A High-Performance and Low-Complexity 5G LDPC Decoder: Algorithm and Implementation

5G New Radio (NR) has stringent demands on both performance and complexity for the design of low-density parity-check (LDPC) decoding algorithms and corresponding VLSI implementations. Furthermore, decoders must fully support the wide range of all 5G NR blocklengths and code rates, which is a significant challenge. In this paper, we present a high-performance and low-complexity LDPC decoder, tailor-made to fulfill the 5G requirements. First, to close the gap between belief propagation (BP) decoding and its approximations in hardware, we propose an extension of adjusted min-sum decoding, called generalized adjusted min-sum (GA-MS) decoding. This decoding algorithm flexibly truncates the incoming messages at the check node level and carefully approximates the non-linear functions of BP decoding to balance the error-rate and hardware complexity. Numerical results demonstrate that the proposed fixed-point GAMS has only a minor gap of 0.1 dB compared to floating-point BP under various scenarios of 5G standard specifications. Secondly, we present a fully reconfigurable 5G NR LDPC decoder implementation based on GA-MS decoding. Given that memory occupies a substantial portion of the decoder area, we adopt multiple data compression and approximation techniques to reduce 42.2% of the memory overhead. The corresponding 28nm FD-SOI ASIC decoder has a core area of 1.823 mm2 and operates at 895 MHz. It is compatible with all 5G NR LDPC codes and achieves a peak throughput of 24.42 Gbps and a maximum area efficiency of 13.40 Gbps/mm2 at 4 decoding iterations.Comment: 14 pages, 14 figure

VLSI architectures design for encoders of High Efficiency Video Coding (HEVC) standard

The growing popularity of high resolution video and the continuously increasing demands for high quality video on mobile devices are producing stronger needs for more efficient video encoder. Concerning these desires, HEVC, a newest video coding standard, has been developed by a joint team formed by ISO/IEO MPEG and ITU/T VCEG. Its design goal is to achieve a 50% compression gain over its predecessor H.264 with an equal or even higher perceptual video quality. Motion Estimation (ME) being as one of the most critical module in video coding contributes almost 50%-70% of computational complexity in the video encoder. This high consumption of the computational resources puts a limit on the performance of encoders, especially for full HD or ultra HD videos, in terms of coding speed, bit-rate and video quality. Thus the major part of this work concentrates on the computational complexity reduction and improvement of timing performance of motion estimation algorithms for HEVC standard. First, a new strategy to calculate the SAD (Sum of Absolute Difference) for motion estimation is designed based on the statistics on property of pixel data of video sequences. This statistics demonstrates the size relationship between the sum of two sets of pixels has a determined connection with the distribution of the size relationship between individual pixels from the two sets. Taking the advantage of this observation, only a small proportion of pixels is necessary to be involved in the SAD calculation. Simulations show that the amount of computations required in the full search algorithm is reduced by about 58% on average and up to 70% in the best case. Secondly, from the scope of parallelization an enhanced TZ search for HEVC is proposed using novel schemes of multiple MVPs (motion vector predictor) and shared MVP. Specifically, resorting to multiple MVPs the initial search process is performed in parallel at multiple search centers, and the ME processing engine for PUs within one CU are parallelized based on the MVP sharing scheme on CU (coding unit) level. Moreover, the SAD module for ME engine is also parallelly implemented for PU size of 32×32. Experiments indicate it achieves an appreciable improvement on the throughput and coding efficiency of the HEVC video encoder. In addition, the other part of this thesis is contributed to the VLSI architecture design for finding the first W maximum/minimum values targeting towards high speed and low hardware cost. The architecture based on the novel bit-wise AND scheme has only half of the area of the best reference solution and its critical path delay is comparable with other implementations. While the FPCG (full parallel comparison grid) architecture, which utilizes the optimized comparator-based structure, achieves 3.6 times faster on average on the speed and even 5.2 times faster at best comparing with the reference architectures. Finally the architecture using the partial sorting strategy reaches a good balance on the timing performance and area, which has a slightly lower or comparable speed with FPCG architecture and a acceptable hardware cost

