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Author: Sudarsan Vasista Srinivasan Ranganathan
Publisher:
ISBN:
Category :
Languages : en
Pages : 168
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This dissertation consists of three parts. The first part focuses on a class of modern channel codes known as protograph-based low-density parity-check (LDPC) codes. Also known as protograph LDPC codes, these powerful error-correcting codes have enabled communication systems of the past fifteen years to achieve very high throughputs. The first part of the dissertation presents a new design method based on an upper bound on minimum distance to obtain rate-compatible, protograph quasi-cyclic (QC) LDPC codes called Protograph-based Raptor-like LDPC codes (PBRL codes). A major contribution here is a very-low-complexity PBRL design algorithm that is provably efficient. The second part of the dissertation continues the focus on protograph LDPC codes, first exploring how the decoding complexity of PBRL codes can be reduced and whether the extending structure that provides rate-compatibility to a PBRL code is optimal or not. Then, this part considers the problem of design of PBRL codes for any increment ordering. The degree-1 extending structure yields naturally to the design of PBRL codes that decode efficiently even when increments arrive out-of-order. This part finally considers the following question: What is the shortest block-length required to obtain a protograph QC-LDPC code with a girth of at least 6 or 8 from a (3, L) complete protograph? An affirmative answer is given for girth of at least 6 and directions are explored for girth of at least 8. Finally, the dissertation turns to communication theory and tackles a rate allocation problem previously studied in literature, but with an important twist. Consider a cross-layer coding scheme with packet-level erasure coding and physical-layer channel coding. It is known from previous work that some erasure coding is necessary even in the limit of large physical-layer codeword block-lengths if the physical-layer fading channel does not provide diversity that grows with block-length. However, is erasure coding still required in the limit of large block-lengths if the physical layer allows for diversity to grow with block-length? The theoretical answer turns out to be a resounding "no" in the case of Rayleigh fading that allows diversity to increase linearly with block-length.
Author: Sudarsan Vasista Srinivasan Ranganathan
Publisher:
ISBN:
Category :
Languages : en
Pages : 168
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Book Description
This dissertation consists of three parts. The first part focuses on a class of modern channel codes known as protograph-based low-density parity-check (LDPC) codes. Also known as protograph LDPC codes, these powerful error-correcting codes have enabled communication systems of the past fifteen years to achieve very high throughputs. The first part of the dissertation presents a new design method based on an upper bound on minimum distance to obtain rate-compatible, protograph quasi-cyclic (QC) LDPC codes called Protograph-based Raptor-like LDPC codes (PBRL codes). A major contribution here is a very-low-complexity PBRL design algorithm that is provably efficient. The second part of the dissertation continues the focus on protograph LDPC codes, first exploring how the decoding complexity of PBRL codes can be reduced and whether the extending structure that provides rate-compatibility to a PBRL code is optimal or not. Then, this part considers the problem of design of PBRL codes for any increment ordering. The degree-1 extending structure yields naturally to the design of PBRL codes that decode efficiently even when increments arrive out-of-order. This part finally considers the following question: What is the shortest block-length required to obtain a protograph QC-LDPC code with a girth of at least 6 or 8 from a (3, L) complete protograph? An affirmative answer is given for girth of at least 6 and directions are explored for girth of at least 8. Finally, the dissertation turns to communication theory and tackles a rate allocation problem previously studied in literature, but with an important twist. Consider a cross-layer coding scheme with packet-level erasure coding and physical-layer channel coding. It is known from previous work that some erasure coding is necessary even in the limit of large physical-layer codeword block-lengths if the physical-layer fading channel does not provide diversity that grows with block-length. However, is erasure coding still required in the limit of large block-lengths if the physical layer allows for diversity to grow with block-length? The theoretical answer turns out to be a resounding "no" in the case of Rayleigh fading that allows diversity to increase linearly with block-length.
