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Optimization of NB QC-LDPC Block Codes and Their Performance Analysis [article]

Irina E. Bocharova, Boris D. Kudryashov, Evgenii P. Ovsyannikov, Vitaly Skachek, Tähvend Uustalu
2020 arXiv   pre-print
This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the so-called generalized girth of the NB LDPC code  ...  Tanner graph.  ...  The authors wish to thank Victor Krachkovsky, Oleg Kurmaev, Alexey Mayevskiy and Hongchen Yu for helpful discussions.  ... 
arXiv:2006.12147v2 fatcat:uwnc4xodfzho3hijutavaaesca

Rate-Compatible LDPC Codes Based on Puncturing and Extension Techniques for Short Block Lengths [article]

J. Liu, R. C. de Lamare
2014 arXiv   pre-print
In this paper, we investigate novel strategies for generating rate-compatible (RC) irregular low-density parity-check (LDPC) codes with short/moderate block lengths.  ...  The first puncturing scheme employs a counting cycle algorithm and a grouping strategy for variable nodes having short cycles of equal length in the Tanner Graph (TG).  ...  Low-Density Parity-Check (LDPC) codes were invented by Gallager [4] and re-discovered by MacKay et al.  ... 
arXiv:1407.5136v1 fatcat:sg374odnznh4jpnpt7kpyecgay

Analyzing the turbo decoder using the Gaussian approximation

H. El Gamal, A.R. Hammons
2001 IEEE Transactions on Information Theory  
Examples are given for parallel concatenated convolutional codes, serially concatenated convolutional codes, and the generalized low-density parity-check (LDPC) codes of Gallager and Cheng-McEliece.  ...  In this paper, we introduce a simple technique for analyzing the iterative decoder that is broadly applicable to different classes of codes defined over graphs in certain fading as well as additive white  ...  ACKNOWLEDGMENT The authors wish to thank the anonymous reviewers for this careful review and the reference to S. ten Brink's work [14] .  ... 
doi:10.1109/18.910581 fatcat:65bv3gvkkvbt7fxs6zajsjdilq

Product Accumulate Codes: A Class of Codes With Near-Capacity Performance and Low Decoding Complexity

J. Li, K.R. Narayanan, C.N. Georghiades
2004 IEEE Transactions on Information Theory  
We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code.  ...  Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1 2.  ...  Some widely used high-rate codes are Reed-Solomon (RS) codes, punctured convolutional codes, turbo codes, and low-density parity-check (LDPC) codes.  ... 
doi:10.1109/tit.2003.821995 fatcat:jl5vpjsbrnhjxos2imuqllwaxu

Efficient Search and Elimination of Harmful Objects in Optimized QC SC-LDPC Codes [article]

Massimo Battaglioni, Franco Chiaraluce, Marco Baldi, David Mitchell
2019 arXiv   pre-print
The error correction performance of low-density parity-check (LDPC) codes under iterative message-passing decoding is degraded by the presence of certain harmful objects existing in their Tanner graph  ...  In this paper, we propose a general procedure based on edge spreading that enables the design of quasi-cyclic (QC) spatially coupled low-density parity-check codes (SC-LDPCCs) that are derived from QC-LDPC  ...  INTRODUCTION Low-density parity-check (LDPC) block codes were first introduced by Gallager [1] and have attracted significant interest over time due to their capacity-approaching performance.  ... 
arXiv:1904.07158v1 fatcat:lgd4nllmfnc2pkryeo3iguzfsy

Joint Iterative Decoding of Spatially Coupled Low-Density Parity-Check Codes for Position Errors in Racetrack Memories

Ryo SHIBATA, Gou HOSOYA, Hiroyuki YASHIMA
2018 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
Then, we propose a joint iterative decoding algorithm for spatially coupled low-density parity-check (SC-LDPC) codes over such a channel.  ...  Moreover, we show the performance improvement produced by adjusting the order of the SC-LDPC codeword bits in RM. key words: insertion and deletion errors, spatially coupled low-density parity-check code  ...  The authors would like to thank the reviewers for their constructive comments that have helped improving the overall quality of the paper.  ... 
doi:10.1587/transfun.e101.a.2055 fatcat:lzws2p5uhnhovip2rj7opxnhy4

Peeling Decoding of LDPC Codes with Applications in Compressed Sensing

Weijun Zeng, Huali Wang
2016 Mathematical Problems in Engineering  
We present a new approach for the analysis of iterative peeling decoding recovery algorithms in the context of Low-Density Parity-Check (LDPC) codes and compressed sensing.  ...  The iterative recovery algorithm is particularly interesting for its low measurement cost and low computational complexity.  ...  As a special class of sparse matrices, the paritycheck matrices of Low-Density Parity-Check (LDPC) codes can be used as good measurement matrices for CS under ℓ 1 norm minimization [3] .  ... 
doi:10.1155/2016/6340430 fatcat:iq32aigubffxxdcrsjs55jmkdq