Récepteur itératif pour les systèmes MIMO-OFDM basé sur le décodage sphérique : convergence, performance et complexité

Recently, iterative processing has been widely considered to achieve near-capacity performance and reliable high data rate transmission, for future wireless communication systems. However, such an iterative processing poses significant challenges for efficient receiver design. In this thesis, iterative receiver combining multiple-input multiple-output (MIMO) detection with channel decoding is investigated for high data rate transmission. The convergence, the performance and the computational complexity of the iterative receiver for MIMO-OFDM system are considered. First, we review the most relevant hard-output and soft-output MIMO detection algorithms based on sphere decoding, K-Best decoding, and interference cancellation. Consequently, a low-complexity K-best (LCK- Best) based decoder is proposed in order to substantially reduce the computational complexity without significant performance degradation. We then analyze the convergence behaviors of combining these detection algorithms with various forward error correction codes, namely LTE turbo decoder and LDPC decoder with the help of Extrinsic Information Transfer (EXIT) charts. Based on this analysis, a new scheduling order of the required inner and outer iterations is suggested. The performance of the proposed receiver is evaluated in various LTE channel environments, and compared with other MIMO detection schemes. Secondly, the computational complexity of the iterative receiver with different channel coding techniques is evaluated and compared for different modulation orders and coding rates. Simulation results show that our proposed approaches achieve near optimal performance but more importantly it can substantially reduce the computational complexity of the system. From a practical point of view, fixed-point representation is usually used in order to reduce the hardware costs in terms of area, power consumption and execution time. Therefore, we present efficient fixed point arithmetic of the proposed iterative receiver based on LC-KBest decoder. Additionally, the impact of the channel estimation on the system performance is studied. The proposed iterative receiver is tested in a real-time environment using the MIMO WARP platform.Pour permettre l’accroissement de débit et de robustesse dans les futurs systèmes de communication sans fil, les processus itératifs sont de plus considérés dans les récepteurs. Cependant, l’adoption d’un traitement itératif pose des défis importants dans la conception du récepteur. Dans cette thèse, un récepteur itératif combinant les techniques de détection multi-antennes avec le décodage de canal est étudié. Trois aspects sont considérés dans un contexte MIMOOFDM: la convergence, la performance et la complexité du récepteur. Dans un premier temps, nous étudions les différents algorithmes de détection MIMO à décision dure et souple basés sur l’égalisation, le décodage sphérique, le décodage K-Best et l’annulation d’interférence. Un décodeur K-best de faible complexité (LC-K-Best) est proposé pour réduire la complexité sans dégradation significative des performances. Nous analysons ensuite la convergence de la combinaison de ces algorithmes de détection avec différentes techniques de codage de canal, notamment le décodeur turbo et le décodeur LDPC en utilisant le diagramme EXIT. En se basant sur cette analyse, un nouvel ordonnancement des itérations internes et externes nécessaires est proposé. Les performances du récepteur ainsi proposé sont évaluées dans différents modèles de canal LTE, et comparées avec différentes techniques de détection MIMO. Ensuite, la complexité des récepteurs itératifs avec différentes techniques de codage de canal est étudiée et comparée pour différents modulations et rendement de code. Les résultats de simulation montrent que les approches proposées offrent un bon compromis entre performance et complexité. D’un point de vue implémentation, la représentation en virgule fixe est généralement utilisée afin de réduire les coûts en termes de surface, de consommation d’énergie et de temps d’exécution. Nous présentons ainsi une représentation en virgule fixe du récepteur itératif proposé basé sur le décodeur LC K-Best. En outre, nous étudions l’impact de l’estimation de canal sur la performance du système. Finalement, le récepteur MIMOOFDM itératif est testé sur la plateforme matérielle WARP, validant le schéma proposé

