Low-Density Parity-Check Codes: Construction and Implementation

Low-Density Parity-Check Codes: Construction and Implementation

[1]  Adnan Aziz,et al.  Synthesizing interconnect-efficient low density parity check codes , 2004, Proceedings. 41st Design Automation Conference, 2004..

[2]  G. Richter,et al.  An Improvement of the PEG Algorithm for LDPC Codes in the Waterfall Region , 2005, EUROCON 2005 - The International Conference on "Computer as a Tool".

[3]  Frank R. Kschischang,et al.  Multi-Gbit/sec low density parity check decoders with reduced interconnect complexity , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[4]  Lei Yang,et al.  Code construction and FPGA implementation of a low-error-floor multi-rate low-density Parity-check code decoder , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Geoffrey Exoo A Simple Method for Constructing Small Cubic Graphs of Girths 14, 15, and 16 , 1996, Electron. J. Comb..

[6]  V. Benes Optimal rearrangeable multistage connecting networks , 1964 .

[7]  Joseph R. Cavallaro,et al.  Semi-parallel reconfigurable architectures for real-time LDPC decoding , 2004, International Conference on Information Technology: Coding and Computing, 2004. Proceedings. ITCC 2004..

[8]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[9]  A. J. Blanksby,et al.  A 690-mW 1-Gb/s 1024-b, rate-1/2 low-density parity-check code decoder , 2001, IEEE J. Solid State Circuits.

[10]  G. Malema,et al.  Very Large Girth Column-weight two Quasi-cyclic LDPC Codes , 2006, 2006 8th international Conference on Signal Processing.

[11]  G. Malema,et al.  Programmable low-density parity-check decoder , 2004, Proceedings of 2004 International Symposium on Intelligent Signal Processing and Communication Systems, 2004. ISPACS 2004..

[12]  Nae-Soo Kim,et al.  Complexity‐Reduced Algorithms for LDPC Decoder for DVB‐S2 Systems , 2005 .

[13]  Nenad Miladinovic,et al.  Systematic recursive construction of LDPC codes , 2004, IEEE Communications Letters.

[14]  D. Mackay,et al.  Evaluation of Gallager Codes for Short Block Length and High Rate Applications , 2001 .

[15]  Norman Biggs,et al.  Constructions for Cubic Graphs with Large Girth , 1998, Electron. J. Comb..

[16]  Li Ping,et al.  Decoding low density parity check codes with finite quantization bits , 2000, IEEE Communications Letters.

[17]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[18]  Urs Niesen,et al.  Grouping-and-shifting designs for structured LDPC codes with large girth , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[19]  Venkat Anantharam,et al.  Iterative decoder architectures , 2003, IEEE Commun. Mag..

[20]  R. M. Tanner,et al.  A Class of Group-Structured LDPC Codes , 2001 .

[21]  Amir H. Banihashemi,et al.  A heuristic search for good low-density parity-check codes at short block lengths , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[22]  Hongwei Song,et al.  Large girth cycle codes for partial response channels , 2004, IEEE Transactions on Magnetics.

[23]  Evangelos Eleftheriou,et al.  Progressive edge-growth Tanner graphs , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[24]  I. Djordjevic,et al.  High code rate low-density parity-check codes for optical communication systems , 2004, IEEE Photonics Technology Letters.

[25]  Sarah J. Johnson,et al.  Regular low-density parity-check codes from combinatorial designs , 2001, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).

[26]  D.E. Hocevar,et al.  A reduced complexity decoder architecture via layered decoding of LDPC codes , 2004, IEEE Workshop onSignal Processing Systems, 2004. SIPS 2004..

[27]  Tong Zhang,et al.  Design of VLSI implementation-oriented LDPC codes , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[28]  Keshab K. Parhi,et al.  Overlapped message passing for quasi-cyclic low-density parity check codes , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Payam Pakzad,et al.  Abstract—two Decoding Schedules and the Corresponding Serialized Architectures for Low-density Parity-check (ldpc) , 2001 .

[30]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[31]  Krishna R. Narayanan,et al.  Memory-efficient sum-product decoding of LDPC codes , 2004, IEEE Transactions on Communications.

