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Efficient iterative LP decoding of LDPC codes with alternating direction method of multipliers

Xiaojie Zhang, Paul H. Siegel
2013 2013 IEEE International Symposium on Information Theory  
variables of check j.LP Formulation• LP decoding solves the following optimization problem:▫ where is the vector of LLRs for received vector LP Solver for Decoding LDPC codes Outline • Motivation  ...  large and need saturated  Output codeword is not necessarily the ML-codeword Alternative Decoding MethodLinear Programming (LP) decoding ▫ ML-certificate, i.e., all integer solutions are MLcodewords  ...  algorithms, requires only local information. • Our proposed projection algorithm improves the decoding speed of existing ADMM-based LP decoder by more than a factor of 2.  ... 
doi:10.1109/isit.2013.6620477 dblp:conf/isit/ZhangS13 fatcat:k7g4x77qbzemzn6qak5idwcrlu

Improved Check Node Decomposition for Linear Programming Decoding

Xiaopeng Jiao, Jianjun Mu
2013 IEEE Communications Letters  
It is demonstrated on an LDPC code and a BCH code that the decoding time of the degree-4 decomposition is the smallest among the different decomposition methods.  ...  For the linear programming decoding (LPD) proposed by Feldman et al., the number of constraints increases exponentially with check degrees.  ...  Acknowledgment The authors would like to thank the anonymous reviewers for their constructive comments which helped improve the quality of this letter.  ... 
doi:10.1109/lcomm.2012.122012.122396 fatcat:rc7luelwyrbjfpanipej7dej24

A New Linear Programming Approach to Decoding Linear Block Codes

Kai Yang, Xiaodong Wang, Jon Feldman
2008 IEEE Transactions on Information Theory  
In this paper, we propose a new linear programming formulation for the decoding of general linear block codes.  ...  We then propose a branch-and-bound method to compute a lower bound to the minimum distance of any linear code by solving a corresponding linear integer programming problem.  ...  In this section, we develop a fast decoding method for the SPC product code based on the Lagrange dual method for integer programming problem (cf. [18, Ch. 11] ).  ... 
doi:10.1109/tit.2007.915712 fatcat:zninfi7pl5f77hmkfdq32lbt7q

Minimum-Polytope-Based Linear Programming Decoder for LDPC Codes via ADMM Approach [article]

Jing Bai, Yongchao Wang, Francis C. M. Lau
2019 arXiv   pre-print
In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes.  ...  Then, to solve the resulting LP problem, we propose an efficient iterative algorithm based on the alternating direction method of multipliers (ADMM) technique.  ...  INTRODUCTION Linear programming (LP) decoding has been considered as a promising decoding approach for low-density paritycheck (LDPC) codes [1] .  ... 
arXiv:1901.07806v1 fatcat:rgosnumvpnhlnh3wytsb2phjmi

Joint detection and decoding of LDPC coded distributed space-time signaling in wireless relay networks via linear programming

Kun Wang, Wenhao Wu, Zhi Ding
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We develop a linear programming based approach for the joint detection and decoding of LDPC coded distributed space-time signaling transmitted in a wireless relay network.  ...  We exploit the constraints imposed on the channel input signals and jointly consider the training symbols as well as the LDPC code information by formulating a unified linear programming (LP) receiver.  ...  Unlike traditional dis- joint or belief propagation receivers, we jointly utilize the feature of QAM signals, the available pilots, and LDPC code constraints in an integrated linear programming receiver  ... 
doi:10.1109/icassp.2014.6853930 dblp:conf/icassp/WangWD14 fatcat:ouvkc4avorekpczylkre43d4ei

Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Michael Helmling, Stefan Ruzika, Akın Tanatmis
2012 IEEE Transactions on Information Theory  
This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.  ...  Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory.  ...  Vontobel and Frank Kienle for their comments and suggestions. We also thank the anonymous referees for the helpful reviews.  ... 
doi:10.1109/tit.2012.2191697 fatcat:zyv2tbnkxvhlzps5mleuxln4va

LP Decoding of Regular LDPC Codes in Memoryless Channels [article]

Nissim Halabi, Guy Even
2011 arXiv   pre-print
We study error bounds for linear programming decoding of regular LDPC codes.  ...  For memoryless binary-input AWGN channel, we prove lower bounds on the threshold for regular LDPC codes whose factor graphs have logarithmic girth under LP-decoding.  ...  Acknowledgment The authors would like to thank P. O. Vontobel and the anonymous reviewers for their constructive comments and suggestions that helped to improve the paper.  ... 
arXiv:1002.3117v3 fatcat:nbkvkfxlsfclnkxrps2w6umoxi

