Performances of Chaos Coded Modulation Schemes Based on Mod-MAP Mapping and High Dimensional LDPC Based Mod-MAP Mapping with Belief Propagation

Naim Khodor, Jean-pierre Cances, Vahid Meghdadi, Raymond Quere

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DOI: 10.4236/ijcns.2010.36067                

Abstract

In this paper, we propose to generalize the coding schemes first proposed by Kozic & al to high spectral efficient modulation schemes. We study at first Chaos Coded Modulation based on the use of small dimensional modulo-MAP encoding process and we give a solution to study the distance spectrum of such coding schemes to accurately predict their performances. However, the obtained performances are quite poor. To improve them, we use then a high dimensional modulo-MAP mapping process similar to the low-density generator-matrix codes (LDGM) introduced by Kozic & al. The main difference with their work is that we use an encoding and decoding process on GF (2m) which enables to obtain better performances while preserving a quite simple decoding algorithm when we use the Extended Min-Sum (EMS) algorithm of Declercq & Fossorier.

Keywords

Chaos Coded Modulation, Expectation Maximization, Gaussian or Rayleigh Mixtures, Low-Density Parity-Check (LDPC), Low-Density Generator-Matrix (LDGM), Factor Graph, Extended Min-Sum (EMS)

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. R. Frey, “Chaotic Digital Encoding: An Approach to Secure Communication,” IEEE Transactions on Circuits and Systems II, Vol. 40, No. 10, 1993, pp. 660-666.
[2]	A. Layec, “Développement de modèles de CAO pour la simulation système des systèmes de communication. Application aux communications chaotiques,” Ph.D. Thesis, Xlim University of Limoges, 2006.
[3]	F. J. Escribano, L. Lopez, M. A. F. Sanjuan, “Evaluation of Channel Coding And Decoding Algorithms Using Discrete Chaotic Maps,” Chaos, American Institute of Physics, Issue 16, 2006, pp. 1054-1500.
[4]	I. P. Marino, L. Lopez, M. A. F. Sanjuan, “Channel Coding in Communications Using Chaos,” Physics Letters Elsevier Science, Vol. 295, No. 4, 2002, pp. 185-191,
[5]	E. Bollt, Y. C. Lai, C. Grebogi, “Channel Channel Capacity and Noise Resistance in Communicating with Chaos,” Physical Review Letters American Physical Society, Vol. 79, No. 19, pp. 3787-3790.
[6]	T. Schimming and M. Hasler, “Coded Modulation Based On Controlled 1-D And 2-D Piecewise Linear Chaotic Maps,” IEEE International Symposium on Circuits and Systems (ISCAS), pp. 762-765.
[7]	B. Chen and G. W. Wornel, “Analog Error Correcting Codes Based on Chaotical Dynamical Systems,” IEEE Transactions on Communications, Vol. 46, No. 7, pp. 881-890.
[8]	T. Erseghe and N. Bramante, “Pseudo Chaotic Encoding Applied to Ultra-Wide-Band Impulse Radio,” IEEE Vehicular Technology Conference, Vancouver, Sept. 2002, pp.1711-1715.
[9]	J. Lee, C. Lee and D. B. Williams, “Secure Communi- cations Using Chaos,” IEEE Globecom’95, Singapore, Nov. 1995, pp. 1183-1187.
[10]	J. Lee, S. Choi, and D. Hong, “Secure Communications Using a Chaos System in a Mobile Channel,” IEEE Globecom’98, Sydney, Nov. 1998. pp. 2520- 2525.
[11]	C. Lee and D. B. Williams, “A Noise Reduction Method for Chaotic Signals,” 44th IEEE Acoustic, Sensor and Signal Processing Conference (ICASSP), Detroit, May 1995, pp.1348–1351.
[12]	A. M. Guidi, “Turbo and LDPC Coding for the AWGN and Space-Time Channel,” Ph.D. Thesis, University of South Australia, South Australia, June 2006.
[13]	S. A. Barbulescu, A. Guidi and S. S. Pietrobon, “Chaotic Turbo Codes,” IEEE Conference International Sympo- sium on Information Theory (ISIT), June 2000, pp. 123.
[14]	X. L. Zhou, J. B. Liu, W. T. Song and H. W. Luo, “Chaotic Turbo Codes in Secure Communications,” Conference EUROCON’2001, International Conference on Trends in Communications, July 2001, pp. 199-201.
[15]	A. Abel and W. Schwarz, “Chaos Communications- Principles, Schemes, and System Analysis,” Proceedings of the IEEE, Vol. 90, No. 5, May 2002, pp. 691-710.
[16]	W. M. Tam, F. C. M. Lau and C. K. Tse, “Digital Communications with Chaos,” Elsevier, Oxford, 2007.
[17]	S. Kozic, K. Oshima and T. Schimming, “How to Repair CSK Using Small Perturbation Control-Case Study and Performance Analysis,” Proceedings of ECCTD, Krakow, Aug. 2003.
[18]	Y. S. Lau, Z. M. Hussain, “A New Approach in Chaos Shift Keying for Secure Communication,” Proceedings of the third International Conference on Information Tech- nology and Applications (ICITA’05), Sydney, pp. 630- 633.
[19]	H. Dedieu, M. P. Kennedy and M. Hasler, “Chaos Shift Keying: Modulation and Demodulation of a Chaotic Carrier Using Self-Synchronizing Chua’s Circuits,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 40, No. 10, 1993, pp. 634-642.
[20]	J. Schweitzer, “The Performance of Chaos Shift Keying: Synchronization Versus Symbolic Backtracking,” Pro- ceedings of the IEEE International Symposium on Cir- cuits and Systems (ISCAS), Monterey, 1998, pp. 469- 472.
[21]	F. J. Escribano, L. Lopez and M. A. F. Sanjuan, “Parallel Concatenated Chaos Coded Modulations,” IEEE Con- ference 15th International Conference on Software, Tele- communications and Computer Networks, Softcom 2007.
[22]	F. J. Escribano, L. Lopez and M. A. F. Sanjuan, “Iteratively Decoding Chaos Encoded Binary Signals,” Proceedings of the Eighth International Symposium on Signal Processing and Its Applications, 2005, Sydney, Aug. 2005, pp. 275-278.
[23]	S. Kozic, T. Schimming and M. Hasler, “Controlled One- and Multidimensional Modulations Using Chaotic Maps,” IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 53, No. 9, Sept. 2006, pp. 2048-2059.
[24]	F. J. Escribano, L. Lopez and M. A. F. Sanjuan, “Chaos-Coded Modulations Over Rician and Rayleigh Flat Fading Channels”, IEEE Transactions on Circuits and Systems II, Vol. 55, No. 6, June 2008, pp. 581-585.