Fast Min-Sum Algorithms for Decoding of LDPC over GF(q)

In this paper, we present a fast min-sum algorithm for decoding LDPC codes over GF(q). Our algorithm is different from the one presented by David Declercq and Marc Fossorier (2005) only at the way of speeding up the horizontal scan in the min-sum algorithm. The Declercq and Fossorier's algorithm speeds up the computation by reducing the number of configurations, while our algorithm uses the dynamic programming instead. Compared with the configuration reduction algorithm, the dynamic programming one is simpler at the design stage because it has less parameters to tune. Furthermore, it does not have the performance degradation problem caused by the configuration reduction because it searches the whole configuration space efficiently through dynamic programming. Both algorithms have the same level of complexity and use simple operations which are suitable for hardware implementations

[1]  Stig K. Andersen,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

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

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

[4]  Jr. G. Forney,et al.  The viterbi algorithm , 1973 .

[5]  Jinghu Chen,et al.  Reduced complexity decoding algorithms for low-density parity check codes and turbo codes , 2003 .

[6]  D. Declercq,et al.  Fast Decoding Algorithm for LDPC over GF(2q) , 2003 .

[7]  David J. C. MacKay,et al.  Good Codes Based on Very Sparse Matrices , 1995, IMACC.

[8]  David J. C. MacKay,et al.  Low-density parity check codes over GF(q) , 1998, IEEE Communications Letters.

[9]  Xiaofei Huang,et al.  COOPERATIVE OPTIMIZATION FOR SOLVING LARGE SCALE COMBINATORIAL PROBLEMS , 2004 .

[10]  Xiaofei Huang,et al.  Near perfect decoding of LDPC codes , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

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

[12]  David Declercq,et al.  Extended MinSum Algorithm for Decoding LDPC Codes over GF ( q ) , .

[13]  Henk Wymeersch,et al.  Log-domain decoding of LDPC codes over GF(q) , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[14]  David Declercq,et al.  Extended minsum algorithm for decoding LDPC codes over GF(/sub q/ , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[15]  Hideki Imai,et al.  Reduced complexity iterative decoding of low-density parity check codes based on belief propagation , 1999, IEEE Trans. Commun..

[16]  David Declercq,et al.  Fast decoding algorithm for LDPC over GF(2/sup q/) , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

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

[18]  D. Mackay,et al.  Low-Density Parity Check Codes over , 1998 .