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Tree-based construction of LDPC codes

D. Sridhara, C. Kelley, J. Rosenthal
2005 Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.  
We present a construction of LDPC codes that have minimum pseudocodeword weight equal to the minimum distance, and perform well with iterative decoding.  ...  The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on mutually orthogonal Latin squares to close the tree.  ...  Fig. 1 . 1 Tree construction of Type I-A LDPC code. Fig. 2 . 2 Type I-A LDPC constraint graph having degree d = 3 and girth g = 10. Fig. 3 . 3 Tree construction of Type I-B LDPC code.  ... 
doi:10.1109/isit.2005.1523456 dblp:conf/isit/SridharaKR05 fatcat:tioprk4eevbfhn2jq6g3eymrg4

Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights [article]

Christine Kelley, Deepak Sridhara, Joachim Rosenthal
2006 arXiv   pre-print
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding.  ...  The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree.  ...  The tree-based code constructions are then analyzed as p-ary LDPC codes.  ... 
arXiv:cs/0510009v2 fatcat:jwxiqhje6ncqjitrsurvg3a73y

Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights

Christine A. Kelley, Deepak Sridhara, Joachim Rosenthal
2007 IEEE Transactions on Information Theory  
We present a tree-based construction of low-density parity-check (LDPC) codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding  ...  The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree.  ...  The tree-based code constructions are then analyzed as -ary LDPC codes. Interpreting the tree-based codes as -ary LDPC codes when the degree is or yields codes with rates and good distances.  ... 
doi:10.1109/tit.2007.892774 fatcat:elgcqejnojaf3eqmg7vogspxoe

Iterative Construction of Regular LDPC Codes from Independent Tree-Based Minimum Distance Bounds

Eric Psota, Lance C. Perez
2011 IEEE Communications Letters  
An independent tree-based method for lower bounding the minimum distance of low-density parity-check (LDPC) codes is presented.  ...  This lower-bound is then used as the decision criterion during the iterative construction of regular LDPC codes.  ...  Iterative Construction of Regular LDPC Codes from Independent Tree-Based Minimum Distance Bounds Eric Psota and Lance C.  ... 
doi:10.1109/lcomm.2011.011311.102252 fatcat:77wpuedwmfgfhayu2pz2hcvtza

TS-LDPC Codes: Turbo-Structured Codes With Large Girth

Jin Lu, Jos M. F. Moura
2007 IEEE Transactions on Information Theory  
We consider turbo-structured low-density paritycheck (TS-LDPC) codes-structured regular codes whose Tanner graph is composed of two trees connected by an interleaver.  ...  TS-LDPC codes with good girth properties are easy to construct: careful design of the interleaver component prevents short cycles of any desired length in its Tanner graph.  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their suggestions that significantly improved the presentation of the results in this paper and to Dr. Marc P. C.  ... 
doi:10.1109/tit.2006.890690 fatcat:ywbluxer5rhxvlfzwnwykkccge

Design of Nonbinary Quasi-Cyclic LDPC Cycle Codes

Rong-Hui Peng, Rong-Rong Chen
2007 2007 IEEE Information Theory Workshop  
First, we construct a special class of nonbinary LDPC cycle codes with low error floors.  ...  In this paper, we study the design of nonbinary low-density parity-check (LDPC) cycle codes over Galois field GF(q).  ...  The girth of the code is 16 (in tanner graph). In addition, we also construct another nonbinary LDPC code over GF(16) based on the PEG construction.  ... 
doi:10.1109/itw.2007.4313042 fatcat:mx6wzqekejgodmahj26ysqysbu

Application of Nonbinary LDPC Cycle Codes to MIMO Channels

Ronghui Peng, Rong-Rong Chen
2008 IEEE Transactions on Wireless Communications  
We construct a special class of nonbinary LDPC cycle codes called the parallel sparse encodable (PSE) codes.  ...  The PSE code, consisting of a quasi-cyclic (QC) LDPC cycle code and a simple tree code, has the attractive feature that it is not only linearly encodable, but also allows parallel encoding which can reduce  ...  We will show that, starting from any base QC nonbinary LDPC cycle code, we can obtain a PSE code consisting of a QC subcode, modified from the base code, and a simple tree subcode.  ... 
doi:10.1109/twc.2008.070057 fatcat:gndxswkgxzdlvbp234lmm6dthq

Constructing LDPC Codes with Any Desired Girth

Chaohui Gao, Sen Liu, Dong Jiang, Lijun Chen
2021 Sensors  
Theoretical and experimental evidence of this study shows that the LDPC codes we construct have better decoding performance and less power consumption than the PEG-based and QC-based codes.  ...  Algorithms based on progressive-edge-growth (PEG) pattern and quasi-cyclic (QC) pattern are the mainstream approaches to constructing LDPC codes with good performance.  ...  Construction Algorithms of LDPC Codes There are many construction algorithms of LDPC codes, among which PEG-based and QC-based algorithms are the two main kinds of methods.  ... 
doi:10.3390/s21062012 pmid:33809154 pmcid:PMC8000767 fatcat:zaqhlhavwvduvb2xdpo3dndy5m

