Minimum distance and pseudodistance lower bounds for generalised LDPC codes

Two different ways of obtaining generalised low-density parity-check (LDPC) codes are considered. Lower bounds on the minimum distance, stopping distance and pseudodistance are derived for these codes using graph-based analysis. These bounds are generalisations of Tanner's bit- and parity-oriented bound for simple (LDPC) codes. The new bounds are useful in predicting the performance of generalised LDPC codes under maximum-likelihood decoding, graph-based iterative decoding and linear programming decoding, and rely on the connectivity of the Tanner graph.

[1]  Deepak Sridhara,et al.  Eigenvalue bounds on the pseudocodeword weight of expander codes , 2007, Adv. Math. Commun..

[2]  Ralf Koetter,et al.  Lower bounds on the minimum pseudoweight of linear codes , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[3]  Daniel A. Spielman,et al.  Expander codes , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[4]  Niclas Wiberg,et al.  Codes and Decoding on General Graphs , 1996 .

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

[6]  Robert Michael Tanner,et al.  Minimum-distance bounds by graph analysis , 2001, IEEE Trans. Inf. Theory.

[7]  Wen-Ching Winnie Li,et al.  Characterizations of Pseudo-Codewords of LDPC Codes , 2005, ArXiv.

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

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

[10]  P. Vontobel,et al.  Graph-covers and iterative decoding of nite length codes , 2003 .

[11]  Richard M. Wilson,et al.  A course in combinatorics , 1992 .

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

[13]  Deepak Sridhara,et al.  Pseudocodewords of Tanner Graphs , 2005, IEEE Transactions on Information Theory.

[14]  Hong-Yeop Song,et al.  Generalization of Tanner's minimum distance bounds for LDPC codes , 2005, IEEE Communications Letters.

[15]  R. Koetter,et al.  On the Effective Weights of Pseudocodewords for Codes Defined on Graphs with Cycles , 2001 .

[16]  Heeralal Janwa,et al.  On Tanner Codes: Minimum Distance and Decoding , 2003, Applicable Algebra in Engineering, Communication and Computing.