Flexible encoder and decoder of low density parity check codes

У дисертацији су предложена брза, флексибилна и хардверски ефикасна решења за кодовање и декодовање изузетно нерегуларних кодова са проверама парности мале густине (енгл. low-density parity-check, LDPC, codes) захтевана у савременим комуникационим стандардима. Један део доприноса дисертације је у новој делимично паралелној архитектури LDPC кодера за пету генерацију мобилних комуникација. Архитектура је заснована на флексибилној мрежи за кружни померај која омогућава паралелно процесирање више делова контролне матрице кратких кодова чиме се остварује сличан ниво паралелизма као и при кодовању дугачких кодова. Поред архитектуралног решења, предложена је оптимизација редоследа процесирања контролне матрице заснована на генетичком алгоритму, која омогућава постизање великих протока, малог кашњења и тренутно најбоље ефикасности искоришћења хардверских ресурса. У другом делу дисертације предложено је ново алгоритамско и архитектурално решење за декодовање структурираних LDPC кодова. Често коришћени приступ у LDPC декодерима је слојевито декодовање, код кога се услед проточне обраде јављају хазарди података који смањују проток. Декодер предложен у дисертацији у конфликтним ситуацијама на погодан начин комбинује слојевито и симултано декодовање чиме се избегавају циклуси паузе изазвани хазардима података. Овај приступ даје могућност за увођење великог броја степени проточне обраде чиме се постиже висока учестаност сигнала такта. Додатно, редослед процесирања контролне матрице је оптимизован коришћењем генетичког алгоритма за побољшане перформансе контроле грешака. Остварени резултати показују да, у поређењу са референтним решењима, предложени декодер остварује значајна побољшања у протоку и најбољу ефикасност за исте перформансе контроле грешака.The dissertation proposes high speed, flexible and hardware efficient solutions for coding and decoding of highly irregular low-density parity-check (LDPC) codes, required by many modern communication standards. The first part of the dissertation’s contributions is in the novel partially parallel LDPC encoder architecture for 5G. The architecture was built around the flexible shifting network that enables parallel processing of multiple parity check matrix elements for short to medium code lengths, thus providing almost the same level of parallelism as for long code encoding. In addition, the processing schedule was optimized for minimal encoding time using the genetic algorithm. The optimization procedure contributes to achieving high throughputs, low latency, and up to date the best hardware usage efficiency (HUE). The second part proposes a new algorithmic and architectural solution for structured LDPC code decoding. A widely used approach in LDPC decoders is a layered decoding schedule, which frequently suffers from pipeline data hazards that reduce the throughput. The decoder proposed in the dissertation conveniently incorporates both the layered and the flooding schedules in cases when hazards occur and thus facilitates LDPC decoding without stall cycles caused by pipeline hazards. Therefore, the proposed architecture enables insertion of many pipeline stages, which consequently provides a high operating clock frequency. Additionally, the decoding schedule was optimized for better signal-to-noise ratio (SNR) performance using genetic algorithm. The obtained results show that the proposed decoder achieves great throughput increase and the best HUE when compared with the state of the art for the same SNR performance

Codage de sources avec information adjacente et connaissance incertaine des corrélations

