Improving the Performance of Protograph LDPC Codes by Using Different Transmission Energies

Irregular low-density parity-check (LDPC) codes constructed from small protographs are one of the most powerful LDPC codes. In this paper, we show that the performance of LDPC codes based on small protographs can be further improved by using different transmission energies for every variable node of the protograph. Thus, a protograph is now described by a set of variable nodes, a set of check nodes, edges connecting variable nodes and check nodes, and the transmission energy used for every variable node, which is called the energy distribution. We optimize the energy distribution of protographs by choosing the energy distribution with the highest threshold calculated with a generalization of the discretized density evolution. Furthermore, we show by simulations that the performance of long LDPC codes based on protographs can be improved as expected from the thresholds.

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

[2]  Lars K. Rasmussen,et al.  Multiple parallel concatenated codes with optimal puncturing and energy distribution , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[3]  Dariush Divsalar,et al.  Construction of Protograph LDPC Codes with Linear Minimum Distance , 2006, 2006 IEEE International Symposium on Information Theory.

[4]  Johannes B. Huber,et al.  Design of \Multiple{Turbo{Codes" with Transfer Characteristics of Component Codes , 2002 .

[5]  D. Divsalar,et al.  Multiple turbo codes for deep-space communications , 1995 .

[6]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[7]  Kenta Kasai,et al.  Detailedly Represented Irregular Low-Density Parity-Check Codes , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[8]  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).

[9]  Sae-Young Chung,et al.  On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit , 2001, IEEE Communications Letters.

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

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

[12]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[13]  Martin Bossert,et al.  Optimized Asymptotic Puncturing Distributions for Different LDPC Code Constructions , 2006, 2006 IEEE International Symposium on Information Theory.

[14]  J. Thorpe.  Low-Density Parity-Check (LDPC) Codes Constructed from Protographs , 2003 .

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