Algebraic Construction of LDPC Codes for the AWGN and Erasure Channels PDF Download
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Author: Ying Yu Tai
Publisher:
ISBN:
Category :
Languages : en
Pages : 356
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Book Description
Author: Ying Yu Tai
Publisher:
ISBN:
Category :
Languages : en
Pages : 356
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Book Description
Author: Lan Lan
Publisher:
ISBN:
Category :
Languages : en
Pages : 340
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Book Description
Author: Juane Li
Publisher: Cambridge University Press
ISBN: 1107175682
Category : Computers
Languages : en
Pages : 259
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Book Description
In this book, leading authorities unify algebraic- and graph-based LDPC code designs and constructions into a single theoretical framework.
Author: Marc Fossorier
Publisher: Springer
ISBN: 3540314245
Category : Computers
Languages : en
Pages : 348
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Book Description
The 25 revised full papers presented here together with 7 invited papers address subjects such as block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.
Author: Keke Liu
Publisher:
ISBN: 9781321806663
Category :
Languages : en
Pages :
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Book Description
The algebraic low-density parity-check (LDPC) codes have received great attention in the practical applications to communication and data storage systems due to their fruitful structural properties and excellent overall performances. This dissertation investigates the following topics regarding the construction, analysis and decoding of the algebraic LDPC codes.The first contribution is a comprehensive rank analysis of the algebraic quasi-cyclic (QC) LDPC (QC-LDPC) codes constructed based on two arbitrary subsets of a finite field, which generalizes the rank analysis results in the previous literature. Also investigated is a flexible algebraic construction of QC-LDPC codes with large row redundancy based on field partitions. This construction results in a large class of binary regular QC-LDPC codes with flexible choices of rates and lengths that are shown to perform well over the additive white Gaussian noise (AWGN) channel. Secondly, to resolve the issue of decoder complexity caused by relatively high density of the parity-check matrices of algebraic LDPC codes, an effective revolving iterative decoding (RID) scheme is developed for algebraic cyclic and QC-LDPC codes. The proposed RID scheme significantly reduces the hardware implementation complexities. Also presented is a variation of the RID scheme, called merry-go-round (MGR) decoding scheme, which maintains the circulant permutation matrix (CPM) structure that is desirable for the hardware implementation but lost in the RID scheme, while preserving the merits of reducing decoder complexity. The proposed RID and MGR decoding schemes may enhance the applications of algebraic LDPC codes.Lastly, a general algebraic construction of QC-LDPC convolutional codes, also called spatially coupled (SC) QC-LDPC codes, is proposed. Simulation results show that the constructed algebraic SC-QC-LDPC codes can outperform their non-algebraic counterparts. Also investigated is the rate compatibility of the constructed SC-QC-LDPC codes using the regular puncturing scheme.
Author: Shu Lin
Publisher: Cambridge University Press
ISBN: 1316512622
Category : Computers
Languages : en
Pages : 843
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Book Description
An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.
Author: Juane Li
Publisher:
ISBN: 9781369201024
Category :
Languages : en
Pages :
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Book Description
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: Shumei Song
Publisher:
ISBN:
Category :
Languages : en
Pages : 286
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Book Description
Author: Bo Zhou
Publisher:
ISBN:
Category :
Languages : en
Pages : 292
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Book Description
Author: Predrag Ivaniš
Publisher: Springer
ISBN: 3319493701
Category : Technology & Engineering
Languages : en
Pages : 517
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Book Description
This book is offers a comprehensive overview of information theory and error control coding, using a different approach then in existed literature. The chapters are organized according to the Shannon system model, where one block affects the others. A relatively brief theoretical introduction is provided at the beginning of every chapter, including a few additional examples and explanations, but without any proofs. And a short overview of some aspects of abstract algebra is given at the end of the corresponding chapters. The characteristic complex examples with a lot of illustrations and tables are chosen to provide detailed insights into the nature of the problem. Some limiting cases are presented to illustrate the connections with the theoretical bounds. The numerical values are carefully selected to provide in-depth explanations of the described algorithms. Although the examples in the different chapters can be considered separately, they are mutually connected and the conclusions for one considered problem relate to the others in the book.
