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Author: Stephen B. Wicker
Publisher: Springer Science & Business Media
ISBN: 0306477947
Category : Technology & Engineering
Languages : en
Pages : 241
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Book Description
Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
Author: Stephen B. Wicker
Publisher: Springer Science & Business Media
ISBN: 0306477947
Category : Technology & Engineering
Languages : en
Pages : 241
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Book Description
Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
Author: Alexander Reznik
Publisher:
ISBN:
Category :
Languages : en
Pages : 116
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Book Description
Author: Xiangyu Tang
Publisher:
ISBN:
Category :
Languages : en
Pages : 308
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Book Description
Author: John L. Fan
Publisher: Springer Science & Business Media
ISBN: 1461515254
Category : Technology & Engineering
Languages : en
Pages : 268
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Book Description
Constrained Coding and Soft Iterative Decoding is the first work to combine the issues of constrained coding and soft iterative decoding (e.g., turbo and LDPC codes) from a unified point of view. Since constrained coding is widely used in magnetic and optical storage, it is necessary to use some special techniques (modified concatenation scheme or bit insertion) in order to apply soft iterative decoding. Recent breakthroughs in the design and decoding of error-control codes (ECCs) show significant potential for improving the performance of many communications systems. ECCs such as turbo codes and low-density parity check (LDPC) codes can be represented by graphs and decoded by passing probabilistic (a.k.a. `soft') messages along the edges of the graph. This message-passing algorithm yields powerful decoders whose performance can approach the theoretical limits on capacity. This exposition uses `normal graphs,' introduced by Forney, which extend in a natural manner to block diagram representations of the system and provide a simple unified framework for the decoding of ECCs, constrained codes, and channels with memory. Soft iterative decoding is illustrated by the application of turbo codes and LDPC codes to magnetic recording channels. For magnetic and optical storage, an issue arises in the use of constrained coding, which places restrictions on the sequences that can be transmitted through the channel; the use of constrained coding in combination with soft ECC decoders is addressed by the modified concatenation scheme also known as `reverse concatenation.' Moreover, a soft constraint decoder yields additional coding gain from the redundancy in the constraint, which may be of practical interest in the case of optical storage. In addition, this monograph presents several other research results (including the design of sliding-block lossless compression codes, and the decoding of array codes as LDPC codes). Constrained Coding and Soft Iterative Decoding will prove useful to students, researchers and professional engineers who are interested in understanding this new soft iterative decoding paradigm and applying it in communications and storage systems.
Author: Sundararajan Sankaranarayanan
Publisher:
ISBN:
Category :
Languages : en
Pages : 312
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Book Description
The growing popularity of a class of linear block codes called the low-density parity-check (LDPC) codes can be attributed to the low complexity of the iterative decoders, and their potential to achieve performance very close to the Shannon capacity. This makes them an attractive candidate for ECC applications in communication systems. This report proposes methods to systematically construct regular and irregular LDPC codes. A class of regular LDPC codes are constructed from incidence structures in finite geometries like projective geometry and affine geometry. A class of irregular LDPC codes are constructed by systematically splitting blocks of balanced incomplete block designs to achieve desired weight distributions. These codes are decoded iteratively using message-passing algorithms, and the performance of these codes for various channels are presented in this report. The application of iterative decoders is generally limited to a class of codes whose graph representations are free of small cycles. Unfortunately, the large class of conventional algebraic codes, like RS codes, has several four cycles in their graph representations. This report proposes an algorithm that aims to alleviate this drawback by constructing an equivalent graph representation that is free of four cycles. It is theoretically shown that the four-cycle free representation is better suited to iterative erasure decoding than the conventional representation. Also, the new representation is exploited to realize, with limited success, iterative decoding of Reed-Solomon codes over the additive white Gaussian noise channel. Wiberg, Forney, Richardson, Koetter, and Vontobel have made significant contributions in developing theoretical frameworks that facilitate finite length analysis of codes. With an exception of Richardson's, most of the other frameworks are much suited for the analysis of short codes. In this report, we further the understanding of the failures in iterative decoders for the binary symmetric channel. The failures of the decoder are classified into two categories by defining trapping sets and propagating sets. Such a classification leads to a successful estimation of the performance of codes under the Gallager B decoder. Especially, the estimation techniques show great promise in the high signal-to-noise ratio regime where the simulation techniques are less feasible.
