The hard-disk storage industry is at a critical time as the current technologies are incapable of achieving densities beyond 500 Gb/in2, which will be reached in a few years. Many radically new storage architectures have been proposed, which along with advanced signal processing algorithms are expected to achieve much higher densities. In this dissertation, various signal processing algorithms are developed to improve the performance of current and next-generation magnetic storage systems.Low-density parity-check (LDPC) error correction codes are known to provide excellent performance in magnetic storage systems and are likely to replace or supplement currently used algebraic codes. Two methods are described to improve their performance in such systems. In the first method, the detector is modified to incorporate auxiliary LDPC parity checks. Using graph theoretical algorithms, a method to incorporate maximum number of such checks for a given complexity is provided. In the second method, a joint detection and decoding algorithm is developed that, unlike all other schemes, operates on the non-binary channel output symbols rather than input bits. Though sub-optimal, it is shown to provide the best known decoding performance for channels with memory more than 1, which are practically the most important.This dissertation also proposes a ternary magnetic recording system from a signal processing perspective. The advantage of this novel scheme is that it is capable of making magnetic transitions with two different but predetermined gradients. By developing optimal signal processing components like receivers, equalizers and detectors for this channel, the equivalence of this system to a two-track/two-head system is determined and its performance is analyzed. Consequently, it is shown that it is preferable to store information using this system, than to store using a binary system with inter-track interference. Finally, this dissertation provides a number of insights into the unique characteristics of heat-assisted magnetic recording (HAMR) and two-dimensional magnetic recording (TDMR) channels. For HAMR channels, the effects of laser spot on transition characteristics and non-linear transition shift are investigated. For TDMR channels, a suitable channel model is developed to investigate the two-dimensional nature of the noise.

We study and analyze the performance of iterative equalization and decoding (IED) using an M-BCJR equalizer. We use bit error rate (BER), frame error rate simulations and extrinsic information transfer (EXIT) charts to study and compare the performances of M-BCJR and BCJR equalizers on precoded and non-precoded channels. Using EXIT charts, the achievable channel capacities with IED using the BCJR, M-BCJR and MMSE LE equalizers are also compared. We predict the BER performance of IED using the M-BCJR equalizer from EXIT charts and explain the discrepancy between the observed and predicted performances by showing that the extrinsic outputs of the $M$-BCJR algorithm are not true logarithmic-likelihood ratios (LLR's). We show that the true LLR's can be estimated if the conditional distributions of the extrinsic outputs are known and finally we design a practical estimator for computing the true LLR's from the extrinsic outputs of the M-BCJR equalizer.

While the focus of this work is on turbo equalization, there is also an examination of equalization techniques including MMSE linear and DFE equalizers and Precoding. The losses and capacity associated with the ISI channel are also examined. Iterative decoding of concatenated codes is briefly reviewed and the MAP algorithm is explained.

