Multiple Parallel Concatenated Gallager Codes and Their Applications

Due to the increasing demand of high data rate of modern wireless communications, there is a significant interest in error control coding. It now plays a significant role in digital communication systems in order to overcome the weaknesses in communication channels. This thesis presents a comprehensive investigation of a class of error control codes known as Multiple Parallel Concatenated Gallager Codes (MPCGCs) obtained by the parallel concatenation of well-designed LDPC codes. MPCGCs are constructed by breaking a long and high complexity of conventional single LDPC code into three or four smaller and lower complexity LDPC codes. This design of MPCGCs is simplified as the option of selecting the component codes completely at random based on a single parameter of Mean Column Weight (MCW). MPCGCs offer flexibility and scope for improving coding performance in theoretical and practical implementation. The performance of MPCGCs is explored by evaluating these codes for both AWGN and flat Rayleigh fading channels and investigating the puncturing of these codes by a proposed novel and efficient puncturing methods for improving the coding performance. Another investigating in the deployment of MPCGCs by enhancing the performance of WiMAX system. The bit error performances are compared and the results confirm that the proposed MPCGCs-WiMAX based IEEE 802.16 standard physical layer system provides better gain compared to the single conventional LDPC-WiMAX system. The incorporation of Quasi-Cyclic QC-LDPC codes in the MPCGC structure (called QC-MPCGC) is shown to improve the overall BER performance of MPCGCs with reduced overall decoding complexity and improved flexibility by using Layered belief propagation decoding instead of the sum-product algorithm (SPA). A proposed MIMO-MPCGC structure with both a 2X2 MIMO and 2X4 MIMO configurations is developed in this thesis and shown to improve the BER performance over fading channels over the conventional LDPC structure

New Algorithms for High-Throughput Decoding with Low-Density Parity-Check Codes using Fixed-Point SIMD Processors

Most digital signal processors contain one or more functional units with a single-instruction, multiple-data architecture that supports saturating fixed-point arithmetic with two or more options for the arithmetic precision. The processors designed for the highest performance contain many such functional units connected through an on-chip network. The selection of the arithmetic precision provides a trade-off between the task-level throughput and the quality of the output of many signal-processing algorithms, and utilization of the interconnection network during execution of the algorithm introduces a latency that can also limit the algorithm\u27s throughput. In this dissertation, we consider the turbo-decoding message-passing algorithm for iterative decoding of low-density parity-check codes and investigate its performance in parallel execution on a processor of interconnected functional units employing fast, low-precision fixed-point arithmetic. It is shown that the frequent occurrence of saturation when 8-bit signed arithmetic is used severely degrades the performance of the algorithm compared with decoding using higher-precision arithmetic. A technique of limiting the magnitude of certain intermediate variables of the algorithm, the extrinsic values, is proposed and shown to eliminate most occurrences of saturation, resulting in performance with 8-bit decoding nearly equal to that achieved with higher-precision decoding. We show that the interconnection latency can have a significant detrimental effect of the throughput of the turbo-decoding message-passing algorithm, which is illustrated for a type of high-performance digital signal processor known as a stream processor. Two alternatives to the standard schedule of message-passing and parity-check operations are proposed for the algorithm. Both alternatives markedly reduce the interconnection latency, and both result in substantially greater throughput than the standard schedule with no increase in the probability of error

Towards Quantum Belief Propagation for LDPC Decoding in Wireless Networks

We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, performing sensitivity analyses on a variety of parameter settings. Our design achieves a bit error rate of $10^{-8}$ in 20 $\mu$s and a 1,500 byte frame error rate of $10^{-6}$ in 50 $\mu$s at SNR 9 dB over a Gaussian noise wireless channel. Further experiments measure performance over real-world wireless channels, requiring 30 $\mu$s to achieve a 1,500 byte 99.99$\%$ frame delivery rate at SNR 15-20 dB. QBP achieves a performance improvement over an FPGA based soft belief propagation LDPC decoder, by reaching a bit error rate of $10^{-8}$ and a frame error rate of $10^{-6}$ at an SNR 2.5--3.5 dB lower. In terms of limitations, QBP currently cannot realize practical protocol-sized ($\textit{e.g.,}$ Wi-Fi, WiMax) LDPC codes on current QA processors. Our further studies in this work present future cost, throughput, and QA hardware trend considerations

LDPC-coded modulation for transmission over AWGN and flat rayleigh fading channels

