Roadmad to design and implementation of chaos-based communitacions
Chaos-based Coded Modulations:a roadmap to design & implementation Francisco J. Escribano Departamento de Teoría de la Señal y Comunicaciones, Universidad de Alcalá COMB Seminar Alcalá de Henares, 11th July 2012
Preliminars Do not ask how to get rid of chaos and nonlinearity, ask yourself how to take advantage of it. The eternal question: chaos, what is it good for? Right, some procrastinators still keep working on it: lets see what they propose...
1. Challenges in design Nonlinearity: ➤ No Uniform Error Property (UEP) for the typical error events. ➤ dmin is no longer the key factor for BER requirements. E.g.: bound in AWGN: Expanded 2 distance di Eb P b ∑ w d ⋅erfc 2 R spectrum: Reduced multiplicities: d 2 i i 4P N 0 difficulty asset w Linear vs.1/8 Nonlinear di2
1. Challenges in design Use of the bounds as cost functions for heuristic optimization algorithms: ➤ Problem: need to parametrize chaos-based coded modulations One possible test approach: ➤ Parametrize pdf shaping function g(x) with splines & go! bn xn zn g(x) At each optimization step, calculate the associated distance spectrum, the bound & compare. ➤ Drawback: burdensome2/8
1. Challenges in design Some preliminary results in the uncorrelated Rayleigh (K=0) fast flat fading channel with CSI: Pairwise error probability3/8 Courtesy of Jesús Paris, final project student
2. Traveling towards efficiency Serially / parallel concatenated systems built over chaos-based coded modulations: ➤ Achieve good performances in both AWGN, uncorrelated flat fast fading channels. ➤ Systems tested so far at 0.5 bit/s/Hz. ➤ Turbo-trellis coded modulations (TTCMs) achieve similar results with same complexity and higher spectral efficiencies. bn x1n One possibility: puncturing? Chaos-based coded modulator bn cn dn Chaos-based xn Convolutional encoder Interleaver coded modulator Interleaver To channel cn Puncture to achieve up to 1 bit/s/Hz Chaos-based x2n4/8 coded modulator
2. Traveling towards efficiency Promising preliminary results for both kinds of systems. Parallel: keeps properties in fading Serial: converges in AWGN5/8 Courtesy of Alexandre Wagemakers, collaborator at URJC
3. Coping with implementation A. Wagemakers, F. J. Escribano, L. López and M. A. F. Sanjuán, ‘Competitive Decoders for Turbo-Like Chaos-Based Systems’, IET COM, 2012 (accepted). After intensive work with a parallel system in a TMS320C6713 DSP starter kit, we got: ● Code debugging ● Remove & optimize loops ● Optimal use of instruction pipeline ● Optimal use of DSP registry ● Data types trade-offs ● Operational trade-offs (LUTs) ● …......... In the same platform, comparable 3G turbocodes achieve up to 8x better results. ➤ But 3G results in early implementation stages were quite similar.6/8
3. Coping with implementation One advantage on the side of chaos-based systems: ➤ Much better behavior in uncorrelated fast flat fading channels. Getting insight on the trade-offs As channel degrades,7/8 chaos endures the odds better
4. Conclusions Work in progress is nowadays pointing towards good prospectives for chaos-based communications. Going along with the wave: ➤ So as successful MIMO relies on the principle “lets co-exist better with the rudeness of real channels”, chaos and nonlinearity, once despised, could become assets in communications? There is still a wide gap to jump: ➤ Generalization of related theory. ➤ Provide clear design tools & principles. ➤ Get better insight on properties and limits. ➤ Test more realistic scenarios (plug an antenna and see!).8/8
5. Previous work1. F. J. Escribano, L. López and M. A. F. Sanjuán, ‘Iteratively Decoding Chaos Encoded Binary Signals’, Proc. of the 8th IEEE Int. Symp. on Signal Processing and its Applications (2005).2. , ‘Evaluation of Channel Coding and Decoding Algorithms Using Discrete Chaotic Maps’, CHAOS 16, 013103 (2006).3. , ‘Exploiting Symbolic Dynamics in Chaos Coded Communications with Maximum a Posteriori Algorithm’, Electron. Lett. 42, 984 (2006).4. , ‘Serial Concatenation of Channel and Chaotic Encoders’, Proc. of the 14th Int. Workshop on Nonlinear Dynamics of Electronic Systems (2006).5. F. J. Escribano, L. López and M. A. F. Sanjuán, ‘Chaos Coded Modulations over Rician and Rayleigh Flat Fading Channels’, IEEE TCAS-II, 2008.6. F. J. Escribano, S. Kozic, L. López, M. A. F. Sanjuán and M. Hassler, ‘Turbo- Like Structures for Chaos Coding and Decoding’, IEEE TCOM, 2009.7. F. J. Escribano, L. López and M. A. F. Sanjuán, ‘Improving the Performance of Chaos Based Coded Modulations via Serial Concatenation’, IEEE TCAS-I, 2010.8. F.J. Escribano, L. López and M. A. F. Sanjuán, ‘Analysis of Chaos-Based Coded Modulations under Intersymbol Interference’, Journal of computers, 2010.9. A. Wagemakers, F. J. Escribano, L. López and M. A. F. Sanjuán, ‘Competitive Decoders for Turbo-Like Chaos-Based Systems’, IET COM, 2012 (accepted). Thanks for your attention
A particular slide catching your eye?
Clipping is a handy way to collect important slides you want to go back to later.