Low-rate generalized low-density parity-check codes with hadamard constraints

We consider the design and analysis of generalized low-density parity-check (GLDPC) codes specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that a rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10-5 at -1.44 dB, only 0.15 dB away from the ultimate Shannon limit (-1.592 dB)

[1]  J. Boutros,et al.  Generalized low density (Tanner) codes , 1999, 1999 IEEE International Conference on Communications (Cat. No. 99CH36311).

[2]  Stephan ten Brink,et al.  Extrinsic information transfer functions: A model and two properties , 2002 .

[3]  Guosen Yue,et al.  IRA code design for MIMO systems with iterative receivers , 2004, First International Symposium on Control, Communications and Signal Processing, 2004..

[4]  Daniel A. Spielman,et al.  Analysis of low density codes and improved designs using irregular graphs , 1998, STOC '98.

[5]  Michael Tuchler,et al.  EXIT charts of irregular codes , 2002 .

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

[7]  Stephan ten Brink,et al.  Convergence behavior of iteratively decoded parallel concatenated codes , 2001, IEEE Trans. Commun..

[8]  Michael Lentmaier,et al.  On generalized low-density parity-check codes based on Hamming component codes , 1999, IEEE Communications Letters.

[9]  Stephan ten Brink,et al.  Extrinsic information transfer functions: model and erasure channel properties , 2004, IEEE Transactions on Information Theory.

[10]  Michael Lentmaier,et al.  Iterative decoding of generalized low-density parity-check codes , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[11]  Stephan ten Brink,et al.  Design of low-density parity-check codes for modulation and detection , 2004, IEEE Transactions on Communications.

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