Decoding performance of binary and non-binary LDPC codes for IEEE 802.11n standard

LDPC codes, a kind of error correcting codes, performs near Shannon limit and are recommended for many practical applications. Non-binary LDPC codes excels binary LDPC in error correcting property especially for short and moderate block length. Construction of parity check matrix for IEEE 802.11n standard non-binary LDPC code has been done here. Comparison of binary LDPC and non-binary LDPC codes for IEEE 802.11n standard based on their decoding performance for probability domain and log domain decoding algorithms which has not been made so far is done in this paper. Decoding performance measured in terms of bit error rate and frame error rate shows that the non-binary codes outperforms binary codes for 802.11n LDPC with increasing order of Galois field.

[1]  Pierre Penard,et al.  A comparison study of binary and non-binary LDPC codes decoding , 2010, SoftCOM 2010, 18th International Conference on Software, Telecommunications and Computer Networks.

[2]  David Declercq,et al.  Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ , 2007, IEEE Transactions on Communications.

[3]  C. Spagnol,et al.  Hardware Implementation of ${\rm GF}(2^{m})$ LDPC Decoders , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  C. Spagnol,et al.  Hardware Implementation of LDPC Decoders , 2009 .

[5]  T. Moon Error Correction Coding: Mathematical Methods and Algorithms , 2005 .

[6]  D. Mackay,et al.  Low density parity check codes over GF(q) , 1998, 1998 Information Theory Workshop (Cat. No.98EX131).

[7]  R. Townsend,et al.  Self-orthogonal quasi-cyclic codes , 1967, IEEE Trans. Inf. Theory.

[8]  Valentin Savin,et al.  Min-Max decoding for non binary LDPC codes , 2008, 2008 IEEE International Symposium on Information Theory.

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

[10]  Patrick Fitzpatrick,et al.  Algebraic structure of quasicyclic codes , 2001, Discret. Appl. Math..

[11]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

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