[32]  A. Blanksby,et al.  A 690-mW 1-Gb/s 1024-b, rate-1/2 low-density parity-check code decoder , 2001, IEEE J. Solid State Circuits.

[33]  Felix Lazebnik,et al.  Explicit Construction of Graphs with an Arbitrary Large Girth and of Large Size , 1995, Discret. Appl. Math..

[34]  Alexander Vardy,et al.  The intractability of computing the minimum distance of a code , 1997, IEEE Trans. Inf. Theory.

[35]  Todd K. Moon,et al.  Introduction to Low-Density Parity-Check Codes , 2003, Fundamentals of Classical and Modern Error-Correcting Codes.

[36]  Yu-Cheng He,et al.  Fast decoding of LDPC codes using quantisation , 2002 .

[37]  Kyeongcheol Yang,et al.  Quasi-cyclic LDPC codes for fast encoding , 2005, IEEE Transactions on Information Theory.

[38]  Sarah J. Johnson,et al.  Construction of low-density parity-check codes from Kirkman triple systems , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[39]  Sae-Young Chung,et al.  On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit , 2001, IEEE Communications Letters.

[40]  Yanni Chen,et al.  A FPGA and ASIC implementation of rate 1/2, 8088-b irregular low density parity check decoder , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[41]  Michael Liebelt,et al.  High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs , 2007, EURASIP J. Wirel. Commun. Netw..

[42]  Yufei Wu,et al.  Forward computation of backward path metrics for MAP decoder , 2000, VTC2000-Spring. 2000 IEEE 51st Vehicular Technology Conference Proceedings (Cat. No.00CH37026).

[43]  Rajeev Motwani,et al.  Optimizing iterative decoding of low-density parity check codes on programmable pipelined parallel architectures , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[44]  Khaled A. S. Abdel-Ghaffar,et al.  On algebraic construction of Gallager and circulant low-density parity-check codes , 2004, IEEE Transactions on Information Theory.

[45]  Michael Liebelt,et al.  Low Complexity Regular LDPC codes for Magnetic Storage Devices , 2007, IEC.

[46]  Pak-Ken Wong,et al.  Cages - a survey , 1982, J. Graph Theory.

[47]  Rüdiger L. Urbanke,et al.  Design of capacity-approaching irregular low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[48]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[49]  Sarah J. Johnson,et al.  A family of irregular LDPC codes with low encoding complexity , 2003, IEEE Communications Letters.

[50]  Zongwang Li,et al.  Efficient encoding of quasi-cyclic low-density parity-check codes , 2006, IEEE Trans. Commun..

[51]  M. Meringer Fast generation of regular graphs and construction of cages , 1999, Journal of Graph Theory.

[52]  B. V. K. Vijaya Kumar,et al.  Low complexity LDPC codes for partial response channels , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[53]  Tong Zhang,et al.  On finite precision implementation of low density parity check codes decoder , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[54]  Samuel Dolinar,et al.  A scalable architecture of a structured LDPC decoder , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[55]  Claude E. Shannon,et al.  A Mathematical Theory of Communications , 1948 .

[56]  Norman Biggs Cubic Graphs with Large Girth , 1989 .

[57]  G. Malema Constructing Quasi-Cyclic LDPC codes Using a Search Algorithm , 2007, 2007 IEEE International Symposium on Signal Processing and Information Technology.

[58]  J. Moura,et al.  Structured low-density parity-check codes , 2004, IEEE Signal Processing Magazine.

[59]  T. Richardson,et al.  Design of provably good low-density parity check codes , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[60]  Amin Shokrollahi,et al.  An Introduction to Low-Density Parity-Check Codes , 2000, Theoretical Aspects of Computer Science.

[61]  Hongwei Song,et al.  Low-density parity check codes for partial response channels , 2004, IEEE Signal Process. Mag..

[62]  Marc P. C. Fossorier,et al.  Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices , 2004, IEEE Trans. Inf. Theory.

[63]  Naresh R. Shanbhag,et al.  Memory-efficient turbo decoder architectures for LDPC codes , 2002, IEEE Workshop on Signal Processing Systems.

