Numerical issues affecting LDPC error floors

Numerical issues related to the occurrence of error floors in floating-point simulations of belief propagation (BP) decoders are examined. Careful processing of messages corresponding to highly-certain bit values can sometimes reduce error floors by several orders of magnitude. Computational solutions for properly handling such messages are provided for the sum-product algorithm (SPA) and several variants.

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

[2]  William Ryan,et al.  Channel Codes by William Ryan , 2009 .

[3]  Jing Sun Studies on graph-based coding systems , 2004 .

[4]  Paul H. Siegel,et al.  Quantized min-sum decoders with low error floor for LDPC codes , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[5]  James Demmel,et al.  IEEE Standard for Floating-Point Arithmetic , 2008 .

[6]  David J. C. MacKay,et al.  Encyclopedia of Sparse Graph Codes , 1999 .

[7]  Rüdiger L. Urbanke,et al.  Modern Coding Theory , 2008 .

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

[9]  Alexander Vardy,et al.  Which codes have cycle-free Tanner graphs? , 1999, IEEE Trans. Inf. Theory.

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

[11]  Ajay Dholakia,et al.  Efficient implementations of the sum-product algorithm for decoding LDPC codes , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[12]  Martin Bossert,et al.  Optimization of a reduced-complexity decoding algorithm for LDPC codes by density evolution , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[13]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .

[14]  Achilleas Anastasopoulos,et al.  A comparison between the sum-product and the min-sum iterative detection algorithms based on density evolution , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[15]  Paul H. Siegel,et al.  Error floor approximation for LDPC codes in the AWGN channel , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[16]  Jinghu Chen,et al.  Density evolution for BP-based decoding algorithms of LDPC codes and their quantized versions , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[17]  William E. Ryan,et al.  Low-floor decoders for LDPC codes , 2009, IEEE Transactions on Communications.

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

[19]  William Ryan,et al.  Channel Codes: Classical and Modern , 2009 .

[20]  Vincent C. Gaudet,et al.  Soft-bit decoding of regular low-density parity-check codes , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.