Generalized Low-Density Parity-Check Codes Based on Hadamard Constraints

Guosen Yue, Li Ping, Xiaodong Wang
2007 IEEE Transactions on Information Theory  
In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels.  ...  The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints.  ...  Therefore we can conclude that the proposed LDPC-Hadamard codes are most suitable for designing good low-rate in the very-low SNR region.  ... 
doi:10.1109/tit.2006.890694 fatcat:vionulnscjbznfdxtphm7yu46q

Message from the general chairs

Ramesh Jain, Mohan Kumar
2008 2008 International Symposium on a World of Wireless, Mobile and Multimedia Networks  
the construction of rate-compatible spatially coupled low-density parity-check (SC-LDPC) codes.  ...  Density Parity Check (LDPC) code and the mapper.  ... 
doi:10.1109/wowmom.2008.4594797 dblp:conf/wowmom/JainK08 fatcat:ziu25issdvga7cmqjgbtqtdu7q

Design of Joint Sparse Graph for OFDM System

Lei Wen, Razieh Razavi, Muhammad Ali Imran, Pei Xiao
2015 IEEE Transactions on Wireless Communications  
Low density signature orthogonal frequency division multiplexing (LDS-OFDM) and low density parity-check (LDPC) codes are multiple access and forward error correction (FEC) techniques, respectively.  ...  In this paper, we construct a joint sparse graph combining the single graphs of LDS-OFDM and LDPC codes, namely joint sparse graph for OFDM (JSG-OFDM).  ...  ACKNOWLEDGMENT The authors would like to thank Jing Lei, Jibo Wei and Dandan Liang for their constructive and insightful comments.  ... 
doi:10.1109/twc.2014.2373379 fatcat:zfwhhhebyzbbboyb4trid6knli

Finding All Small Error-Prone Substructures in LDPC Codes

Chih-Chun Wang, Sanjeev R. Kulkarni, H. Vincent Poor
2009 IEEE Transactions on Information Theory  
Index Terms-Branch-and-bound, error floors, exhaustive search, low-density parity-check (LDPC) codes, stopping distance, stopping/trapping sets, support trees.  ...  It is proven in this work that it is NP-complete to exhaustively enumerate small error-prone substructures in arbitrary, finite-length low-density parity-check (LDPC) codes.  ...  For example, a simple parity-check code with can be mapped bijectively to a bipartite graph as in Fig. 1 .  ... 
doi:10.1109/tit.2009.2015993 fatcat:c37fnj7c7rgbbcaxzfuvdw52de

Design of Rate-Compatible Punctured Repeat-Accumulate Codes

Shiva K. Planjery, T. Aaron Gulliver
2007 IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference  
In addition, we require coding schemes that are simple in terms of complexity but give good performance.  ...  The design involves optimizing the punctured profile of the code such that the resulting high rate codes give good performance.  ...  Another type of turbo-like codes, were the Low Density Parity check (LDPC) codes introduced by Gallager[5], which was based on introducing randomness by constructing a sparse parity check matrix.  ... 
doi:10.1109/glocom.2007.285 dblp:conf/globecom/PlanjeryG07 fatcat:wudyspoc4nflxhtpmfq5dva3dy

Recent Advances in Turbo Code Design and Theory

Branka Vucetic, Yonghui Li, Lance C. Perez, Fan Jiang
2007 Proceedings of the IEEE  
ABSTRACT | The discovery of turbo codes and the subsequent rediscovery of low-density parity-check (LDPC) codes represent major milestones in the field of channel coding.  ...  The relationship between turbo codes and LDPC codes is explored via an explicit formulation of the parity-check matrix of a turbo code, and simulation results are given for sum product decoding of a turbo  ...  Acknowledgment The authors would like to thank Eric Psota of the University of Nebraska-Lincoln for the simulations in Figs. 13-15.  ... 
doi:10.1109/jproc.2007.897975 fatcat:gw6i3uwvyzeihlxmj76tqjdrxy

Design of serial concatenated msk schemes based on density evolution

K.R. Narayanan, I. Altunbas, R.S. Narayanaswami
2003 IEEE Transactions on Communications  
For low density parity check codes, we show that codes designed for binary phase shift keying are optimal for MSK only if the non-recursive realization is used; for the recursive realization, we design  ...  We then consider the design of convolutionally coded systems and low density parity check codes with MSK to obtain near-capacity performance.  ...  We begin with the graph structure of MSK and the low density parity check code. Consider the recursive CPE shown in Fig. 2(a) .  ... 
doi:10.1109/tcomm.2003.815076 fatcat:mnvdga25kfcmlfpdtztyvclqpy

Performance Bound for Finite-Length LDPC Coded Modulation

H. G. VU, H. H. NGUYEN, D. E. DODDS
2007 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
Coded modulation systems based on low density parity check (LDPC) codes of finite lengths are considered.  ...  For mediumlength codes, performance of the sum-product decoding can asymptotically approach the bounds.  ...  Introduction The error performance of infinite-length low-density parity check (LDPC) codes [1] under the iterative decoding or sum-product algorithm has been widely investigated.  ... 
doi:10.1093/ietfec/e90-a.12.2975 fatcat:i2noafrpgrcc7by2bzuqdek2ue
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