p'); }, function () { return new ActiveXObject('Microsoft.XMLHTTP'); } ) || null; }, post: function (sUrl, sArgs, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { //alert(errmsg); } } }; xhr2.open('POST', encodeURI(sUrl), bAsync); xhr2.setRequestHeader('Content-Length', sArgs.length); xhr2.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded'); xhr2.send(sArgs); }, get: function (sUrl, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { alert(errmsg); } } }; xhr2.open('GET', encodeURI(sUrl), bAsync); xhr2.send('Null'); } } function SetSearchLink(item) { var url = "../journal/recordsearchinformation.aspx"; var skid = $(":hidden[id$=HiddenField_SKID]").val(); var args = "skid=" + skid; url = url + "?" + args + "&urllink=" + item; window.setTimeout("showSearchUrl('" + url + "')", 300); } function showSearchUrl(url) { var callback2 = function (xhr2) { } ajax2.get(url, true, callback2, "try"); }
JSIP> Vol.5 No.4, November 2014
Share This Article:
Cite This Paper >>

Tree Matrix Algorithm of LDPC Codes

Abstract Full-Text HTML XML Download Download as PDF (Size:2558KB) PP. 191-197
DOI: 10.4236/jsip.2014.54020    2,777 Downloads   3,471 Views   Citations
Author(s)    Leave a comment
Huanming Zhang

Affiliation(s)

Electronics and Information Engineering Institute, Foshan University, Foshan, China.

ABSTRACT

LDPC codes are finding increasing use in applications requiring reliable and highly efficient information transfer over bandwidth. An LDPC code is defined by a sparse parity-check matrix and can be described by a bipartite graph called Tanner graph. Loops in Tanner graph prevent the sum-product algorithm from converging. Further, loops, especially short loops, degrade the performance of LDPC decoder, because they affect the independence of the extrinsic information exchanged in the iterative decoding. This paper, by graph theory, deduces cut-node tree graph of LDPC code, and depicts it with matrix. On the basis of tree matrix algorithm, whole depictions of loops can be figured out, providing of foundation for further research of relations between loops and LDPC codes’ performance.

KEYWORDS

LDPC, Belief Propagation (BP), Graph, Iterative Decoding, Loop, Cycle

Cite this paper

Zhang, H. (2014) Tree Matrix Algorithm of LDPC Codes. Journal of Signal and Information Processing, 5, 191-197. doi: 10.4236/jsip.2014.54020.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Gallager, R.G. (1963) Low-Density Parity Check Codes. MIT Press, Cambridge.
[2] Mackay, D.J.C. (1999) Good Error-Correcting Codes Based on Very Sparse Matrices. IEEE Transactions on Information Theory, 45, 399-431. http://dx.doi.org/10.1109/18.748992
[3] Tanner, R.M. (1981) A Recursive Approach to Low Complexity Codes. IEEE Transactions on Information Theory, 27, 533-547. http://dx.doi.org/10.1109/TIT.1981.1056404
[4] Kschischang, R., Frey, B.J. and Loeliger, H.A. (2001) Factor Graphs and the Sum-Product Algorithm. IEEE Transactions on Information Theory, 47, 498-519. http://dx.doi.org/10.1109/18.910572
[5] Wiberg, N. (1996) Codes and Decoding on General Graphs, Linkoping Studies in Science and Technology. Ph.D. Dissertation, No. 440, Linkoping University, Linkoping.
[6] Reinhard, D. (1997) Graph Theory. Springer-Verlag, New York.
[7] Wainwright, M.J. (2007) Sparse Graph Codes for Side Information and Binning. IEEE Signal Processing Magazine, 47, 47-57.
[8] Forney Jr., G.D. (2001) Codes on Graphs: Normal Realizations. IEEE Transactions on Information Theory, 47, 520-548. http://dx.doi.org/10.1109/18.910573
[9] Loeliger, H.A. (2004) An Introduction to Factor Graph. IEEE Signal Processing Magazine, 28-41.
[10] Kschischang, F.R. (2003) Codes Defined on Graphs. IEEE Communications Magazine, 118-125.
[11] Vontobel, P.O. (2004) A Factor-Graph Approach to the Context-Tree Weighting Method. Proceedings of the Data Compression Conference (DCC’04), 571.
[12] Wainwright, M., Jaakkola, T. and Willsky, A. (2002) Tree-Based Reparameterization Analysis of Belief Propagation and Related Algorithms for Approximate Inference on Graphs with Cycles. ISIT2002, Lausanne, 30 June-5 July 2002.

  
comments powered by Disqus
JSIP Subscription
E-Mail Alert
JSIP Most popular papers
Publication Ethics & OA Statement
JSIP News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.