Dans cette thèse, nous nous sommes intéressés au problème de codage de sources avec information adjacente au décodeur seulement. Plus précisément, nous avons considéré le cas où la distribution jointe entre la source et l'information adjacente n'est pas bien connue. Dans ce contexte, pour un problème de codage sans pertes, nous avons d'abord effectué une analyse de performance à l'aide d'outils de la théorie de l'information. Nous avons ensuite proposé un schéma de codage pratique efficace malgré le manque de connaissance sur la distribution de probabilité jointe. Ce schéma de codage s'appuie sur des codes LDPC non-binaires et sur un algorithme de type Espérance-Maximisation. Le problème du schéma de codage proposé, c'est que les codes LDPC non-binaires utilisés doivent être performants. C'est à dire qu'ils doivent être construits à partir de distributions de degrés qui permettent d'atteindre un débit proche des performances théoriques. Nous avons donc proposé une méthode d'optimisation des distributions de degrés des codes LDPC. Enfin, nous nous sommes intéressés à un cas de codage avec pertes. Nous avons supposé que le modèle de corrélation entre la source et l'information adjacente était décrit par un modèle de Markov caché à émissions Gaussiennes. Pour ce modèle, nous avons également effectué une analyse de performance, puis nous avons proposé un schéma de codage pratique. Ce schéma de codage s'appuie sur des codes LDPC non-binaires et sur une reconstruction MMSE. Ces deux composantes exploitent la structure avec mémoire du modèle de Markov caché.In this thesis, we considered the problem of source coding with side information available at the decoder only. More in details, we considered the case where the joint distribution between the source and the side information is not perfectly known. In this context, we performed a performance analysis of the lossless source coding scheme. This performance analysis was realized from information theory tools. Then, we proposed a practical coding scheme able to deal with the uncertainty on the joint probability distribution. This coding scheme is based on non-binary LDPC codes and on an Expectation-Maximization algorithm. For this problem, a key issue is to design efficient LDPC codes. In particular, good code degree distributions have to be selected. Consequently, we proposed an optimization method for the selection of good degree distributions. To finish, we considered a lossy coding scheme. In this case, we assumed that the correlation channel between the source and the side information is described by a Hidden Markov Model with Gaussian emissions. For this model, we performed again some performance analysis and proposed a practical coding scheme. The proposed scheme is based on non-binary LDPC codes and on MMSE reconstruction using an MCMC method. In our solution, these two components are able to exploit the memory induced by the Hidden Markov model.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Capacity-Achieving Coding Mechanisms: Spatial Coupling and Group Symmetries

The broad theme of this work is in constructing optimal transmission mechanisms for a wide variety of communication systems. In particular, this dissertation provides a proof of threshold saturation for spatially-coupled codes, low-complexity capacity-achieving coding schemes for side-information problems, a proof that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels, and a mathematical framework to design delay sensitive communication systems. Spatially-coupled codes are a class of codes on graphs that are shown to achieve capacity universally over binary symmetric memoryless channels (BMS) under belief-propagation decoder. The underlying phenomenon behind spatial coupling, known as “threshold saturation via spatial coupling”, turns out to be general and this technique has been applied to a wide variety of systems. In this work, a proof of the threshold saturation phenomenon is provided for irregular low-density parity-check (LDPC) and low-density generator-matrix (LDGM) ensembles on BMS channels. This proof is far simpler than published alternative proofs and it remains as the only technique to handle irregular and LDGM codes. Also, low-complexity capacity-achieving codes are constructed for three coding problems via spatial coupling: 1) rate distortion with side-information, 2) channel coding with side-information, and 3) write-once memory system. All these schemes are based on spatially coupling compound LDGM/LDPC ensembles. Reed-Muller and Bose-Chaudhuri-Hocquengham (BCH) are well-known algebraic codes introduced more than 50 years ago. While these codes are studied extensively in the literature it wasn’t known whether these codes achieve capacity. This work introduces a technique to show that Reed-Muller and primitive narrow-sense BCH codes achieve capacity on erasure channels under maximum a posteriori (MAP) decoding. Instead of relying on the weight enumerators or other precise details of these codes, this technique requires that these codes have highly symmetric permutation groups. In fact, any sequence of linear codes with increasing blocklengths whose rates converge to a number between 0 and 1, and whose permutation groups are doubly transitive achieve capacity on erasure channels under bit-MAP decoding. This pro-vides a rare example in information theory where symmetry alone is sufficient to achieve capacity. While the channel capacity provides a useful benchmark for practical design, communication systems of the day also demand small latency and other link layer metrics. Such delay sensitive communication systems are studied in this work, where a mathematical framework is developed to provide insights into the optimal design of these systems