Abstract This thesis focuses on advanced multi-antenna receiver and transmission techniques to improve the utilization efficiencies of radio resources in broadband single carrier communications. Special focus is devoted to the development of computationally efficient frequency domain (FD) turbo equalization techniques for single and multiuser MIMO frequency selective channels. Another special emphasis is given to transmission power optimization for single user MIMO communications, which takes into account the convergence properties of the iterative equalizer. A new iterative FD soft cancellation (SC) and minimum mean square error (MMSE) filtering based joint-over-antenna (JA) multiuser MIMO signal detection technique for multiuser MIMO uplink transmission in frequency-selective channels is proposed. The proposed FD multiuser MIMO detection technique requires significantly lower computational complexity than its time-domain counterpart. Furthermore, significant performance gains can be achieved with the proposed JA turbo receiver compared to an antenna-by-antenna (AA) turbo receiver when the total number of transmitter antennas and users is larger than the number of receiver antennas, as well as in the presence of spatial correlation. The impact of existing linear precoding techniques, e.g, maximum information rate (MaxRate) and minimum sum mean square error (MinSumMSE), on the performance of frequency domain turbo equalization is investigated by utilizing extrinsic information transfer (EXIT) chart analysis. A novel transmission power minimization framework based on an EXIT analysis of single carrier MIMO transmission with iterative FD SC-MMSE equalization is then proposed. The proposed optimization framework explicitly takes into account the convergence properties of the iterative equalizer. The proposed convergence constrained power allocation (CCPA) technique decouples the spatial interference between streams using singular value decomposition (SVD), and minimizes the transmission power while achieving the mutual information target for each stream after iterations at the receiver side. The transmission power allocation can be formulated as a convex optimization problem. A special case having only two mutual information constraints is considered, for which the Lagrange dual function is derived and its dual problem is solved. Inspired by the Lagrange duality, two CCPA based heuristic schemes are developed. The numerical results demonstrate that the proposed CCPA schemes outperform the existing power allocation schemes. / Tiivistelmä Tässä työssä tutkitaan edistyksellisten moniantennivastaanotto- ja lähetysmenetelmien käyttöä radioresurssien tehokkuuden parantamiseen laajakaistaisessa yhden kantoaallon kommunikaatiossa. Työssä keskitytään erityisesti laskennallisesti tehokkaiden taajuustasossa suoritettavien iteratiivisten kanavakorjaintekniikoiden kehittämiseen yhden ja usean käyttäjän multiple-input multiple-output (MIMO) -kommunikaatiossa taajuusselektiivisen radiokanavan yli. Toinen tutkimuksen painopiste on lähetystehon optimointi yhden käyttäjän MIMO-kommunikaatiossa, jossa iteratiivisen kanavakorjaimen konvergenssiominaisuudet otetaan huomioon. Työssä ehdotetaan uudenlaista iteratiivista taajuustasossa suoritettavaa soft-cancellation (SC) ja minimum mean square error (MMSE) -suodatukseen pohjautuvaa joint-over-antenna (JA) monen käyttäjän ilmaisumenetelmää nousevan siirtokanavan tiedonsiirtoon taajuusselektiivisessa radiokanavassa. Ehdotettu tajuustasossa suoritettava usean käyttäjän MIMO-lähetyksen ilmaisumenetelmä vaatii selvästi vähemmän laskentatehoa verrattuna aikatason menetelmään. Tämän lisäksi ehdotetulla menetelmällä voidaan saavuttaa merkittävää suorituskykyhyötyä verrattuna antenna-by-antenna (AA) -pohjaiseen iteratiiviseen vastaanottimeen kun lähetysantennien ja käyttäjien kokonaislukumäärä on suurempi kuin vastaanotinantennien. Suorituskykyhyöty pätee myös tilakorrelaation tapauksessa. Työssä tutkitaan lisäksi olemassa olevien lineaaristen esikoodaustekniikoiden, esim. maximum information rate (MaxRate) and minimum sum mean square error (MinSumMSE), vaikutusta taajuustasossa suoritettavaan iteratiivisen kanavakorjaimen konvergenssiominaisuuksiin xtrinsic information transfer (EXIT) -analyysin avulla. Työssä ehdotetaan uudenlaista EXIT-analyysi-pohjaista lähetystehon minimointimenetelmää yhden kantoaallon MIMO-lähetykseen käyttäen iteratiivista taajuustason SC-MMSE-kanavakorjainta. Menetelmä ottaa huomioon iteratiivisen kanavakorjaimen konvergenssiominaisuudet. Ehdotettu convergence constrained power allocation (CCPA) -menetelmä erottaa tilatason häiriön lähetteiden välillä hyödyntäen singular value decomposition (SVD) -tekniikkaa ja minimoi lähetystehon ja saavuttaa samalla keskinäisinformaatiotavoitteet jokaiselle lähetteelle iteraatioiden jälkeen vastaanottimessa. Lähetystehon minimointiongelma voidaan muotoilla konveksiksi optimointiongelmaksi. Kahden keskinäisinformaatiorajoitteen erityistapaukselle johdetaan Lagrangen duaalifunktio ja ratkaistaan sen duaalifunktio. Työssä kehitetään lisäksi kaksi CCPA-pohjaista heuristista menetelmää. Numeeriset tulokset osoittavat ehdotettujen CCPA-pohjaisten menetelmien suoriutuvan paremmin verrattuna olemassa oleviin menetelmiin.