Author:
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Category : French language
Languages : en
Pages :
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Author: Yizeng Sun
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Non-binary LDPC codes can outperform binary LDPC codes using sum-product algorithm with higher computation complexity. Non-binary LDPC codes based on protographs have the advantage of simple hardware architecture. In the first part of this thesis, we will use EXIT chart analysis to compute the thresholds of different protographs over GF(q). Based on threshold computation, some non-binary protograph-based LDPC codes are designed and their frame error rates are compared with binary LDPC codes. For maximum-likelihood decoder, weight enumerator can predict frame error rate of an LDPC code. In the second part of this thesis, we calculate weight enumerators of protograph-based non-binary LDPC code ensembles both for finite length case and asymptotic case. In addition, the trapping set and stopping set enumerators are presented.
Author: Thuy Van Nguyen
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 198
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In this dissertation, a systematic framework is proposed to design practical protograph-based low-density parity check (LDPC) coding schemes that address simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. This dissertation consists of four closely inter-related parts. In the first part, the design of rate-compatible protograph codes for the hybrid automatic repeat request protocol is presented. A high-performance family of protograph codes that has the iterative decoding threshold within a gap of a fraction of dB to capacity in the AWGN channel over a wide range of rates is reported. In the second part, protograph-based LDPC coding schemes are designed for half-duplex relay channels. A simple new methodology for evaluating the end-to-end error performance of relay coding systems is then developed and used to highlight the performance of the proposed codes. In the third part, a general mapping method is devised for using protograph-based LDPC codes in bit-interleaved coded modulation. The reported coding scheme operates close to the coded modulation capacity. In the fourth part, the design of rate-compatible protograph codes in inter-symbol interference channels is proposed. The design problem is non-trivial due to the joint design of structured LDPC codes and the state structure of ISI channels using the BCJR equalizer. High-performance protograph-based LDPC codes that have iterative thresholds close to i.u.d capacity of ISI channels are reported.
Author: Brian K. Butler
Publisher:
ISBN: 9781303193347
Category :
Languages : en
Pages : 159
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Since their rediscovery in the late 1990s, low-density parity-check (LDPC) codes have rapidly become one the most important classes of error correcting codes. LDPC codes have a graphical description and are generally decoded iteratively. The graph of an iteratively decoded code's error rate performance versus the channel quality is typically divided into two regions. The error floor region appears at higher channel quality and is characterized by a more gradual decrease in error rate as channel quality improves. For iterative decoders the error floor is apparently determined by small structures within the code that are specific to the selected graphical description of the code and subtle details of the decoding algorithm. This thesis addresses several issues of LDPC error floors in the additive white Gaussian noise channel. First, we find the source of several well publicized error floors to be numerical issues within the message-passing decoder. We propose numerical improvements to several decoding formulations which substantially lower error floors. Next, we examine and refine error-floor prediction models. A time-variant linear state-space model is presented and analyzed. Graph theory is applied to analyze the small error-prone structures within the code. While we find our techniques encounter considerable problems in determining the error floors for iterative decoders with unrestricted dynamic range, their predictions are quite accurate when significant range restrictions are present. The final issue of LDPC error floors which we address relates to the minimum distance of quasi-cyclic (QC) LDPC codes. We derive improved minimum distance upper bounds for codes which are punctured and codes which contain a significant number of zeros in their protomatrices. These bound are then applied to a family of protograph-based LDPC codes standardized for use in deep-space communications. In the case of the rate-1/2 code, our upper bounds demonstrate that the previously promulgated ensemble lower bounds do not apply to QC constructions at block lengths beyond 4400 bits. The last part of this dissertation is a fairly separate piece of work on bounding the spectral radius of a large class of nonnegative matrices. We apply these bounds to digraphs and derive several associated equality conditions.
Author: Jeremy Thorpe
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 166
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Author: Matthew L. Grimes
Publisher:
ISBN:
Category :
Languages : en
Pages : 122
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In this thesis, we propose a method to design nested protograph-based low-density parity-check (LDPC) codes for network communications with low error-floors via a graph modification procedure. Lowering the error-floor of nested LDPC codes is essential for certain applications that require very low decoded error rates in moderate to high signal-to-noise-ratios (SNRs) like optical communication and data storage. The multi-level method we propose improves upon existing state-of-the-art algebraic designs by the identification and removal of harmful graph structures from nested LDPC codes based on protographs, effectively improving the performance of each of the nested codes in their error-floor region. Simulation results are provided to confirm the expected performance improvement.