Author: Aamod Khandekar
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 210
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Author: Chris Heegard
Publisher: Springer Science & Business Media
ISBN: 1475729995
Category : Technology & Engineering
Languages : en
Pages : 226
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Book Description
When the 50th anniversary of the birth of Information Theory was celebrated at the 1998 IEEE International Symposium on Informa tion Theory in Boston, there was a great deal of reflection on the the year 1993 as a critical year. As the years pass and more perspec tive is gained, it is a fairly safe bet that we will view 1993 as the year when the "early years" of error control coding came to an end. This was the year in which Berrou, Glavieux and Thitimajshima pre sented "Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes" at the International Conference on Communications in Geneva. In their presentation, Berrou et al. claimed that a combi nation of parallel concatenation and iterative decoding can provide reliable communications at a signal to noise ratio that is within a few tenths of a dB of the Shannon limit. Nearly fifty years of striving to achieve the promise of Shannon's noisy channel coding theorem had come to an end. The implications of this result were immediately apparent to all -coding gains on the order of 10 dB could be used to dramatically extend the range of communication receivers, increase data rates and services, or substantially reduce transmitter power levels. The 1993 ICC paper set in motion several research efforts that have permanently changed the way we look at error control coding.
Author: Tom Richardson
Publisher: Cambridge University Press
ISBN: 1139469649
Category : Technology & Engineering
Languages : en
Pages : 589
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Book Description
Having trouble deciding which coding scheme to employ, how to design a new scheme, or how to improve an existing system? This summary of the state-of-the-art in iterative coding makes this decision more straightforward. With emphasis on the underlying theory, techniques to analyse and design practical iterative coding systems are presented. Using Gallager's original ensemble of LDPC codes, the basic concepts are extended for several general codes, including the practically important class of turbo codes. The simplicity of the binary erasure channel is exploited to develop analytical techniques and intuition, which are then applied to general channel models. A chapter on factor graphs helps to unify the important topics of information theory, coding and communication theory. Covering the most recent advances, this text is ideal for graduate students in electrical engineering and computer science, and practitioners. Additional resources, including instructor's solutions and figures, available online: www.cambridge.org/9780521852296.
Author: Junsheng Han
Publisher:
ISBN:
Category :
Languages : en
Pages : 155
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Book Description
Key to the success of modern error correcting codes is the effectiveness of message-passing iterative decoding (MPID). Unlike maximum-likelihood (ML) decoding, the performance of MPID depends not only on the code, but on how the code is represented. In particular, the performance of MPID is potentially improved by using a redundant representation. We focus on Tanner graphs and study combinatorial structures therein that help explain the performance disparity among different representations of the same code. Emphasis is placed on the complexity-performance tradeoff, as more and more check nodes are allowed in the graph. Our discussion applies to MPID as well as linear programming decoding (LPD), which we collectively refer to as graph-based decoding. On an erasure channel, it is well-known that the performance of MPID or LPD is determined by stopping sets. Following Schwartz and Vardy, we define the stopping redundancy as the smallest number of check nodes in a Tanner graph such that smallest size of a non-empty stopping set is equal to the minimum Hamming distance of the code. Roughly speaking, stopping redundancy measures the complexity requirement (in number of check nodes) for MPID of a redundant graph representation to achieve performance comparable to ML decoding (up to a constant factor for small channel erasure probability). General upper bounds on stopping redundancy are obtained. One of our main contribution is a new upper bound based on probabilistic analysis, which is shown to be by far the strongest. From this bound, it can be shown, for example, that for a fixed minimum distance, the stopping redundancy grows just linearly with the redundancy (codimension). Specific results on the stopping redundancy of Golay and Reed-Muller codes are also obtained. We show that the stopping redundancy of maximum distance separable (MDS) codes is bounded in between a Turan number and a single-exclusion (SE) number --- a purely combinatorial quantity that we introduce. By studying upper bounds on the SE number, new results on the stopping redundancy of MDS codes are obtained. Schwartz and Vardy conjecture that the stopping redundancy of an MDS code should only depend on its length and minimum distance. Our results provide partial confirmation, both exact and asymptotic, to this conjecture. Stopping redundancy can be large for some codes. We observe that significantly fewer checks are needed if a small number of small stopping sets are allowed. These small stopping sets can then be dealt with by ``guessing'' during the iterative decoding process. Correspondingly, the guess-g stopping redundancy is defined and it is shown that the savings in number of required check nodes are potentially significant. Another theoretically interesting question is when MPID of a Tanner graph achieves the same word error rate an ML decoder. This prompts us to define and study ML redundancy. Applicability and possible extensions of the current work to a non-erasure channel are discussed. A framework based on pseudo-codewords is considered and shown to be relevant. However, it is also observed that the polytope characterization of pseudo-codewords is not complete enough to be an accurate indicator of MPID performance. Finally, in a separate piece of work, the probability of undetected error (PUE) for over-extended Reed-Solomon codes is studied through the weight distribution bounds of the code. The resulting PUE expressions are shown to be tight in a well-defined sense.
Author: Aliazam Abbasfar
Publisher: Springer
ISBN: 9789048176236
Category : Technology & Engineering
Languages : en
Pages : 0
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Book Description
This book introduces turbo error correcting concept in a simple language, including a general theory and the algorithms for decoding turbo-like code. It presents a unified framework for the design and analysis of turbo codes and LDPC codes and their decoding algorithms. A major focus is on high speed turbo decoding, which targets applications with data rates of several hundred million bits per second (Mbps).