L’objectif de cette thèse est l’étude de récepteurs MIMO LDPC itératifs. Les techniques MIMO permettent d’augmenter la capacité des réseaux sans fil sans la nécessité de ressources fréquentielles additives. Associées aux schémas de modulations multiporteuses CP-OFDM, les techniques MIMO sont ainsi devenues la pierre angulaire pour les systèmes sans fil à haute efficacité spectrale. La réception optimale peut être obtenue à l’aide d’une réception conjointe (Egalisation/Décodage). Étant très complexe, la réception conjointe n’est pas envisagée et l’égalisation et le décodage sont réalisés disjointement au coût d’une dégradation significative en performances. Entre ces deux solutions, la réception itérative trouve son intérêt pour sa capacité à s’approcher des performances optimales avec une complexité réduite. La conception de récepteurs itératifs pour certaines applications, de type WiFi à titre d’exemple doit respecter la structure du code imposée par la norme. Ces codes ne sont pas optimisés pour des récepteurs itératifs. En observant l’effet du nombre d' itérations dans le processus itératif, on montre par simulation que l’ordonnancement des itérations décodage LDPC/Turbo-égalisation joue un rôle important dans la complexité et le délai du récepteur. Nous proposons de définir des ordonnancements permettant de réduire la complexité globale du récepteur. Deux approches sont proposées, une approche statique ainsi qu'une autre dynamique. Ensuite nous considérons un système multi-utilisateur avec un accès multiple par répartition spatiale. Nous étudions l’intérêt de la réception itérative dans ce contexte tenant en compte la différence de puissance signale utile/interférence. / The aim of this thesis is to address the design of iterative MIMO receivers using LDPC Error Correcting codes. MIMO techniques enable capacity increase in wireless networks with no additional frequency ressources. The associationof MIMO with multicarrier modulation techniques OFDM made them the cornerstone of emerging high rate wireless networks. Optimal reception can be achieved using joint detection and decoding at the expense of a huge complexity making it impractical. Disjoint reception is then the most used. The design of iterative receivers for some applications using LDPC codes like Wifi (IEEE 802.11n) is constrained by the standard code structure which is not optimized for such kind of receivers. By observing the effect of the number of iterations on performance and complexity we underline the interest of scheduling LDPC decoding iterations and turboequalization iterations. We propose to define schedules for the iterative receiver in order to reduce its complexity while preserving its performance. Two approaches are used : static and dynamic scheduling. The second part of this work is concerns Multiuser MIMO using Spatial Division Multiple Access. We explore and evaluate the interest of using iterative reception to cancel residual inter-user interference.

The unifying theme of this dissertation is the development of new solutions for decoding and inference problems based on convex optimization methods. Th first part considers the joint detection and decoding problem for low-density parity-check (LDPC) codes on finite-state channels (FSCs). Hard-disk drives (or magnetic recording systems), where the required error rate (after decoding) is too low to be verifiable by simulation, are most important applications of this research. Recently, LDPC codes have attracted a lot of attention in the magnetic storage industry and some hard-disk drives have started using iterative decoding. Despite progress in the area of reduced-complexity detection and decoding algorithms, there has been some resistance to the deployment of turbo-equalization (TE) structures (with iterative detectors/decoders) in magnetic-recording systems because of error floors and the difficulty of accurately predicting performance at very low error rates. To address this problem for channels with memory, such as FSCs, we propose a new decoding algorithms based on a well-defined convex optimization problem. In particular, it is based on the linear-programing (LP) formulation of the joint decoding problem for LDPC codes over FSCs. It exhibits two favorable properties: provable convergence and predictable error-floors (via pseudo-codeword analysis). Since general-purpose LP solvers are too complex to make the joint LP decoder feasible for practical purposes, we develop an efficient iterative solver for the joint LP decoder by taking advantage of its dual-domain structure. The main advantage of this approach is that it combines the predictability and superior performance of joint LP decoding with the computational complexity of TE. The second part of this dissertation considers the matrix completion problem for the recovery of a data matrix from incomplete, or even corrupted entries of an unknown matrix. Recommender systems are good representatives of this problem, and this research is important for the design of information retrieval systems which require very high scalability. We show that our IMP algorithm reduces the well-known cold-start problem associated with collaborative filtering systems in practice.

Digital communication systems invariably employ an underlying analog communication channel. At the transmitter, data is modulated to obtain an analog waveform which is input to the channel. At the receiver, the output of the channel needs to be mapped back into the discrete domain. To this effect, the continuous-time received waveform is sampled at instants chosen by the timing recovery block. Therefore, timing recovery is an essential component of digital communication systems. A widely used timing recovery method is based on a phase-locked loop (PLL), which updates its timing estimates based on a decision-directed device. Timing recovery performance is a strong function of the reliability of decisions, and hence, of the channel signal-to-noise ratio (SNR). Iteratively decodable error-control codes (ECCs) like turbo codes and LDPC codes allow operation at SNRs lower than ever before, thus exacerbating timing recovery. We propose iterative timing recovery, where the timing recovery block, the equalizer and the ECC decoder exchange information, giving the timing recovery block access to decisions that are much more reliable than the instantaneous ones. This provides significant SNR gains at a marginal complexity penalty over a conventional turbo equalizer where the equalizer and the ECC decoder exchange information. We also derive the Cramer-Rao bound, which is a lower bound on the estimation error variance of any timing estimator, and propose timing recovery methods that outperform the conventional PLL and achieve the Cramer-Rao bound in some cases. At low SNR, timing recovery suffers from cycle slips, where the receiver drops or adds one or more symbols, and consequently, almost always the ECC decoder fails to decode. Iterative timing recovery has the ability to corrects cycle slips. To reduce the number of iterations, we propose cycle slip detection and correction methods. With iterative timing recovery, the PLL with cycle slip detection and correction recovers most of the SNR loss of the conventional receiver that separates timing recovery and turbo equalization.