Polarization and Spatial Coupling:Two Techniques to Boost Performance

During the last two decades we have witnessed considerable activity in building bridges between the fields of information theory/communications, computer science, and statistical physics. This is due to the realization that many fundamental concepts and notions in these fields are in fact related and that each field can benefit from the insight and techniques developed in the others. For instance, the notion of channel capacity in information theory, threshold phenomena in computer science, and phase transitions in statistical physics are all expressions of the same concept. Therefore, it would be beneficial to develop a common framework that unifies these notions and that could help to leverage knowledge in one field to make progress in the others. A particularly striking example is the celebrated belief propagation algorithm. It was independently invented in each of these fields but for very different purposes. The realization of the commonality has benefited each of the areas. We investigate polarization and spatial coupling: two techniques that were originally invented in the context of channel coding (communications) thus resulting for the first time in efficient capacity-achieving codes for a wide range of channels. As we will discuss, both techniques play a fundamental role also in computer science and statistical physics and so these two techniques can be seen as further fundamental building blocks that unite all three areas. We demonstrate applications of these techniques, as well as the fundamental phenomena they provide. In more detail, this thesis consists of two parts. In the first part, we consider the technique of polarization and its resultant class of channel codes, called polar codes. Our main focus is the analysis and improvement of the behavior of polarization towards the most significant aspects of modern channel-coding theory: scaling laws, universality, and complexity (quantization). For each of these aspects, we derive fundamental laws that govern the behavior of polarization and polar codes. Even though we concentrate on applications in communications, the analysis that we provide is general and can be carried over to applications of polarization in computer science and statistical physics. As we will show, our investigations confirm some of the inherent strengths of polar codes such as their robustness with respect to quantization. But they also make clear in which aspects further improvement of polar codes is needed. For example, we will explain that the scaling behavior of polar codes is quite slow compared to the optimal one. Hence, further research is required in order to enhance the scaling behavior of polar codes towards optimality. In the second part of this thesis, we investigate spatial coupling. By now, there exists already a considerable literature on spatial coupling in the realm of information theory and communications. We therefore investigate mainly the impact of spatial coupling on the fields of statistical physics and computer science. We consider two well-known models. The first is the Curie-Weiss model that provides us with the simplest model for understanding the mechanism of spatial coupling in the perspective of statistical physics. Many fundamental features of spatial coupling can be simply explained here. In particular, we will show how the well-known Maxwell construction in statistical physics manifests itself through spatial coupling. We then focus on a much richer class of graphical models called constraint satisfaction problems (CSP) (e.g., K-SAT and Q-COL). These models are central to computer science. We follow a general framework: First, we introduce interpolation procedures for proving that the coupled and standard (un-coupled) models are fundamentally related, in that their static properties (such as their SAT/UNSAT threshold) are the same. We then use tools from spin glass theory (cavity method) to demonstrate the so-called phenomenon of threshold saturation in these coupled models. Finally, we present the algorithmic implications and argue that all these features provide a new avenue for obtaining better, provable, algorithmic lower bounds on static thresholds of the individual standard CSP models. We consider simple decimation algorithms (e.g., the unit clause propagation algorithm) for the coupled CSP models and provide a machinery to analyze these algorithms. These analyses enable us to observe that the algorithmic thresholds on the coupled model are significantly improved over the standard model. For some models (e.g., 3-SAT, 3-COL), these coupled algorithmic thresholds surpass the best lower bounds on the SAT/UNSAT threshold in the literature and provide us with a new lower bound. We conclude by pointing out that although we only considered some specific graphical models, our results are of general nature hence applicable to a broad set of models. In particular, a main contribution of this thesis is to firmly establish both polarization, as well as spatial coupling, in the common toolbox of information theory/communication, statistical physics, and computer science