Turbo codes and turbo algorithms

In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding

Exploiting diversity in wireless channels with bit-interleaved coded modulation and iterative decoding (BICM-ID)

This dissertation studies a state-of-the-art bandwidth-efficient coded modulation technique, known as bit interleaved coded modulation with iterative decoding (BICM-ID), together with various diversity techniques to dramatically improve the performance of digital communication systems over wireless channels. For BICM-ID over a single-antenna frequency non-selective fading channel, the problem of mapping over multiple symbols, i.e., multi-dimensional (multi-D) mapping, with 8-PSK constellation is investigated. An explicit algorithm to construct a good multi-D mapping of 8-PSK to improve the asymptotic performance of BICM-ID systems is introduced. By comparing the performance of the proposed mapping with an unachievable lower bound, it is conjectured that the proposed mapping is the global optimal mapping. The superiority of the proposed mapping over the best conventional (1-dimensional complex) mapping and the multi-D mapping found previously by computer search is thoroughly demonstrated. In addition to the mapping issue in single-antenna BICM-ID systems, the use of signal space diversity (SSD), also known as linear constellation precoding (LCP), is considered in BICM-ID over frequency non-selective fading channels. The performance analysis of BICM-ID and complex N-dimensional signal space diversity is carried out to study its performance limitation, the choice of the rotation matrix and the design of a low-complexity receiver. Based on the design criterion obtained from a tight error bound, the optimality of the rotation matrix is established. It is shown that using the class of optimal rotation matrices, the performance of BICM-ID systems over a frequency non-selective Rayleigh fading channel approaches that of the BICM-ID systems over an additive white Gaussian noise (AWGN) channel when the dimension of the signal constellation increases. Furthermore, by exploiting the sigma mapping for any M-ary quadrature amplitude modulation (QAM) constellation, a very simple sub-optimal, yet effective iterative receiver structure suitable for signal constellations with large dimensions is proposed. Simulation results in various cases and conditions indicate that the proposed receiver can achieve the analytical performance bounds with low complexity. The application of BICM-ID with SSD is then extended to the case of cascaded Rayleigh fading, which is more suitable to model mobile-to-mobile communication channels. By deriving the error bound on the asymptotic performance, it is first illustrated that for a small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the Rayleigh and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. In the next step, the use of SSD in BICM-ID over frequency selective Rayleigh fading channels employing a multi-carrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is studied. Under the assumption of correlated fading over subcarriers, a tight bound on the asymptotic error performance for the general case of applying SSD over all N subcarriers is derived and used to establish the best achievable asymptotic performance by SSD. It is then shown that precoding over subgroups of at least L subcarriers per group, where L is the number of channel taps, is sufficient to obtain this best asymptotic error performance, while significantly reducing the receiver complexity. The optimal joint subcarrier grouping and rotation matrix design is subsequently determined by solving the Vandermonde linear system. Illustrative examples show a good agreement between various analytical and simulation results. Further, by combining the ideas of multi-D mapping and subcarrier grouping, a novel power and bandwidth-efficient bit-interleaved coded modulation with OFDM and iterative decoding (BI-COFDM-ID) in which multi-D mapping is performed over a group of subcarriers for broadband transmission in a frequency selective fading environment is proposed. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multi-D mapping for BICM-ID in frequency non-selective Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with SSD. Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using SSD and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth and receiver complexity. Finally, the investigation is extended to the application of BICM-ID over a multiple-input multiple-output (MIMO) system equipped with multiple antennas at both the transmitter and the receiver to exploit both time and spatial diversities, where neither the transmitter nor the receiver knows the channel fading coefficients. The concentration is on the class of unitary constellation, due to its advantages in terms of both information-theoretic capacity and error probability. The tight error bound with respect to the asymptotic performance is also derived for any given unitary constellation and mapping rule. Design criteria regarding the choice of unitary constellation and mapping are then established. Furthermore, by using the unitary constellation obtained from orthogonal design with quadrature phase-shift keying (QPSK or 4-PSK) and 8-PSK, two different mapping rules are proposed. The first mapping rule gives the most suitable mapping for systems that do not implement iterative processing, which is similar to a Gray mapping in coherent channels. The second mapping rule yields the best mapping for systems with iterative decoding. Analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs, the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

Polar-Coded OFDM with Index Modulation

Polar codes, as the first error-correcting codes with an explicit construction to provably achieve thesymmetric capacity of memoryless channels, which are constructed based on channel polarization, have recently become a primary contender in communication networks for achieving tighter requirements with relatively low complexity. As one of the contributions in this thesis, three modified polar decoding schemes are proposed. These schemes include enhanced versions of successive cancellation-flip (SC-F), belief propagation (BP), and sphere decoding (SD). The proposed SC-F utilizes novel potential incorrect bits selection criteria and stack to improve its error correction performance. Next, to make the decoding performance of BP better, permutation and feedback structure are utilized. Then, in order to reduce the complexity without compromising performance, a SD by using novel decoding strategies according to modified path metric (PM) and radius extension is proposed. Additionally, to solve the problem that BP has redundant iterations, a new stopping criterion based on bit different ratio (BDR) is proposed. According to the simulation results and mathematical proof, all proposed schemes can achieve corresponding performance improvement or complexity reduction compared with existing works. Beside applying polar coding, to achieve a reliable and flexible transmission in a wireless communication system, a modified version of orthogonal frequency division multiplexing (OFDM) modulation based on index modulation, called OFDM-in-phase/quadrature-IM (OFDM-I/Q-IM), is applied. This modulation scheme can simultaneously improve spectral efficiency and bit-error rate (BER) performance with great flexibility in design and implementation. Hence, OFDM-I/Q-IM is considered as a potential candidate in the new generation of cellular networks. As the main contribution in this work, a polar-coded OFDM-I/Q-IM system is proposed. The general design guidelines for overcoming the difficulties associated with the application of polar codes in OFDM-I/Q-IM are presented. In the proposed system, at the transmitter, we employ a random frozen bits appending scheme which not only makes the polar code compatible with OFDM-I/Q-IM but also improves the BER performance of the system. Furthermore, at the receiver, it is shown that the \textit{a posteriori} information for each index provided by the index detector is essential for the iterative decoding of polar codes by the BP algorithm. Simulation results show that the proposed polar-coded OFDM-I/Q-IM system outperforms its OFDM counterpart in terms of BER performance

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder

Variable Rate Transmission Over Noisy Channels

Hybrid automatic repeat request transmission (hybrid ARQ) schemes aim to provide system reliability for transmissions over noisy channels while still maintaining a reasonably high throughput efficiency by combining retransmissions of automatic repeat requests with forward error correction (FEC) coding methods. In type-II hybrid ARQ schemes, the additional parity information required by channel codes to achieve forward error correction is provided only when errors have been detected. Hence, the available bits are partitioned into segments, some of which are sent to the receiver immediately, others are held back and only transmitted upon the detection of errors. This scheme raises two questions. Firstly, how should the available bits be ordered for optimal partitioning into consecutive segments? Secondly, how large should the individual segments be? This thesis aims to provide an answer to both of these questions for the transmission of convolutional and Turbo Codes over additive white Gaussian noise (AWGN), inter-symbol interference (ISI) and Rayleigh channels. Firstly, the ordering of bits is investigated by simulating the transmission of packets split into segments with a size of 1 bit and finding the critical number of bits, i.e. the number of bits where the output of the decoder is error-free. This approach provides a maximum, practical performance limit over a range of signal-to-noise levels. With these practical performance limits, the attention is turned to the size of the individual segments, since packets of 1 bit cause an intolerable overhead and delay. An adaptive, hybrid ARQ system is investigated, in which the transmitter uses the number of bits sent to the receiver and the receiver decoding results to adjust the size of the first, initial, packet and subsequent segments to the conditions of a stationary channel

Advanced OFDM systems for terrestrial multimedia links

Recently, there has been considerable discussion about new wireless technologies and standards able to achieve high data rates. Due to the recent advances of digital signal processing and Very Large Scale Integration (VLSI) technologies, the initial obstacles encountered for the implementation of Orthogonal Frequency Division Multiplexing (OFDM) modulation schemes, such as massive complex multiplications and high speed memory accesses, do not exist anymore. OFDM offers strong multipath protection due to the insertion of the guard interval; in particular, the OFDM-based DVB-T standard had proved to offer excellent performance for the broadcasting of multimedia streams with bitrates over ten megabits per second in difficult terrestrial propagation channels, for fixed and portable applications. Nevertheless, for mobile scenarios, improving the receiver design is not enough to achieve error-free transmission especially in presence of deep shadow and multipath fading and some modifications of the standard can be envisaged. To address long and medium range applications like live mobile wireless television production, some further modifications are required to adapt the modulated bandwidth and fully exploit channels up to 24MHz wide. For these reasons, an extended OFDM system is proposed that offers variable bandwidth, improved protection to shadow and multipath fading and enhanced robustness thanks to the insertion of deep time-interleaving coupled with a powerful turbo codes concatenated error correction scheme. The system parameters and the receiver architecture have been described in C++ and verified with extensive simulations. In particular, the study of the receiver algorithms was aimed to achieve the optimal tradeoff between performances and complexity. Moreover, the modulation/demodulation chain has been implemented in VHDL and a prototype system has been manufactured. Ongoing field trials are demonstrating the ability of the proposed system to successfully overcome the impairments due to mobile terrestrial channels, like multipath and shadow fading. For short range applications, Time-Division Multiplexing (TDM) is an efficient way to share the radio resource between multiple terminals. The main modulation parameters for a TDM system are discussed and it is shown that the 802.16a TDM OFDM physical layer fulfills the application requirements; some practical examples are given. A pre-distortion method is proposed that exploit the reciprocity of the radio channel to perform a partial channel inversion achieving improved performances with no modifications of existing receivers

Low complexity channel estimation for OFDM based satellite systems

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Reduced Complexity Sequential Monte Carlo Algorithms for Blind Receivers

