On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm

The iterative bit flipping algorithm is applied to the standard regular low-density parity-check (LDPC) code ensemble. In the past, it was shown, for a typical code in the ensemble with left degree at least five and block length sufficiently large, that this algorithm can correct a linear (in the block length) number of worst case errors. In this paper, this result is extended to the case where the left degree is at least four. For the case where the left degree is larger than four, an improvement, compared to existing results, of several orders of magnitude is obtained on the fraction of worst case errors that can be corrected. It is also shown how the results can be further improved when random errors produced by the channel (as opposed to worst case errors) are considered.

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

[2]  David Burshtein.  On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm , 2008, IEEE Trans. Inf. Theory.

[3]  Daniel A. Spielman,et al.  Efficient erasure correcting codes , 2001, IEEE Trans. Inf. Theory.

[4]  Martin J. Wainwright,et al.  LP Decoding Corrects a Constant Fraction of Errors , 2004, IEEE Transactions on Information Theory.

[5]  David Burshtein,et al.  Nondirect convergence radius and number of iterations of the Hopfield associative memory , 1994, IEEE Trans. Inf. Theory.

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

[7]  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).

[8]  D. Burshtein,et al.  Bounds on the performance of belief propagation decoding , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[9]  D. Spielman,et al.  Expander codes , 1996 .

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

[11]  Alexandros G. Dimakis,et al.  Probabilistic Analysis of Linear Programming Decoding , 2007, IEEE Transactions on Information Theory.

[12]  Martin J. Wainwright,et al.  Using linear programming to Decode Binary linear codes , 2005, IEEE Transactions on Information Theory.

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

[14]  D. Burshtein,et al.  Upper bounds on the rate of LDPC codes , 2002, Proceedings IEEE International Symposium on Information Theory,.

[15]  David Burshtein,et al.  Asymptotic enumeration methods for analyzing LDPC codes , 2004, IEEE Transactions on Information Theory.

[16]  David Burshtein,et al.  Expander graph arguments for message-passing algorithms , 2001, IEEE Trans. Inf. Theory.

[17]  Michael Lentmaier,et al.  An analysis of the block error probability performance of iterative decoding , 2005, IEEE Transactions on Information Theory.