Randomized Progressive Edge-Growth (RandPEG)

Auguste Venkiah, David Declercq, Charly Poulliat
2008 2008 5th International Symposium on Turbo Codes and Related Topics  
Then, we illustrate the usefulness of our algorithm for constructing regular binary LDPC codes that perform well in the error floor region.  ...  First, we consider regular columnweight two graphs, which are a class of graphs used for the design of non-binary LDPC codes: for a given target girth gt, this new instance of the PEG algorithm allows  ...  Large girths are obtained by suitably constructing the underlying Tanner graph, and a construction based on a progressive edge-growth (PEG) of the graph was proposed in [5] , which results in LDPC codes  ... 
doi:10.1109/turbocoding.2008.4658712 fatcat:ofxwxanrgna2njba6tkfdllosu

FPGA implementation of rate-adaptive spatially coupled LDPC codes suitable for optical communications

Xiaole Sun, Ivan B. Djordjevic
2019 Optics Express  
(QC) LDPC codes.  ...  The implemented unified structure can be employed for any template QC-LDPC code to achieve a spatially-coupling based code-rate adaptation scheme. K K QC J J J K  ...  Then, based on the template QC-LDPC codes, we provide a simple method of constructing SC-LDPC codes from the template codes.  ... 
doi:10.1364/oe.27.003422 fatcat:rpoawzaxsreelkdftjrdpkbekm

Design of LDPC Codes Based on Progressive Edge Growth Techniques for Block Fading Channels

Andre G. D. Uchoa, Cornelius Healy, Rodrigo C. de Lamare, Richard D. Souza
2011 IEEE Communications Letters  
A novel algorithm to design Root-Check LDPC codes based on Progressive Edge Growth (PEG) techniques for block-fading channels is proposed.  ...  Numerical results show that the codes constructed by the proposed algorithm outperform codes constructed by the existing methods by 0.5dB.  ...  In [4] the construction of structured Root-LDPC codes is proposed by means of tiling circulant matrices, i.e., by designing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes.  ... 
doi:10.1109/lcomm.2011.092911.111520 fatcat:qeycyy7fyjabrnheouz6bdhxfa

Low complexity construction for quasi-cyclic low-density parity-check codes by Progressive-Block Growth

PinYi Ren, Qiang Yuan, Rui Wang, Jun Cai
2011 Science China Information Sciences  
Simulation results show that the proposed QC-LDPC codes can outperform both the random regular LDPC codes with short to moderate block lengths, and the proposed construction method LDPC codes based on  ...  In this paper, a novel method for constructing quasi-cyclic LDPC codes with low complexity is proposed.  ...  Performances of the two structured LDPC codes, the QC-LDPC codes constructed by PBG and the LDPC codes based on projective geometry are shown in Figure 5 , where the (1057, 813) PG-LDPC with rate R =  ... 
doi:10.1007/s11432-010-4152-0 fatcat:cr47ugcinfdcxc22awr3zttuna

Enhanced EMD-Driven PEG Construction for Structured LDPC Codes

C. T. Healy, R. C. de Lamare
2013 2013 IEEE 77th Vehicular Technology Conference (VTC Spring)  
A novel algorithm to construct structured LDPC codes based on graph connectivity and cycle quality is proposed.  ...  The code constructions provided are flexible in rate and length and demonstrate that the enhanced EMD-driven PEG-based approach proposed may be applied to a number of other structured LDPC code classes  ...  Fig. 4 shows the performance of the QC-LDPC code constructed using the proposed PEG-based EEMD algorithm of Section V and a QC-LDPC PEG-based construction using the metric of [10] .  ... 
doi:10.1109/vtcspring.2013.6692551 dblp:conf/vtc/HealyL13 fatcat:sfvm6ttfj5fdxan7dyhatngt7m

LDPC Block and Convolutional Codes Based on Circulant Matrices

R.M. Tanner, D. Sridhara, A. Sridharan, T.E. Fuja, D.J. Costello
2004 IEEE Transactions on Information Theory  
The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths.  ...  The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the  ...  CONCLUSION An algebraic construction based on circulant matrices for designing LDPC codes has been proposed. The properties of the LDPC codes resulting from this construction have been examined.  ... 
doi:10.1109/tit.2004.838370 fatcat:cmfsithkwzbt3pj4qou5utmygu

Quasi-cyclic low-density parity-check codes based on decoder optimised progressive edge growth for short blocks

C. T. Healy, R. C. de Lamare
2012 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
A novel construction for quasi-cyclic (QC) regular and irregular low-density parity-check (LDPC) codes based on a modification of the QC Progressive Edge Growth (PEG) algorithm is presented.  ...  Edge placement of the PEG-based algorithm is enhanced by use of the sum-product algorithm in the design of the parity-check matrix.  ...  In the PEG algorithm and its modification for constructing QC-LDPC codes, the neighbourhood to depth l of a VN vj is the set of all CNs in the tree expanded from VN vj with l levels and is denoted N l  ... 
doi:10.1109/icassp.2012.6288543 dblp:conf/icassp/HealyL12 fatcat:qmcrhy4khfcunoz7a5obs6bhc4
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