In satellite communications, non-linear interference is created by the non-linear power amplifier aboard the satellite. Even in the case of a memoryless power amplifier, the channel is a non-linear system with memory due to the presence of linear filters on ground and aboard the satellite. The non-linear interference degrades the system performance, especially when considering high-order modulations or in case of several signals being amplified by the same power amplifier. In this thesis, we have proposed algorithms at the transmitter and at the receiver to digitally compensate this interference. In particular, a new predistortion algorithm has been proposed, which significantly improves state-of-the-art algorithms. Since the complexity of this algorithm is an issue, low-complexity algorithms have also been proposed and achieve almost the same performance as the initial algorithm. We have also proposed joint predistortion and turbo-equalization algorithms to further improve the system performance. / En communications par satellite, de l’interférence non-linéaire est créée par l’amplificateur de puissance non-linéaire à bord du satellite. Même si l’amplificateur peut être considéré comme sans mémoire, le canal est malgré tout un système non-linéaire avec mémoire de par la présence de filtres linéaires au sol ou à bord du satellite. L'interférence non-linéaire dégrade les performances du système, en particulier lorsqu’on considère des modulations d’ordre élevé ou plusieurs signaux amplifiés par le même amplificateur de puissance. Dans cette thèse, nous avons proposé des algorithmes à l’émetteur et au récepteur pour compenser numériquement cette interférence. En particulier, nous avons proposé un nouvel algorithme de prédistorsion qui améliore de façon significative les algorithmes de l’état-de-l’art. La complexité de l’algorithme étant très élevée, nous avons proposé des algorithmes de plus faible complexité atteignant pratiquement les mêmes performances par rapport à l’algorithme initial. Nous avons aussi proposé des algorithmes de prédistorsion et d’égalisation conjointes, permettant d'atteindre des performances plus élevées qu'avec la prédistorsion seule. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

In this thesis, we present low latency general concatenated code structures suitable for parallel processing. We propose parallel decodable serially concatenated codes (PDSCCs) which is a general structure to construct many variants of serially concatenated codes. Using this most general structure we derive parallel decodable serially concatenated convolutional codes (PDSCCCs). Convolutional product codes which are instances of PDSCCCs are studied in detail. PDSCCCs have much less decoding latency and show almost the same performance compared to classical serially concatenated convolutional codes. Using the same idea, we propose parallel decodable turbo codes (PDTCs) which represent a general structure to construct parallel concatenated codes. PDTCs have much less latency compared to classical turbo codes and they both achieve similar performance. We extend the approach proposed for the construction of parallel decodable concatenated codes to trellis coded modulation, turbo channel equalization, and space time trellis codes and show that low latency systems can be constructed using the same idea. Parallel decoding operation introduces new problems in implementation. One such problem is memory collision which occurs when multiple decoder units attempt accessing the same memory device. We propose novel interleaver structures which prevent the memory collision problem while achieving performance close to other interleavers.

This research investigates techniques for iterative channel estimation to maximize channel capacity and communication security. The contributions of this dissertation are as follows: i) An accurate, low-complexity approach to pilot-assisted fast-fading channel estimation for single-carrier modulation with a turbo equalizer and a decoder is proposed. The channel is estimated using a Kalman filter (KF) followed by a zero-phase filter (ZPF) as a smoother. The combination of the ZPF with the KF of the channel estimator makes it possible to reduce the estimation error to near the Wiener bound. ii) A new semi-blind channel estimation technique is introduced for multiple-input-multiple-output channels. Once the channel is estimated using a few pilots, a low-order KF is employed to progressively predict the channel gains for the upcoming blocks. iii) The capacity of radio channels is investigated when iterative channel estimation, data detection, and decoding are employed. By taking the uncertainty in decoded data bits into account, the channel Linear Minimum Mean Square Error (LMMSE) estimator of an iterative receiver with a given pilot ratio is obtained. The derived error value is then used to derive a bound on capacity. It is shown that in slow fading channels, iterative processing provides only a marginal advantage over non-iterative approach to channel estimation. Knowing the capacity gain from iterative processing versus purely pilot-based channel estimation helps a designer to compare the performance of an iterative receiver against a non-iterative one and select the best balance between performance and cost. iv) A Radio channel is characterized by random parameters which can be used to generate shared secret keys by the communicating parties when the channel is estimated. This research studies upper bounds on the rate of the secret keys extractable from iteratively estimated channels. Various realistic scenarios are considered where the transmission is half-duplex and/or the channel is sampled under the Nyquist rate. The effect of channel sampling interval, fading rate and noise on the key rate is demonstrated. The results of this research can be beneficial for the design and analysis of reliable and secure mobile wireless systems. / Graduate / 0544