Non‐binary protograph low‐density parity‐check codes for space communications

SUMMARY Protograph-based non-binary low-density parity-check (LDPC) codes with ultra-sparse parity-check matrices are compared with binary LDPC and turbo codes (TCs) from space communication standards. It is shown that larger coding gains are achieved, outperforming the binary competitors by more than 0.3dB on the additive white Gaussian noise channel (AWGN). In the short block length regime, the designed codes gain more than 1dB with respect to the binary protograph LDPC codes recently proposed for the next generation up-link standard of the Consultative Committee for Space Data Systems. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  Pedro Velez-Belchi.  Interaction channel for satellite distribution systems , 2000 .

[2]  Marco Chiani,et al.  Turbo Codes Based on Time-Variant Memory-1 Convolutional Codes over Fq , 2011, 2011 IEEE International Conference on Communications (ICC).

[3]  Dariush Divsalar,et al.  The Development of Turbo and LDPC Codes for Deep-Space Applications , 2007, Proceedings of the IEEE.

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

[5]  D. Mackay,et al.  Evaluation of Gallager Codes for Short Block Length and High Rate Applications , 2001 .

[6]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[7]  Dariush Divsalar,et al.  Accumulate repeat accumulate codes , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[8]  Yifei Zhang,et al.  Structured IRA Codes: Performance Analysis and Construction , 2007, IEEE Transactions on Communications.

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

[10]  David Declercq,et al.  Low-complexity decoding for non-binary LDPC codes in high order fields , 2010, IEEE Transactions on Communications.

[11]  William Ryan,et al.  Channel Codes by William Ryan , 2009 .

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

[13]  Marco Chiani,et al.  On the performance of moderate-length non-binary LDPC codes for space communications , 2010, 2010 5th Advanced Satellite Multimedia Systems Conference and the 11th Signal Processing for Space Communications Workshop.

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

[15]  Theodore S. Rappaport,et al.  5.85-GHz radio path loss and penetration loss measurements in and around homes and trees , 1998, IEEE Communications Letters.

[16]  David Declercq,et al.  Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images , 2008, IEEE Transactions on Communications.

[17]  William E. Ryan,et al.  Design of efficiently encodable moderate-length high-rate irregular LDPC codes , 2004, IEEE Transactions on Communications.

[18]  William E. Ryan,et al.  Quasi-cyclic generalized ldpc codes with low error floors , 2007, IEEE Transactions on Communications.

[19]  Gianluigi Liva,et al.  Graph-Based Analysis and Optimization of Contention Resolution Diversity Slotted ALOHA , 2011, IEEE Transactions on Communications.

[20]  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).

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

[22]  Riccardo De Gaudenzi,et al.  Advances in Random Access protocols for satellite networks , 2009, 2009 International Workshop on Satellite and Space Communications.

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

[24]  Marco Chiani,et al.  High Throughput Random Access via Codes on Graphs: Coded Slotted ALOHA , 2011, 2011 IEEE International Conference on Communications (ICC).

[25]  Marco Chiani,et al.  Channel Coding for Future Space Missions: New Requirements and Trends , 2007, Proceedings of the IEEE.

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

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

[28]  Riccardo De Gaudenzi,et al.  Advances in Random Access protocols for satellite networks , 2009 .

[29]  David Declercq,et al.  Rate-compatible non-binary LDPC codes concatenated with multiplicative repetition codes , 2010, 2010 IEEE International Symposium on Information Theory.

[30]  M. Fossorier,et al.  Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images , 2008, IEEE Transactions on Communications.

[31]  Claude Berrou,et al.  Improving the distance properties of turbo codes using a third component code: 3D turbo codes - [transactions letters] , 2009, IEEE Transactions on Communications.

[32]  Stefano Cioni,et al.  The very short frame of mobile DVB‐RCS: Code design and QoS Performance , 2010, Int. J. Satell. Commun. Netw..

[33]  William Ryan,et al.  Channel Codes: Classical and Modern , 2009 .

[34]  Riccardo De Gaudenzi,et al.  Contention Resolution Diversity Slotted ALOHA (CRDSA): An Enhanced Random Access Schemefor Satellite Access Packet Networks , 2007, IEEE Transactions on Wireless Communications.

[35]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[36]  Dariush Divsalar,et al.  Short Protograph-Based LDPC Codes , 2007, MILCOM 2007 - IEEE Military Communications Conference.

[37]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[38]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .