Error Correction Code Aided Channel Estimation

This volumes discusses various aspects regarding the capacity/achievable data rate of stationary Rayleigh fading channels. First, it analyses bounds on the achievable data rate with zero-mean proper Gaussian input symbols, which are capacity achieving in the coherent case, i.e., in case of perfect channel knowledge at the receiver. These bounds are tight in the sense that the difference between the upper and the lower bound is bounded for all SNRs. The lower bound converges to the coherent capacity for asymptotically small channel dynamics. Furthermore, these bounds are extended to the case of multiple-input multiple-output (MIMO) channels and to the case of frequency selective channels. In a further part, the present work studies the achievable rate with receivers based on synchronized detection and a code-aided channel estimation. For a specific type of such a receiver an approximate upper bound on the achievable rate is derived. The comparison of this approximate upper bound and the achievable data rate with receivers using synchronized detection based on a solely pilot based channel estimation gives an approximate upper bound on the possible gain by using this kind of code-aided channel estimation in comparison to the conventional receiver using a solely pilot based channel estimation. In addition, the achievable data rate with an optimal joint processing of pilot and data symbols is studied and a lower bound on the achievable rate for this case is derived. In this context, it is also shown which part of the mutual information of the transmitter and the receiver is discarded when using the conventional receiver with synchronized detection based on a solely pilot based channel estimation.

Error-correction coding is being used on an almost routine basis in most new communication systems. Not only is coding equipment being used to increase the energy efficiency of communication links, but coding ideas are also providing innovative solutions to many related communication problems. Among these are the elimination of intersymbol interference caused by filtering and multipath and the improved demodulation of certain frequency modulated signals by taking advantage of the "natural" coding provided by a continuous phase. Although several books and nu merous articles have been written on coding theory, there are still noticeable deficiencies. First, the practical aspects of translating a specific decoding algorithm into actual hardware have been largely ignored. The information that is available is sketchy and is widely dispersed. Second, the information required to evaluate a particular technique under situations that are en countered in practice is available for the most part only in private company reports. This book is aimed at correcting both of these problems. It is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory. The book U"Ses a minimum of mathematics and entirely avoids the classical theorem/proof approach that is often seen in coding texts.

5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.

This book provides thorough coverage of error correcting techniques. It includes essential basic concepts and the latest advances on key topics in design, implementation, and optimization of hardware/software systems for error correction. The book’s chapters are written by internationally recognized experts in this field. Topics include evolution of error correction techniques, industrial user needs, architectures, and design approaches for the most advanced error correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This book provides access to recent results, and is suitable for graduate students and researchers of mathematics, computer science, and engineering. • Examines how to optimize the architecture of hardware design for error correcting codes; • Presents error correction codes from theory to optimized architecture for the current and the next generation standards; • Provides coverage of industrial user needs advanced error correcting techniques. Advanced Hardware Design for Error Correcting Codes includes a foreword by Claude Berrou.

Covering the fast evolving area of advanced coding, Error Control Coding for B3G/4G Wireless Systems targets IMT-Advanced systems to present the latest findings and implementation solutions. The book begins by detailing the fundamentals of advanced coding techniques such as Coding, Decoding, Design, and Optimization. It provides not only state-of-the-art research findings in 3D Turbo-codes, non-binary LDPC Codes, Fountain, and Raptor codes, but also insights into their real-world implementation by examining hardware architecture solutions, for example VLSI complexity, FPGA, and ASIC. Furthermore, special attention is paid to Incremental redundancy techniques, which constitute a key feature of Wireless Systems. A promising application of these advanced coding techniques, the Turbo-principle (also known as iterative processing), is illustrated through an in-depth discussion of Turbo-MIMO, Turbo-Equalization, and Turbo-Interleaving techniques. Finally, the book presents the status of major standardization activities currently implementing such techniques, with special interest in 3GPP UMTS, LTE, WiMAX, IEEE 802.11n, DVB-RCS, DVB-S2, and IEEE 802.22. As a result, the book coherently brings together academic and industry vision by providing readers with a uniquely comprehensive view of the whole topic, whilst also giving an understanding of leading-edge techniques. Includes detailed coverage of coding, decoding, design, and optimization approaches for advanced codes Provides up to date research findings from both highly reputed academics and industry standpoints Presents the latest status of standardization activities for Wireless Systems related to advanced coding Describes real-world implementation aspects by giving insights into architecture solutions for both LDPC and Turbo-codes Examines the most advanced and promising concepts of turbo-processing applications: Turbo-MIMO, Turbo-Equalization, Turbo-Interleaving

The increasing demand for high data rate transmission over broadband radio channels has imposed significant challenges in wireless communications. Accurate channel estimation has a major impact onthe whole system performance. Specifically, reliable estimate of the channel state information (CSI) is more challenging for orthogonal frequency division multiplexing (OFDM) systems in doubly selective fading channels than for the slower fading channels over which OFDM has been deployed traditionally. With the help of a basis expansion model (BEM), a novel multivariate autoregressive (AR) process is developed to model the time evolution of the fast fading channel. Relying on pilot symbol aided modulation (PSAM), a novel Kalman smoothing algorithm based on a second-order dynamic model is exploited, where the mean square error (MSE) of the channel estimator is near to that of the optimal Wiener filter. To further improve the performance of channel estimation, a novellow-complexity iterative joint channel estimation and symbol detection procedure is developed for fast fading channels with a small number of pilots and low pilot power to achieve the bit errorrate (BER) performance close to when the CSI is known perfectly. The new channel estimation symbol detection technique is robust to variations of the radio channel from the design values and applicable to multiple modulation and coding types. By use of the extrinsic information transfer (EXIT) chart, we investigate the convergence behavior of the new algorithm and analyze the modulation, pilot density, and error correction code selection for good system performance for a given power level. The algorithms developed in this thesis improve the performance of the whole system requiring only low ratios of pilot to data for excellent performance in fast fading channels.

Providing an all-encompassing self-contained treatment of Near-Capacity Multi-Functional MIMO Systems , the book starts by categorizing the family of Multiple-Input Multiple-Output (MIMO) schemes as diversity techniques, multiplexing schemes, multiple access arrangements and beam-forming techniques. Sophisticated coherent and low-complexity non-coherent MIMO receivers dispensing with channel estimation are considered in both classic and cooperation-aided scenarios. It is demonstrated that in the presence of correlated shadow-fading, cooperation-assisted systems may be expected to outperform their non-cooperative counterparts. The book contains a 100-page chapter on the unified treatment of all block codes in the context of high-flexibility, cutting-edge irregular Linear Dispersion Codes (LDC), which approach the MIMO-capacity. The majority of the book’s solutions are in the optimum sphere-packing frame-work. Sophisticated amalgam of five year’s near-capacity MIMO research Detailed examination of wireless landscape, including the fields of channel coding, spacetime coding and turbo detection techniques Novel tool of Extrinsic Information Transfer Charts (EXIT) used to address recent developments Material presented logically, allowing advanced readers to turn directly to any specific chapter of interest One of the only books to cover these subjects, giving equal weighting to each