Guest Editorial Recent Advances in Capacity Approaching Codes

Erdal Arikan, Daniel J. Costello, Joerg Kliewer, Michael Lentmaier, Paul Siegel, Ruediger Urbanke, Michael Pursley
2016 IEEE Journal on Selected Areas in Communications  
iterative decoding error probability for a class of LDPC codes operating on the AWGN channel.  ...  The paper by Presman et al. introduces a novel construction for polar codes, called a mixed-kernel construction, based on code decomposition.  ... 
doi:10.1109/jsac.2015.2508219 fatcat:pq7svpzseza7ljrrz6rlzl2fw4

A Compressed Sensing-Based Low-Density Parity-Check Real-Number Code

Zaixing He, Takahiro Ogawa, Miki Haseyama, Xinyue Zhao, Shuyou Zhang
2013 Radioengineering  
The proposed code has high error correction performance and decoding efficiency. The comparative experimental results demonstrate both advantages of our code. We also apply our code to cryptography.  ...  In this paper, we propose a novel low-density parity-check real-number code, based on compressed sensing.  ...  Acknowledgements This research was supported by the Fundamental Research Funds for the Central Universities and Zhejiang Provincial Natural Science Foundation of China (LQ13F020002 and LQ13F030003).  ... 
doaj:4fcc11ccdfd84d2eb67e2997645f6438 fatcat:s7sygvy5szhkbltx5dubyaxrey

Asymptotic analysis and design of LDPC codes for laurent-based optimal and suboptimal CPM receivers

Tarik Benaddi, Charly Poulliat, Marie-Laure Boucheret, Benjamin Gadat, Guy Lesthievent
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
design of serially concatenated turbo schemes with low density parity check (LDPC) codes and continuous phase modulation (CPM) based on Laurent decomposition.  ...  Furthermore, we discuss the selection of low complexity receivers that works with the same optimized profiles.  ...  This system can be efficiently solved by classical linear programming using discretization of the convergence constraint for y ∈ [0,1].  ... 
doi:10.1109/icassp.2014.6854408 dblp:conf/icassp/BenaddiPBGL14 fatcat:ia4w7m3j3bhfzglplnjbj5huli

Probabilistic Analysis of Linear Programming Decoding

C. Daskalakis, A.G. Dimakis, R.M. Karp, M.J. Wainwright
2008 IEEE Transactions on Information Theory  
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes.  ...  Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in correcting a constant fraction of errors with high probability.  ...  ACKNOWLEDGMENT The authors would like the thank the anonymous referees for their numerous and detailed suggestions that helped to improve this paper.  ... 
doi:10.1109/tit.2008.926452 fatcat:pzhpoqy6sbfuzljsgqr26rrdpi

Reduced Complexity Quasi-Cyclic LDPC Encoder for IEEE 802.11N

Monica Mankar, Gajendra Asutkar, Pravin Dakhole
2016 International Journal of VLSI Design & Communication Systems  
for 648 block length and 1/2 code rate.  ...  Proposed architecture of QC-LDPC encoder will be compatible for high-speed applications.  ...  Zhibin Zeng applies LU decomposition with dynamic programming for LDPC encoder for CMMB. For the 1/2 code rate, encoder work at. [25] .  ... 
doi:10.5121/vlsic.2016.7604 fatcat:xslppi6xkzc3vp6stsjjmdqckm

Near-Capacity Coding for Discrete Multitone Systems with Impulse Noise

Masoud Ardakani, Frank R. Kschischang, Wei Yu
2006 EURASIP Journal on Advances in Signal Processing  
Such a system can perform close to the capacity of the channel and for the same redundancy is significantly more immune to the impulse noise than existing methods based on an outer Reed-Solomon (RS) code  ...  In this paper, we propose a coding system based on low-density parity-check (LDPC) codes and bit-interleaved coded modulation that is capable of taking advantage of the knowledge of erasures.  ...  In this work, we use a method which is based on linear programming and reflects our goal of finding the maximum rate for a given channel.  ... 
doi:10.1155/asp/2006/98738 fatcat:me3tdaxwqjawxdecct7jvfnuza

Message from the general chairs

Ramesh Jain, Mohan Kumar
2008 2008 International Symposium on a World of Wireless, Mobile and Multimedia Networks  
The decomposition scheme allows efficient decoding for MS-MLG decodable cyclic codes.  ...  Several algebraic methods for constructing non-binary LDPC codes are presented.  ... 
doi:10.1109/wowmom.2008.4594797 dblp:conf/wowmom/JainK08 fatcat:ziu25issdvga7cmqjgbtqtdu7q

Deriving Good LDPC Convolutional Codes from LDPC Block Codes [article]

Ali E. Pusane, Roxana Smarandache, Pascal O. Vontobel, Daniel J. Costello Jr
2010 arXiv   pre-print
In this paper we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional  ...  Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes.  ...  ACKNOWLEDGMENTS The authors would like to thank Chris Jones, Michael Lentmaier, David Mitchell, Michael Tanner, and Kamil Zigangirov for their valuable discussions and comments.  ... 
arXiv:1004.5157v3 fatcat:x7viyypw7fhxvm4l7ujq75cmii
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