Open AccessPosted Content
Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates
TLDR
In this paper, the authors considered a deterministic construction of generalized product codes (GPCs) and analyzed the asymptotic performance over the binary erasure channel under iterative decoding.Abstract:
Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed to randomized code ensembles) and analyze the asymptotic performance over the binary erasure channel under iterative decoding. Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, block-wise braided codes, and staircase codes. It is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity. We show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph. Using a convergence result for these graphs, we derive the density evolution equations that characterize the asymptotic decoding performance. As an application, we discuss the design of irregular GPCs employing a mixture of component codes with different erasure-correcting capabilities.read more
Citations
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Journal ArticleDOI
Approaching Miscorrection-Free Performance of Product Codes With Anchor Decoding
Christian Häger,Henry D. Pfister +1 more
TL;DR: A novel iterative decoding algorithm for PCs which can detect and avoid most miscorrections, and can be used to decode many recently proposed classes of generalized PCs, such as staircase, braided, and half-product codes.
Journal ArticleDOI
Approaching Capacity at High Rates With Iterative Hard-Decision Decoding
TL;DR: It is shown that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes, a class of spatially coupled generalized LDPC codes with Bose–Chaudhuri–Hocquengham component codes.
Posted Content
On Low-Complexity Decoding of Product Codes for High-Throughput Fiber-Optic Systems
TL;DR: A novel decoding algorithm is proposed that closes over 50% of the performance gap between iBDD and turbo product decoding (TPD) based on the Chase–Pyndiah algorithm at a bit error rate of 10−5.
Journal ArticleDOI
Probabilistic Amplitude Shaping with Hard Decision Decoding and Staircase Codes
TL;DR: In this paper, probabilistic amplitude shaping with hard decision decoding (HDD) is applied to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code.
Book ChapterDOI
Forward Error Correction for Optical Transponders
TL;DR: This chapter discusses the state-of-the-art FEC schemes for fiber-optic communications, and introduces the main techniques to combine coding and higher-order modulation (coded modulation), including constellation shaping.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
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.
Proceedings ArticleDOI
Random graphs
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.