Cyclic division algebras: a tool for space-time coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes

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

High rate space time code with linear decoding complexity for multiple transmitting antennas

The multipath nature of the wireless channel, results in a superposition of the signals of each path at the receiver. This can lead to either constructive or destructive interference. Strong destructive interference is frequently referred to as deep fade and may result in temporary failure of communication due to the severe drop in the channel\u27s signal-to-noise ratio (SNR). To avoid this situation, signal diversity might be introduced. When having more than one antenna at the transmitter and / or receiver, forming a Multiple-Input Multiple-Output (MIMO) channel, spatial diversity can be employed to overcome the fading problem. Space time block codes (STBC) have been shown to be used well with the MIMO channel. Each type of STBC is designed to optimize a different criteria such as rate and diversity, while other characteristics of the code are its error performance and decoding computational complexity. The Orthogonal STBC (OSTBC) family of codes is known to achieve full diversity as well as very simple implementation of the Maximum Likelihood (ML) decoder. However, it was proven that, with complex symbol constellation one cannot achieve a full rate code when the number of transmitting antennas is larger than two. Quasi OSTBC are codes with full rate but with the penalty of more complex decoding, and in general does not achieve full diversity. In this work, new techniques for OSTBC transmission / decoding are explored, such that a full rate code can be transmitted and decoded with linear complexity. The Row Elimination Method (REM) for OSTBC transmission is introduced, which basically involves the transmission of only part of the original OSTBC codeword, resulting in a full rate code termed Semi-Orthogonal STBC (SSTBC). Novel decoding scheme is presented, such that the SSTBC decoding computational complexity remains linear although the transmitted codeword is not orthogonal anymore. A new OSTBC, that complies with the new scheme\u27s requirements, is presented for any number of transmit antennas. The performance of the new scheme is studied under various settings, such as system with limited feedback and multiple antennas at the receiver. The general decoding techniques presented for STBC, assume perfect channel knowledge at the receiver. It was shown, that the performance of any STBC system is severely degraded due to partial channel state information, results from imperfect channel estimation. To minimize the performance loss, one may lengthen the training sequences used for the channel estimation which, inevitably, results in some rate loss. In addition, complex decoding schemes can be used at the receiver to jointly decode the data while enhancing the channel estimation. It is suggested in this work to apply adaptive techniques to mitigate the performance loss without the penalty of additional rate loss or complex decoding. Namely, the bootstrap algorithm is used to further refine the received signals, resulting in better effective rate and performance in the presence of channel estimation errors. Modified implementations for the bootstrap\u27s weights calculation method are also presented, to improve the convergence rate of the algorithm, as well as to maintain a very low computational burden

OFCDM systems over fading channels

Along with the fast growing demand of information exchange, telecommunication systems are required to provide fast and reliable service to high-data-rate applications such as video conference, real-time broadcasting, and on-line gaming. In downlink transmission, orthogonal frequency and code division multiplexing (OFCDM) has been an attractive technique for high-data-rate applications. With two-dimensional spreading, in both time domain and frequency domain, OFCDM achieves diversity gains in multiuser scenarios. Moreover, the adjustable spreading factors (SF) give OFCDM systems the flexibility in transmission rate and diversity gain. In this thesis, we focus on the downlink of OFCDM communication systems. The performance of OFCDM systems is investigated over Ricean fading channels with Rayleigh fading as special case. Code division multiple access (CDMA) technique is used to support multiuser communications, where users can transmit at the same time using the same frequency with the help of code sequences. We compare different combining methods that are employed to achieve diversity gain. Moreover, channel correlation is examined to see its effect on the system performance. We also propose to combine multiple-input and multiple-output (MIMO) techniques, specifically space-time block coding (STBC), with OFCDM systems. By adding spatial diversity, a MIMO system can provide more reliable transmission compared to a single-input and single-output (SISO) system. The space-time scheme used in our study is Alamouti scheme [1], which employs N = 2 and M antennas at the transmitter side and receiver side respectively. In the thesis, we explain the system structure, transmission and detection methods, and system performance of such MIMO-OFCDM systems. In our study, the expressions of system bit error rate (BER) are considered under the condition that no multi-code interference (MCI) is present. The accuracy of the BER expressions is verified when compared with the simulated ones for both SISO and MIMO-OFCDM systems with different combining methods. These comparisons are carried over different channels and with different system parameters to explore the benefits of OFCDM based systems. Both analytical and simulation results show the large diversity gains achieved when incorporating STBC with OFCDM

