Towards improved LDPC code designs using absorbing set spectrum properties

This paper focuses on methods for a systematic modification of the parity check matrix of regular LDPC codes for improved performance in the low BER region (i.e., the error floor). A judicious elimination of dominant absorbing sets strictly improves the absorbing set spectrum and thereby improves the code performance. This absorbing set elimination is accomplished without compromising code properties and parameters such as the girth, node degree, and the structure of the parity check matrix. For a representative class of practical codes we substantiate theoretical analysis with experimental results obtained in the low BER region. Our results demonstrate at least an order of magnitude improvement of the error floor relative to the original code designs. Given that the conventional code parameters remain intact, the new code can easily be implemented on the existing software or hardware platforms employing high-throughput, compact architectures. As such, the proposed approach provides a step towards the improved code design that is compatible with practical implementation constraints.

[1]  Alon Orlitsky,et al.  Stopping set distribution of LDPC code ensembles , 2003, IEEE Transactions on Information Theory.

[2]  A.I.V. Casado,et al.  Improving LDPC Decoders via Informed Dynamic Scheduling , 2007, 2007 IEEE Information Theory Workshop.

[3]  David Declercq,et al.  Trapping set enumerators for specific LDPC codes , 2010, 2010 Information Theory and Applications Workshop (ITA).

[4]  Bane Vasic,et al.  Coding and Signal Processing for Magnetic Recording Systems , 2004 .

[5]  Lara Dolecek,et al.  Lowering LDPC Error Floors by Postprocessing , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[6]  Naresh R. Shanbhag,et al.  High-throughput LDPC decoders , 2003, IEEE Trans. Very Large Scale Integr. Syst..

[7]  Shuai Zhang,et al.  On the dynamics of the error floor behavior in regular LDPC codes , 2009, 2009 IEEE Information Theory Workshop.

[8]  Jörg Kliewer,et al.  Trapping set enumerators for repeat multiple accumulate code ensembles , 2009, 2009 IEEE International Symposium on Information Theory.

[9]  WangZhongfeng,et al.  Low-complexity high-speed decoder design for quasi-cyclic LDPC codes , 2007 .

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

[11]  Jun Heo,et al.  Two-staged informed dynamic scheduling for sequential belief propagation decoding of LDPC codes , 2009, IEEE Communications Letters.

[12]  Shashi Kiran Chilappagari,et al.  Eliminating trapping sets in low-density parity-check codes by using Tanner graph covers , 2008, IEEE Transactions on Information Theory.

[13]  Simon Litsyn,et al.  Decreasing error floor in LDPC codes by parity-check matrix extensions , 2009, 2009 IEEE International Symposium on Information Theory.

[14]  Lara Dolecek,et al.  Analysis of Absorbing Sets and Fully Absorbing Sets of Array-Based LDPC Codes , 2009, IEEE Transactions on Information Theory.

[15]  Shu Lin,et al.  Error Control Coding , 2004 .

[16]  Daniel J. Costello,et al.  LDPC block and convolutional codes based on circulant matrices , 2004, IEEE Transactions on Information Theory.

[17]  B. Vasic,et al.  Trapping set ontology , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[18]  David J. C. MacKay,et al.  Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check cCodes , 2003, MFCSIT.

[19]  Lara Dolecek,et al.  On absorbing sets of structured sparse graph codes , 2010, 2010 Information Theory and Applications Workshop (ITA).

[20]  Lara Dolecek,et al.  Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices , 2009, IEEE Transactions on Communications.

[21]  Tor Helleseth,et al.  On the minimum distance of array codes as LDPC codes , 2003, IEEE Trans. Inf. Theory.

[22]  Navin Kashyap,et al.  Shortened Array Codes of Large Girth , 2005, IEEE Transactions on Information Theory.

[23]  Emre Telatar,et al.  Finite-length analysis of low-density parity-check codes on the binary erasure channel , 2002, IEEE Trans. Inf. Theory.

[24]  N. Varnica,et al.  Improvements in belief-propagation decoding based on averaging information from decoder and correction of clusters of nodes , 2006, IEEE Communications Letters.

[25]  Thomas J. Richardson,et al.  Error Floors of LDPC Codes , 2003 .

[26]  Lara Dolecek,et al.  GEN03-6: Investigation of Error Floors of Structured Low-Density Parity-Check Codes by Hardware Emulation , 2006, IEEE Globecom 2006.

[27]  O. Milenkovic,et al.  Algorithmic and combinatorial analysis of trapping sets in structured LDPC codes , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

[28]  David G. M. Mitchell,et al.  Trapping set analysis of protograph-based LDPC convolutional codes , 2009, 2009 IEEE International Symposium on Information Theory.

[29]  Johannes B. Huber,et al.  CTH02-4: When Does One Redundant Parity-Check Equation Matter? , 2006, IEEE Globecom 2006.