[64]  D. König Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre , 1916 .

[65]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[66]  Suresh Sivakumar VLSI implementation of encoder and decoder for low-density parity-check codes , 2001 .

[67]  Ajay Dholakia,et al.  Reduced-complexity decoding algorithm for low-density parity-check codes , 2001 .

[68]  Joseph R. Cavallaro,et al.  Tradeoff Analysis and Architecture Design of High Throughput Irregular LDPC Decoders , 2006 .

[69]  In-Cheol Park,et al.  Scheduling algorithm for partially parallel architecture of LDPC decoder by matrix permutation , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[70]  Tiffany Jing Li,et al.  A Class of High-rate, Low-complexity, Well- structured LDPC Codes from Combinatorial Designs and their Applications on ISI Channels , 2002, Communications, Internet, and Information Technology.

[71]  L. Goldberg Abstract , 2003 .

[72]  Rüdiger L. Urbanke,et al.  Efficient encoding of low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[73]  G. Malema,et al.  Interconnection Network for Structured Low-Density Parity-Check Decoders , 2005, 2005 Asia-Pacific Conference on Communications.

[74]  E. Cuthill,et al.  Reducing the bandwidth of sparse symmetric matrices , 1969, ACM '69.

[75]  S. Litsyn,et al.  An efficient message-passing schedule for LDPC decoding , 2004, 2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel.

[76]  Joseph R. Cavallaro,et al.  On Turbo-Schedules for LDPC Decoding , 2006 .

[77]  Daniel A. Spielman,et al.  Improved low-density parity-check codes using irregular graphs and belief propagation , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[78]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[79]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

[80]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[81]  Bane V. Vasic,et al.  Structured iteratively decodable codes based on Steiner systems and their application in magnetic recording , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[82]  E.M. Kurtas,et al.  The search for a practical iterative detector for magnetic recording , 2004, IEEE Transactions on Magnetics.

[83]  Shu Lin,et al.  Low density parity check codes: construction based on finite geometries , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[84]  M. E. O'Sullivan,et al.  Algebraic construction of sparse matrices with large girth , 2006, IEEE Transactions on Information Theory.

[85]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

[86]  Kohichi Sakaniwa,et al.  Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[87]  Keshab K. Parhi,et al.  High throughput overlapped message passing for low density parity check codes , 2003, GLSVLSI '03.

[88]  J. Villasenor,et al.  Approximate-MIN constraint node updating for LDPC code decoding , 2003, IEEE Military Communications Conference, 2003. MILCOM 2003..

[89]  Mustafa Eroz,et al.  DVB‐S2 low density parity check codes with near Shannon limit performance , 2004, Int. J. Satell. Commun. Netw..

[90]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[91]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[92]  William J. Dally,et al.  Imagine: Media Processing with Streams , 2001, IEEE Micro.

[93]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[94]  Stephen B. Wicker,et al.  Fundamentals of Codes, Graphs, and Iterative Decoding , 2002 .

[95]  Hua Xiao,et al.  Improved progressive-edge-growth (PEG) construction of irregular LDPC codes , 2004, IEEE Communications Letters.

[96]  S. Wicker Error Control Systems for Digital Communication and Storage , 1994 .

[97]  Dharmendra S. Modha,et al.  Extended bit-filling and LDPC code design , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[98]  Dharmendra S. Modha,et al.  Designing LDPC codes using bit-filling , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[99]  Shu Lin,et al.  Near-Shannon-limit quasi-cyclic low-density parity-check codes , 2003, IEEE Transactions on Communications.

[100]  Samuel Dolinar,et al.  Encoders for block-circulant LDPC codes , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[101]  Raymond K. Kostuk,et al.  Low-density parity check codes and iterative decoding for long-haul optical communication systems , 2003 .

[102]  Payam Pakzad,et al.  VLSI architectures for iterative decoders in magnetic recording channels , 2001 .

[103]  Euncheol Kim,et al.  LDPC Code for Reduced Routing Decoder , 2005, 2005 Asia-Pacific Conference on Communications.