Regular and irregular progressive edge-growth tanner graphs
We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of...
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| Published in | IEEE transactions on information theory Vol. 51; no. 1; pp. 386 - 398 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.01.2005
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9448 1557-9654 |
| DOI | 10.1109/TIT.2004.839541 |
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| Abstract | We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes. |
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| AbstractList | We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes. We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over hboxGF(q) (q?2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes. [PUBLICATION ABSTRACT] |
| Author | Arnold, D.M. Eleftheriou, E. Xiao-Yu Hu |
| Author_xml | – sequence: 1 surname: Xiao-Yu Hu fullname: Xiao-Yu Hu organization: Zurich Res. Lab., IBM Res., Switzerland – sequence: 2 givenname: E. surname: Eleftheriou fullname: Eleftheriou, E. organization: Zurich Res. Lab., IBM Res., Switzerland – sequence: 3 givenname: D.M. surname: Arnold fullname: Arnold, D.M. organization: Zurich Res. Lab., IBM Res., Switzerland |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16447315$$DView record in Pascal Francis |
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| Keywords | LDPC codes over GF(q) PEG Tanner graphs low-density parity-check (LDPC) codes Iterative method Parity check codes Graph theory Decoding Algorithm Girth Optimization progressive edge growth (PEG) |
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| References | ref13 Erdös (ref30) 1963; 12 Hu (ref39) 2002 ref56 ref15 ref14 Fan (ref24) ref52 ref11 ref55 ref10 ref54 ref17 ref16 ref19 ref18 MacKay (ref50) Rosenthal (ref31) ref51 Forney (ref12) Margulis (ref28) 1988; 24 ref46 ref45 Jin (ref48) ref47 ref42 ref41 ref44 ref43 ref49 ref8 ref7 ref9 ref4 ref3 ref6 ref5 ref40 ref34 ref37 ref36 ref33 ref32 Tanner (ref23) ref2 ref1 ref38 Richter (ref35) ref26 ref25 ref20 ref22 ref21 ref27 ref29 Davey (ref53) 1999 |
| References_xml | – ident: ref38 doi: 10.1109/ICC.2001.936272 – ident: ref34 doi: 10.1007/3-540-46796-3_7 – ident: ref20 doi: 10.1109/4234.905935 – volume-title: Proc. ICSTA 2001 ident: ref23 article-title: A class of group-structured LDPC codes – ident: ref10 doi: 10.1162/089976600300015880 – ident: ref32 doi: 10.1109/ISIT.2001.936086 – ident: ref8 doi: 10.1109/18.910572 – ident: ref40 doi: 10.1109/ICC.2003.1203996 – ident: ref22 doi: 10.1109/18.959255 – ident: ref14 doi: 10.7551/mitpress/4347.001.0001 – start-page: 9 volume-title: Proc. 2nd Int. Symp. Turbo Codes & Related Topics ident: ref12 article-title: Codes on graphs: News and views – ident: ref27 doi: 10.1007/BF02579283 – ident: ref41 doi: 10.1109/LCOMM.2004.839612 – ident: ref56 doi: 10.1007/978-3-7091-2945-6 – ident: ref7 doi: 10.1109/ISIT.1998.708592 – volume-title: Error-correction using low-density parity-check codes year: 1999 ident: ref53 – ident: ref4 doi: 10.1109/18.556669 – ident: ref9 doi: 10.1109/18.771145 – ident: ref19 doi: 10.1109/18.910578 – ident: ref2 doi: 10.1002/ett.4460060507 – ident: ref52 doi: 10.1109/ISIT.1998.708706 – volume-title: Proc. ETH Zurich 2003 Winter School on Coding and Information Theory ident: ref35 article-title: Construction of completely regular LDPC codes with large girth – ident: ref15 doi: 10.1109/ICC.1993.397441 – ident: ref33 doi: 10.1109/TIT.2004.833352 – ident: ref11 doi: 10.1109/18.825794 – ident: ref16 doi: 10.1109/18.748992 – ident: ref1 doi: 10.1109/TIT.1981.1056404 – start-page: 543 volume-title: Proc. 2nd Int. Symp. Turbo Codes & Related Topics ident: ref24 article-title: Array codes as low-density parity-check codes – ident: ref54 doi: 10.1109/4234.681360 – ident: ref43 doi: 10.1109/18.910591 – ident: ref6 doi: 10.1109/49.661110 – ident: ref26 doi: 10.1109/ITW.2001.955146 – ident: ref47 doi: 10.1049/el:19990065 – ident: ref55 doi: 10.1109/4234.775255 – ident: ref46 doi: 10.1109/26.795809 – ident: ref42 doi: 10.1109/LCOMM.2004.825728 – ident: ref25 doi: 10.1109/isit.2002.1023584 – ident: ref21 doi: 10.1109/TIT.2002.1003839 – ident: ref5 doi: 10.1109/49.661103 – ident: ref18 doi: 10.1109/18.910577 – ident: ref44 doi: 10.1145/258533.258573 – ident: ref3 doi: 10.1109/18.556667 – ident: ref49 doi: 10.1109/18.910579 – ident: ref36 doi: 10.1109/GLOCOM.2001.965567 – volume: 12 start-page: 251 year: 1963 ident: ref30 article-title: Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl publication-title: Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Naturwiss. Reine – start-page: 1 volume-title: Proc. 2nd Int. Symp. Turbo Codes & Related Topics ident: ref48 article-title: Irregular repeat-accumulate codes – volume-title: Online Database of Low-Density Parity-Check Codes ident: ref50 – ident: ref13 doi: 10.1109/tit.2001.910571 – volume-title: Low-delay low-complexity error-correcting codes on sparse graphs year: 2002 ident: ref39 – ident: ref37 doi: 10.1109/ISIT.2002.1023752 – start-page: 248 volume-title: Proc. 38th Annu. Allerton Conf. Communication, Computing and Control ident: ref31 article-title: Construction of LDPC codes using Ramanujan graphs and ideas from Margulis – ident: ref51 doi: 10.1109/ICC.2001.936269 – ident: ref29 doi: 10.1007/BF02126799 – volume: 24 start-page: 39 issue: 1 year: 1988 ident: ref28 article-title: Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators publication-title: Probl. Inf. Transm. – ident: ref17 doi: 10.1145/276698.276756 – ident: ref45 doi: 10.1109/18.556668 |
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| Snippet | We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an... |
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| SubjectTerms | Algorithms Applied sciences Bandwidth Codes Coding, codes Computer simulation Construction Entropy Exact sciences and technology Girth Graph representations Graphs Image coding Information systems Information theory Information, signal and communications theory Joints LDPC codes over low-density parity-check (LDPC) codes Lower bounds PEG Tanner graphs progressive edge growth (PEG) Random processes Rate distortion theory Signal and communications theory Signal processing Signal processing algorithms Speech processing Symbols Telecommunications and information theory Video compression |
| Title | Regular and irregular progressive edge-growth tanner graphs |
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