Repeat-punctured turbo coded cooperation.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, 2008.Transmit diversity usually employs multiple antennas at the transmitter. However, many wireless devices such as mobile cellphones, Personal Digital Assistants (PDAs), just to name a few, are limited by size, hardware complexity, power and other constraints to just one antenna. A new paradigm called cooperative communication which allows single antenna mobiles in a multi-user scenario to share their antennas has been proposed lately. This multi-user configuration generates a virtual Multiple-Input Multiple-Output system, leading to transmit diversity. The basic approach to cooperation is for two single-antenna users to use each other's antenna as a relay in which each of the users achieves diversity. Previous cooperative signaling methods encompass diverse forms of repetition of the data transmitted by the partner to the destination. A new scheme called coded cooperation [15] which integrates user cooperation with channel coding has also been proposed. This method maintains the same code rate, bandwidth and transmit power as a similar non-cooperative system, but performs much better than previous signaling methods [13], [14] under various inter-user channel qualities. This dissertation first discusses the coded cooperation framework that has been proposed lately [19], coded cooperation with Repeat Convolutional Punctured Codes (RCPC) codes and then investigates the application of turbo codes in coded cooperation. In this dissertation we propose two new cooperative diversity schemes which are the Repeat-Punctured Turbo Coded cooperation and coded cooperation using a Modified Repeat-Punctured Turbo Codes. Prior to that, Repeat-Punctured Turbo codes are introduced. We characterize the performance of the two new schemes by developing the analytical bounds for bit error rate, which is confirmed by computer simulations. Finally, the turbo coded cooperation using the Forced Symbol Method (FSM) is presented and validated through computer simulations under various inter-user Signal-to-Noise Ratios (SNRs)

Distributed convolutional-based coding for cooperative systems

Whenever size, power, or other constraints preclude the use of multiple-input multiple-output (MIMO) systems, wireless systems cannot benefit from the well-known advantages of space-time coding (STC) methods. Also the complexity (multiple radio-frequency (RF) front ends at both the transmitter and the receiver), channel estimation, and spatial correlation in centralized MIMO systems degrade the performance. In situations like these, the alternative would be to resort to cooperative communications via multiple relay nodes. When these nodes work cooperatively, they form a virtual MIMO system. The destination receives multiple versions of the same message from the source and one or more relays, and combines these to create diversity. There are two main cooperative diversity techniques for transmission between a pair of nodes through a multiple relay nodes: decode-and-forward (DF) and amplify-and-forward (AF) modes. In the DF mode, the signal received from the source node is demodulated and decoded before retransmission. In the AF mode, the relay node simply amplifies and retransmits the signal received from the source node. No demodulation or decoding of the received signal is performed in this case. In encoded cooperative communication networks, the diversity of the system degrades significantly. This diversity degradation is attributed to the errors made at the relay nodes. Consequently, if better reliability is achieved at the relay nodes, the diversity may improve. or even may be preserved. as compared to the error-free case. In light of this, the objective of this thesis is to devise coding schemes suitable for relay channels that aim at improving the end-to-end performance of such systems. In this thesis, we present a coding scheme suitable for cooperative networks where the source and relays share their antennas to create a virtual transmit array to transmit towards their destination. We focus on the problem of coding for the relay channels. While the relays may use several forwarding strategies, including AF and DF, we focus on coded DF relaying. We derive upper bounded expressions for the bit error rate (BER) assuming M -ary phase shift keying ( M -PSK) transmission and show that the proposed scheme achieves large coding gains and frill diversity relative to the coded non-cooperative case for a wide range of signal-to-noise ratio (SNR) of interest. To improve the detection reliability further, we consider antenna/relay selection on the performance of cooperative networks in conjunction with the distributed coding scheme proposed. For simplicity, we assume that there is one relay that is equipped with n R antennas and only the best antenna is selected. For this scenario, assuming DF and AF relaying, we derive upper bounds on the BER for M -PSK transmission. Our analytical results show that the proposed scheme achieves full diversity for the entire range of BER of interest, unlike the case without antenna selection. In the last part of the thesis, we consider the same system considered in the ideal case but now with system imperfections. In particular, we consider the case when the channel state information is estimated at all nodes involved in the transmission process. We derive upper bounds on the performance with imperfect channel estimation. Our results show that there is a performance degradation due to the presence of channel estimation error. However, the observations made in the case of ideal channel state information still hold for the non-ideal case