La modulation codée est une technique de transmission efficace en largeur de bande qui intègre le codage de canal et la modulation en une seule entité et ce, afin d'améliorer les performances tout en conservant la même efficacité spectrale comparé à la modulation non codée. Les codes de parité à faible densité (low-density parity-check codes, LDPC) sont les codes correcteurs d'erreurs les plus puissants et approchent la limite de Shannon, tout en ayant une complexité de décodage relativement faible. L'idée de combiner les codes LDPC et la modulation efficace en largeur de bande a donc été considérée par de nombreux chercheurs. Dans ce mémoire, nous étudions une méthode de modulation codée à la fois puissante et efficace en largeur de bande, ayant d'excellentes performances de taux d'erreur binaire et une complexité d'implantation faible. Ceci est réalisé en utilisant un encodeur rapide, un décoder de faible complexité et aucun entrelaceur. Les performances du système proposé pour des transmissions sur un canal additif gaussien blanc et un canal à évanouissements plats de Rayleigh sont évaluées au moyen de simulations. Les résultats numériques montrent que la méthode de modulation codée utilisant la modulation d'amplitude en quadrature à M niveaux (M-QAM) peut atteindre d'excellentes performances pour toute une gamme d'efficacité spectrale. Une autre contribution de ce mémoire est une méthode simple pour réaliser une modulation codée adaptative avec les codes LDPC pour la transmission sur des canaux à évanouissements plats et lents de Rayleigh. Dans cette méthode, six combinaisons de paires encodeur modulateur sont employées pour une adaptation trame par trame. L'efficacité spectrale moyenne varie entre 0.5 et 5 bits/s/Hz lors de la transmission. Les résultats de simulation montrent que la modulation codée adaptative avec les codes LDPC offre une meilleure efficacité spectrale tout en maintenant une performance d'erreur acceptable

Waveforms and channel coding for 5G

Abstract. The fifth generation (5G) communication systems are required to perform significantly better than the existing fourth generation (4G) systems in data rate, capacity, coverage, latency, energy consumption and cost. Hence, 5G needs to achieve considerable enhancements in the areas of bandwidth, spectral, energy, and signaling efficiencies and cost per bit. The new radio access technology (RAT) of 5G physical layer needs to utilize an efficient waveform to meet the demands of 5G. Orthogonal frequency division multiplexing (OFDM) is considered as a baseline for up to 30 GHz. However, a major drawback of OFDM systems is their large peak to average power ratio (PAPR). Here in this thesis, a simple selective-mapping (SLM) technique using scrambling is proposed to reduce the PAPR of OFDM signals. This technique selects symbol sequences with high PAPR and scrambles them until a PAPR sequence below a specific threshold is generated. The computational complexity of the proposed scheme is considerably lower than that of the traditional SLM. Also, performance of the system is investigated through simulations and more than 4.5 dB PAPR reduction is achieved. In addition, performance of single carrier waveforms is analyzed in multiple-input multiple-output (MIMO) systems as an alternative to OFDM. Performance of a single carrier massive MIMO system is presented for both uplink and downlink with single user and multiple user cases and the effect of pre-coding on the PAPR is studied. A variety of channel configurations were investigated such as correlated channels, practical channels and the channels with errors in channel estimate. Furthermore, the candidate coding schemes are investigated for the new RAT in the 5G standard corresponding the activities in the third generation partnership project (3GPP). The schemes are evaluated in terms of block error rate (BLER), bit error rate (BER), computational complexity, and flexibility. These parameters comprise a suitable set to assess the performance of different services and applications. Turbo, low density parity check (LDPC), and polar codes are considered as the candidate schemes. These are investigated in terms of obtaining suitable rates, block lengths by proper design for a fair comparison. The simulations have been carried out in order to obtain BLER / BER performance for various code rates and block lengths, in additive white Gaussian noise (AWGN) channel. Although polar codes perform well at short block lengths, LDPC has a relatively good performance at all the block lengths and code rates. In addition, complexity of the LDPC codes is relatively low. Furthermore, BLER/BER performances of the coding schemes in Rayleigh fading channels are investigated and found that the fading channel performance follows a similar trend as the performance in the AWGN channel

Evaluation of flexible SPA based LPDC decoder using hardware friendly approximation methods

