reliability imbalance across the sub-channels on the performance of the root-like bit mapping is presented. Simulation results show that the new bit mapping strategy improves performance, and that in the presence of channel variations, the system can, adaptively, apply a new bit mapping without the need of a complex optimization, which can be very useful in practical systems.

Les standards « Long-term evolution » (LTE) et LTE-Advanced (LTE-A) devraient influencer fortement l’avenir de la cinquième génération (5G) des réseaux mobiles. Ces normes exigent de hauts débits de données et une qualité de service de très bon niveau, ce qui permet d’assurer un faible taux d’erreur, avec une faible latence. Par ailleurs, la complexité doit être limitée. Dans le but de déterminer des solutions technologiques modernes qui satisfont ces contraintes fortes, nous étudions dans la thèse des systèmes de communication sans fil MIMO codés. D’abord, nous imposons un simple code convolutif récursif systématique (RSC) pour limiter la complexité et la latence. En considérant des récepteurs itératifs, nous optimisons alors la performance en termes de taux d’erreur de ces systèmes en définissant un précodage linéaire MIMO et des techniques de mapping appropriées. Dans la deuxième partie de la thèse, nous remplaçons le RSC par un LDPC non-binaire (NB-LDPC). Nous proposons d’utiliser les techniques de précodage MIMO afin de réduire la complexité des récepteurs des systèmes MIMO intégrant des codes NB-LDPC. Enfin, nous proposons également un nouvel algorithme de décodage itératif à faible complexité adapté aux codes NB-LDPC. / The long-term evolution (LTE) and the LTE-Advanced (LTE-A) standardizations are predicted to play essential roles in the future fifth-generation (5G) mobile networks. These standardizations require high data rate and high quality of service, which assures low error-rate and low latency. Besides, as discussed in the recent surveys, low complexity communication systems are also essential in the next 5G mobile networks. To adapt to the modern trend of technology, in this PhD thesis, we investigate the multiple-input multiple-output (MIMO) wireless communication schemes. In the first part of this thesis, low-complex forward error correction (FEC) codes are used for low complexity and latency. By considering iterative receivers at the receiver side, we exploit MIMO linear precoding and mapping methods to optimize the error-rate performance of these systems. In the second part of this thesis, non-binary low density parity check (NB-LDPC) codes are investigated. We propose to use MIMO precoders to reduce the complexity for NB-LDPC encoded MIMO systems. A novel low complexity decoding algorithm for NB-LDPC codes is also proposed at the end of this thesis.