Monte Carlo algorithms can be used to estimate the state of a system given relative observations. In this dissertation, these algorithms are applied to physical layer communications system models to estimate channel state information, to obtain soft information about transmitted symbols or multiple access interference, or to obtain estimates of all of these by joint estimation. Initially, we develop and analyze a multiple access technique utilizing mutually orthogonal complementary sets (MOCS) of sequences. These codes deliberately introduce inter-chip interference, which is naturally eliminated during processing at the receiver. However, channel impairments can destroy their orthogonality properties and additional processing becomes necessary. We utilize Monte Carlo algorithms to perform joint channel and symbol estimation for systems utilizing MOCS sequences as spreading codes. We apply Rao-Blackwellization to reduce the required number of particles. However, dense signaling constellations, multiuser environments, and the interchannel interference introduced by the spreading codes all increase the dimensionality of the symbol state space significantly. A full maximum likelihood solution is computationally expensive and generally not practical. However, obtaining the optimum solution is critical, and looking at only a part of the symbol space is generally not a good solution. We have sought algorithms that would guarantee that the correct transmitted symbol is considered, while only sampling a portion of the full symbol space. The performance of the proposed method is comparable to the Maximum Likelihood (ML) algorithm. While the computational complexity of ML increases exponentially with the dimensionality of the problem, the complexity of our approach increases only quadratically. Markovian structures such as the one imposed by MOCS spreading sequences can be seen in other physical layer structures as well. We have applied this partitioning approach with some modification to blind equalization of frequency selective fading channel and to multiple-input multiple output receivers that track channel changes. Additionally, we develop a method that obtains a metric for quantifying the convergence rate of Monte Carlo algorithms. Our approach yields an eigenvalue based method that is useful in identifying sources of slow convergence and estimation inaccuracy.Ph.D.Committee Chair: Douglas B. Williams; Committee Member: Brani Vidakovic; Committee Member: G. Tong zhou; Committee Member: Gordon Stuber; Committee Member: James H. McClella

Channel estimation for SISO and MIMO OFDM communications systems.

Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2010.Telecommunications in the current information age is increasingly relying on the wireless link. This is because wireless communication has made possible a variety of services ranging from voice to data and now to multimedia. Consequently, demand for new wireless capacity is growing rapidly at a very alarming rate. In a bid to cope with challenges of increasing demand for higher data rate, better quality of service, and higher network capacity, there is a migration from Single Input Single Output (SISO) antenna technology to a more promising Multiple Input Multiple Output (MIMO) antenna technology. On the other hand, Orthogonal Frequency Division Multiplexing (OFDM) technique has emerged as a very popular multi-carrier modulation technique to combat the problems associated with physical properties of the wireless channels such as multipath fading, dispersion, and interference. The combination of MIMO technology with OFDM techniques, known as MIMO-OFDM Systems, is considered as a promising solution to enhance the data rate of future broadband wireless communication Systems. This thesis addresses a major area of challenge to both SISO-OFDM and MIMO-OFDM Systems; estimation of accurate channel state information (CSI) in order to make possible coherent detection of the transmitted signal at the receiver end of the system. Hence, the first novel contribution of this thesis is the development of a low complexity adaptive algorithm that is robust against both slow and fast fading channel scenarios, in comparison with other algorithms employed in literature, to implement soft iterative channel estimator for turbo equalizer-based receiver for single antenna communication Systems. Subsequently, a Fast Data Projection Method (FDPM) subspace tracking algorithm is adapted to derive Channel Impulse Response Estimator for implementation of Decision Directed Channel Estimation (DDCE) for Single Input Single Output - Orthogonal Frequency Division Multiplexing (SISO-OFDM) Systems. This is implemented in the context of a more realistic Fractionally Spaced-Channel Impulse Response (FS-CIR) channel model, as against the channel characterized by a Sample Spaced-Channel Impulse Response (SS)-CIR widely assumed by other authors. In addition, a fast convergence Variable Step Size Normalized Least Mean Square (VSSNLMS)-based predictor, with low computational complexity in comparison with others in literatures, is derived for the implementation of the CIR predictor module of the DDCE scheme. A novel iterative receiver structure for the FDPM-based Decision Directed Channel Estimation scheme is also designed for SISO-OFDM Systems. The iterative idea is based on Turbo iterative principle. It is shown that improvement in the performance can be achieved with the iterative DDCE scheme for OFDM system in comparison with the non iterative scheme. Lastly, an iterative receiver structure for FDPM-based DDCE scheme earlier designed for SISO OFDM is extended to MIMO-OFDM Systems. In addition, Variable Step Size Normalized Least Mean Square (VSSNLMS)-based channel transfer function estimator is derived in the context of MIMO Channel for the implementation of the CTF estimator module of the iterative Decision Directed Channel Estimation scheme for MIMO-OFDM Systems in place of linear minimum mean square error (MMSE) criterion. The VSSNLMS-based channel transfer function estimator is found to show improved MSE performance of about -4 MSE (dB) at SNR of 5dB in comparison with linear MMSE-based channel transfer function estimator