Due to computation-intensive nature of LDPC decoders, a lot of research is going towards efficient implementation of their original algorithm (SPA). As "Min-Sum" approximation is basically an overestimation of SPA, this thesis investigates more accurate, yet area efficient, approximations of SPA, to select an optimum one. In a general comparison between main approximation methods (e.g. LUT, PWL, CRI), PWL showed the most area-efficiency. Studying different mathematical formats of SPA, Soft-XOR based format with forward-backward scheme was chosen for hard- ware implementation. Its core function (Soft-XOR) was implemented with CRI approximation, which achieved the highest efficiency, compare to other approxi- mations. Using this core function, a flexible, pipe-lined, Soft-XOR based CNU (the computational unit of LDPC decoders) with forward-backward architecture was developed in 18nm CMOS. The implemented CNU’s area and speed can eas- ily be changed in instantiation. A SPA decoder based on the developed CNU was estimated to have an area of 1.6M as equivalent gate count and a throughput of 10Gb/s, with a frequency of 1.25GHz and for 10 iterations. The decoder uses IEEE 802.11n Wi-Fi standard with flooding schedule. The BER/SNR loss, com- pare to floating-point SPA, is 0.3dB for 10 iterations and less than 0.1dB for 20 iterations.You have to get lost before you can be found, a quote by Jeff Rasley goes very well for Low Density Parity Check (LDPC) codes. First invented by Gallager in 1962 but kind of lost during the journey of evolution of telecommunication networks because of their high complexity and demanding computations, which technology was not so advanced to handle, at that time. However, during late 1990s, success of turbo codes invoked the re-discovery of Low Density Parity Check (LDPC) codes. Recently it has attracted tremendous research interest among the scientific com- munity, as today’s technology is advanced enough and to make LDPC decoders completely commercial. In a wireless network, the information is not just sim- ply sent, but first encoded. In a sense, all the transmitted bits are tied together, according to some mathematical rules. Therefore, if noise destructs parts of the information while traveling, the LDPC decoder at the receiver side, can automat- ically detect and retrieve those parts, based on the other parts. Here, our main focus is on the decoder. For actual hardware implementation of the decoder, some level of approximation of the ideal algorithm is always necessary, which reduces the accuracy depending on the approximation. Ericsson is developing the next-generation wireless network for 5G, and already possesses the "Min-Sum" approximation of the LDPC decoder. As the current requirements demand more accurate decoders, the goal of this thesis is to evalu- ate a more accurate but more costly version of the LDPC decoder, as well as its flexibility. Thus, several candidates were selected and evaluated based on their complexity, cost, and their accuracy towards error correction. After performing several trade-offs, an approximation method is chosen and the corresponding cost is derived. With this acquired data, a trade-off between accuracy and cost can be made, depending on the application