Author: Juane Li
Publisher:
ISBN: 9781369201024
Category :
Languages : en
Pages :
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Due to their capacity-approaching performance which can be achieved with practically implementable iterative decoding algorithms devised based on belief-propagation, low-density parity-check (LDPC) codes have rapid dominance in the applications requiring error control coding. This dissertation is intended to address certain important aspects of the aforementioned issues about LDPC codes. Subjects to be investigated include: (1) flexible and systematic methods for constructing binary LDPC codes with quasi-cyclic structure based on finite fields; (2) construction of high-rate and low-rate quasi-cyclic (QC) LDPC codes to achieve very low error rates without error-floor and with high rate of decoding convergence; (3) construction of binary QC-LDPC codes whose Tanner graphs have girth 8 or larger and contain minimum number of short cycles; (4) developing effective algorithms for enumerating short cycles in the Tanner graph of LDPC codes; (5) devising reduced-complexity decoding schemes and algorithms for binary QC-LDPC codes; (6) effective matrix-theoretic methods for constructing nonbinary (NB) LDPC codes; and (7) reduced-complexity decoding schemes and algorithms for NB LDPC codes. The dissertation presents a simple, flexible and systematic method to construct both binary and nonbinary LDPC codes with quasi-cyclic (QC) structure based on two arbitrary subsets of a finite field. One technique for constructing QC-LDPC codes whose Tanner graphs have girth 8 or larger is also proposed. Simulation results show that these constructed codes perform well over both the additive white Gaussian noise and the binary erasure channels. Also presented in this dissertation is a reduced-complexity decoding scheme to decode binary QC-LDPC codes. The decoding scheme is devised based on the section-wise cyclic structure of the parity-check matrix of a QC-LDPC code. The proposed decoding scheme combined with iterative decoding algorithms of LDPC codes results in no or a relative small performance degradation. Two efficient algorithms for enumerating short cycles in the Tanners graph of LDPC codes are presented. One algorithm is devised based on iterative message-passing algorithm by introducing messages in term of monomials, which is an improvement of the work of Karimi and Banihashemi. The other one is based on the trellis of an LDPC code by finding the partial paths which can form cycles. By removing certain number of cycles, a new code whose Tanner graph has a smaller number of short cycles, a larger girth, or both can be constructed. An algorithm to count and find cycles of lengths four and six in a class of QC-LDPC codes is also proposed. In this dissertation, we also briefly investigate one of the algebraic-based constructions of LDPC code, namely superposition (SP) construction, and one of the graph-based constructions, namely protograph-based (PTG-based) construction. The SP-construction method is re-interpreted in a broader scope from both the algebraic and the graph-theoretic perspectives. From the graph-theoretic point of view, it is shown that the PTG-based construction of LDPC codes is a special case of the SP-construction. An algebraic method for constructing PTG-based QC-LDPC codes through decomposing a small matrix is proposed. Several methods for constructing QC-LDPC codes through the SP-construction are also presented.
Author: Martin Tomlinson
Publisher: Springer
ISBN: 3319511033
Category : Technology & Engineering
Languages : en
Pages : 527
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This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.
