Open AccessBook
Fundamentals of Codes, Graphs, and Iterative Decoding
Stephen B. Wicker,Saejoon Kim +1 more
TLDR
This text discusses codes for low-Density Parity-Check Codes, Convolutional Encoding, and the Elements of Graph Theory, which describes the construction of rings, Domains, and Fields in sets and groups.Abstract:
List of Figures. List of Tables. Preface. 1: Digital Communication. 1. Basics. 2. Algorithms and Complexity. 3. Encoding and Decoding. 4. Bounds. 5. Overview of the Text. 2: Abstract Algebra. 1. Sets and Groups. 2. Rings, Domains, and Fields. 3. Vector Spaces and GF(pm). 4. Polynomials over Galois Fields. 5. Frequency Domain Analysis of Polynomials over GF(q) [x]/(xn-1). Linear Block Codes. 1. Basic Structure of Linear Codes. 2. Repetition and Parity Check Codes. 3. Hamming Codes. 4. Reed-Muller Codes. 5. Cyclic Codes. 6. Quadratic Residue Codes. 7. Golay Codes. 8. BCH and Reed-Solomon Codes. 4: Convolutional and Concatenated Codes. 1. Convolutional Encoders. 2. Analysis of Component Codes. 3. Concatenated Codes. 4. Analysis of Parallel Concatenated Codes. 5: Elements of Graph Theory. 1. Introduction. 2. Martingales. 3. Expansion. 6: Algorithms on Graphs. 1. Probability Models and Bayesian Networks. 2. Belief Propagation Algorithm. 3. Junction Tree Propagation Algorithm. 4. Message Passing and Error Control Decoding. 5. Message Passing in Loops. 7: Turbo Decoding. 1. Turbo Decoding. 2. Parallel Decoding. 3. Notes. 8: Low-Density Parity-Check Codes. 1. Basic Properties. 2. Simple Decoding Algorithms. 3. Explicit Construction. 4. Gallager's Decoding Algorithms. 5. Belief Propagation Decoding. 6. Notes. 9: Low-Density Generator Codes. 1. Introduction. 2. Decoding Analyses. 3. Good Degree Sequences. 4. Irregular Repeat-Accumulate Codes. 5. Cascaded Codes. 6. Notes. References. Index.read more
Citations
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Proceedings ArticleDOI
Optimizing Cauchy Reed-Solomon Codes for Fault-Tolerant Network Storage Applications
James S. Plank,Lihao Xu +1 more
TL;DR: This paper presents an improvement to Cauchy Reed-Solomon coding that is based on optimizing theCauchy distribution matrix, and details an algorithm for generating good matrices and evaluates the performance of encoding using all implementations Reed- Solomon codes, plus the best MDS codes from the literature.
Proceedings ArticleDOI
A practical analysis of low-density parity-check erasure codes for wide-area storage applications
TL;DR: This analysis focuses on the performance of individual codes for finite systems, and addresses several important heretofore unanswered questions about employing LDPC codes in real-world systems.
Journal ArticleDOI
Massively LDPC Decoding on Multicore Architectures
TL;DR: Algorithms and data structures suitable for parallel computing are proposed in this paper to perform LDPC decoding on multicore architectures and achieve throughputs that in some cases approach very well those obtained with VLSI decoders.
Journal ArticleDOI
Gender Differences in Instagram Hashtag Use
TL;DR: In this paper, the authors analyzed 1,382 Instagram posts with the hashtag #Malaysianfood and categorized them as informative/emotional and positive/negative, and found that compared to male users, female users tend to use emotional and positive hashtag descriptions.
Proceedings ArticleDOI
Small parity-check erasure codes - exploration and observations
TL;DR: This paper provides a framework for exploring very small codes, and uses this framework to derive optimal and near-optimal ones for discrete numbers of data bits and coding bits.
References
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Book
Low-Density Parity-Check Codes
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Book ChapterDOI
Coding for noisy channels
TL;DR: This chapter begins with a development of the classic fundamental results of Feinstein regarding reliable communication of block codes and the relation of operational channel capacity to Shannon capacity for discrete channels and a technique of Dobrushin is used to extend Feinstein's results for channels with no input memory or anticipation by making codes robust to small changes in the conditional distributions describing channels.