Non-binary LDPC coded STF-MIMO-OFDM with an iterative joint receiver structure

The aim of the dissertation was to design a realistic, low-complexity non-binary (NB) low density parity check (LDPC) coded space-time-frequency (STF) coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with an iterative joint decoder and detector structure at the receiver. The goal of the first part of the dissertation was to compare the performance of different design procedures for NB-LDPC codes on an additive white Gaussian noise (AWGN) channel, taking into account the constraint on the code length. The effect of quantisation on the performance of the code was also analysed. Different methods for choosing the NB elements in the parity check matrix were compared. For the STF coding, a class of universal STF codes was used. These codes use linear pre-coding and a layering approach based on Diophantine numbers to achieve full diversity and a transmission rate (in symbols per channel use per frequency) equal to the number of transmitter antennas. The study of the system considers a comparative performance analysis of di erent ST, SF and STF codes. The simulations of the system were performed on a triply selective block fading channel. Thus, there was selectivity in the fading over time, space and frequency. The effect of quantisation at the receiver on the achievable diversity of linearly pre-coded systems (such as the STF codes used) was mathematically derived and verified with simulations. A sphere decoder (SD) was used as a MIMO detector. The standard method used to create a soft-input soft output (SISO) SD uses a hard-to-soft process and the max-log-map approximation. A new approach was developed which combines a Hopfield network with the SD. This SD-Hopfield detector was connected with the fast Fourier transform belief propagation (FFT-BP) algorithm in an iterative structure. This iterative system was able to achieve the same bit error rate (BER) performance as the original SISO-SD at a reduced complexity. The use of the iterative Hopfield-SD and FFT-BP decoder system also allows performance to be traded off for complexity by varying the number of decoding iterations. The complete system employs a NB-LDPC code concatenated with an STF code at the transmitter with a SISO-SD and FFT-BP decoder connected in an iterative structure at the receiver. The system was analysed in varying channel conditions taking into account the effect of correlation and quantisation. The performance of different SF and STF codes were compared and analysed in the system. An analysis comparing different numbers of FFT-BP and outer iterations was also done. AFRIKAANS : Die doel van die verhandeling was om ’n realistiese, lae-kompleksiteit nie-binˆere (NB) LDPC gekodeerde ruimte-tyd-frekwensie-gekodeerde MIMO-OFDM-sisteem met iteratiewe gesamentlike dekodeerder- en detektorstrukture by die ontvanger te ontwerp. Die eerstem deel van die verhandeling was om die werkverrigting van verskillende ontwerpprosedures vir NB-LDPC kodes op ’n gesommeerde wit Gausruiskanaal te vergelyk met inagneming van die beperking op die lengte van die kode. Verskillende metodes om die nie-bineêre elemente in die pariteitstoetsmatriks te kies, is gebruik. Vir die ruimte-tyd-frekwensiekodering is ’n klas universele ruimte-tyd-frekwensiekodes gebruik. Hierdie kodes gebruik lineêre pre-kodering en ’n laagbenadering gebaseer op Diofantiese syfers om volle diversiteit te bereik en ’n oordragtempo (in simbole per kanaalgebruik per frekwensie) gelyk aan die aantal senderantennes. Die studie van die sisteem oorweeg ’n vergelykende werkverrigtinganalisie van verskillende ruimte-tyd-, ruimte-freksensie- en ruimte-tyd-frekwensiekodes. Die simulasies van die sisteem is gedoen op ’n drievoudig selektiewe blokwegsterwingskanaal. Daar was dus selektiwiteit in die wegsterwing oor tyd, ruimte en frekwensie. Die effek van kwantisering by die ontvanger op die bereikbare diversiteit van lineêr pre-gekodeerde sisteme (soos die ruimte-tyd-frekwensiekodes wat gebruik is) is matematies afgelei en bevestig deur simulasies. ’n Sfeerdekodeerder (SD) is gebruik as ’n MIMO-detektor. Die standaardmetode wat gebuik is om ’n sagte-inset-sagte-uitset (SISO) SD te skep, gebruik ’n harde-na-sagte proses en die maksimum logaritmiese afbeelding-benadering. ’n Nuwe benadering wat ’n Hopfield-netwerk met die SD kombineer, is ontwikkel. Hierdie SD-Hopfield-detektor is verbind met die FFT-BP-algoritme in iteratiewe strukture. Hierdie iteratiewe sisteem was in staat om dieselfde bisfouttempo te bereik as die oorspronklike SISO-SD, met laer kompleksiteit. Die gebruik van die iteratiewe Hopfield-SD en FFT-BP-dekodeerdersisteem maak ook daarvoor voorsiening dat werkverrigting opgeweeg kan word teen kompleksiteit deur die aantal dekodering-iterasies te varieer. Die volledige sisteem maak gebruik van ’n QC-NB-LDPC-kode wat met ’n ruimte-tyd-frekwensiekode by die sender aaneengeskakel is met ’n SISO-SD en FFT-BP-dekodeerder wat in ’n iteratiewe struktuur by die ontvanger gekoppel is. Die sisteem is onder ’n verskeidenheid kanaalkondisies ge-analiseer met inagneming van die effek van korrelasie en kwantisering. Die werkverrigting van verskillende ruimte-frekwensie- en ruimte-tyd-frekwensiekodes is vergelyk en in die sisteem ge-analiseer. ’n Analise om ’n wisselende aantal FFT-BP en buite-iterasies te vergelyk, is ook gedoen. CopyrightDissertation (MEng)--University of Pretoria, 2010.Electrical, Electronic and Computer Engineeringunrestricte

A Study on High Performance Gbps MIMO Wireless System

九州工業大学博士学位論文 学位記番号:情工博甲第294号　学位授与年月日:平成26年12月25日1 Introduction||2 Wireless System Overview||3 RC4 Encryption Architectures||4 MIMO Detection Algorithm and Architecture||5 LDPC Decoder Architecture||6 Conclusion and Future Wor

ERROR CORRECTION CODE-BASED EMBEDDING IN ADAPTIVE RATE WIRELESS COMMUNICATION SYSTEMS

In this dissertation, we investigated the methods for development of embedded channels within error correction mechanisms utilized to support adaptive rate communication systems. We developed an error correction code-based embedding scheme suitable for application in modern wireless data communication standards. We specifically implemented the scheme for both low-density parity check block codes and binary convolutional codes. While error correction code-based information hiding has been previously presented in literature, we sought to take advantage of the fact that these wireless systems have the ability to change their modulation and coding rates in response to changing channel conditions. We utilized this functionality to incorporate knowledge of the channel state into the scheme, which led to an increase in embedding capacity. We conducted extensive simulations to establish the performance of our embedding methodologies. Results from these simulations enabled the development of models to characterize the behavior of the embedded channels and identify sources of distortion in the underlying communication system. Finally, we developed expressions to define limitations on the capacity of these channels subject to a variety of constraints, including the selected modulation type and coding rate of the communication system, the current channel state, and the specific embedding implementation.Commander, United States NavyApproved for public release; distribution is unlimited