Author: Kasra Vakilinia
Publisher:
ISBN:
Category :
Languages : en
Pages : 201
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This dissertation mainly focuses on two different branches of coding theory and its applications:1) coding to approach capacity in short blocklengths using feedback and 2) LDPC coding for Flash memory systems. In the first area, we study the benefits that feedback with incremental redundancy can provide to increase the maximum achievable rate in communication systems, using carefully designed adaptive non-binary LDPC codes. We show how to achieve over 90% of the idealized throughput of rate-compatible sphere-packing with maximum-likelihood decoding (RCSP-ML) for average blocklengths of 150-450 bits. This is important because it illustrates that feedback greatly reduces the number of transmitted symbols required to achieve near-capacity performance. We then extend these ideas to feedback systems where the number of incremental transmissions is limited. In order to optimize the blocklengths for each incremental transmission we formulate an integer optimization problem involving an approximation based on the inverse-Gaussian p.d.f., the distribution of the blocklength required for successful decoding. The brute-force approach to solve this computationally complex optimization problem quickly becomes infeasible. In order to solve this problem efficiently, we introduce sequential differential optimization (SDO) algorithm that has only linear complexity to identify optimal incremental transmission lengths. The results obtained from SDO are negligibly different from the exponentially complex exhaustive-search solution. By using the optimized incremental transmission lengths (with an average blocklength of less than 500 bits), non-binary LDPC codes achieve a throughput greater than 90% of the capacity with a two-phase scheme. Furthermore, we extend these ideas to the case of using cyclic redundancy checks (CRC). With CRC, even better performance in the blocklength range of about 500 bits is obtainable. The overhead associated with a CRC prevents great performance in short blocklength regime (fewer than 400 bits). We also extend these ideas to systems with larger constellations operating at a higher signal-to-noise ratio (SNR). Another incremental transmission coding scheme studied in this dissertation focuses on de- sign and use of rate-compatible protograph-based raptor-like (PBRL) LDPC codes with various blocklengths and rates that can be used in feedback systems over additive-white Gaussian noise (AWGN) channels. The codes proposed in this work use X-OR operations and density evolution to produce additional degree-one parity bits providing extensive rate compatibility. The protographs are also carefully lifted to avoid undesirable graphical structures such as problematic stopping sets. For a target frame error rate of 10 5, at each rate the k = 1032 and k = 16384 code families perform within 1 dB and 0.4 dB, respectively, of both the Gallager bound and the normal approximation. The k = 16384 code family outperforms the best known standardized code family, the AR4JA and longer DVB-S2 codes. We extend the ideas in design of PBRL codes from AWGN channels to binary symmetric channels (BSC) and binary erasure channels (BEC). We introduce two fast and efficient algorithms to calculate the threshold of LDPC codes used over BSC. These algorithms serve as alternatives to the quite complex density evolution algorithm. Since these new algorithms are quite fast, we use them to design PBRL LDPC codes for BSC. To explore the advantage of feedback in conjunction with other modern coding schemes, in this work we use an extension of reciprocal channel approximation (RCA) to accurately and effi- ciently predict the frame error rate (FER) performance of polar codes by analyzing the probability density function (p.d.f.) of the log-likelihood ratio (LLR) values associated with information bits. The preliminary results show that a feedback scheme in conjunction with a repetition coding sys- tem significantly reduces the blocklength required to achieve a target FER. For example, using a rate-0.5 128-bit polar code as the initially transmitted code, the theoretical analysis verified by simulation shows a 16-fold reduction in blocklength with only about 7.4% of overhead in forward channel transmissions. We also make an improvement to this feedback coding scheme which reduces the overhead to almost 3% for a similar FER performance gain. The second part of this dissertation focuses on design of binary and non-binary LDPC codes for Flash memory systems. Usually the FER requirements in Flash memory systems is more strict than wireless communication systems. In order to improve the error correction capability of the codes used in Flash memory systems, sometimes the same memory cell is read multiple times. In this dissertation, we study the coding gain from multiple reads of the same Flash memory cell with distinct word-line voltages. The subsequent additional reads provide enhanced precision for LDPC decoding. We identify a trade-off in LDPC code design when decoding is performed with multiple precision levels and conclude that the best code at one level of precision is typically not be the best code at a different level of precision. By studying the trade-off in LDPC code design by using extrinsic-information-transfer (EXIT)- function analysis employing the reciprocal channel approximation (RCA), we obtain the optimal LDPC code degree distributions for initial hard decoding (one-bit quantization of the channel out- put) and for decoding with the soft information provided by subsequent additional reads in both SLC (two-level cell) and MLC (four-level-cell) Flash memory. The results indicate that design for hard decoding can provide irregular degree distributions that have good thresholds across a range of possible decoding precisions. Finally, we illustrate that the MMI optimization of word-line voltages for five reads is a quasi-convex problem for the Gaussian model of SLC Flash.
