Francisco J. EscribanoDepartamento de Teoría de la Señal y Comunicaciones, Universidad de Alcalá

Chaos-based Coded Modulations:a roadmap to design & implementation

COMB SeminarCOMB SeminarAlcalá de Henares, 11th July 2012Alcalá de Henares, 11th July 2012

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: let's see what they propose...

Preliminars

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:

1/8

Pb∑d i

2

wd i

2⋅erfc di2

4PR

Eb

N 0

Reduced multiplicities:asset

Expandeddistance

spectrum:difficulty

di

2

w

Linearvs.

Nonlinear

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!

At each optimization step, calculate the associated distance spectrum, the bound & compare.➤ Drawback: burdensome

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bn

xn

zng(x)

1. Challenges in design

Some preliminary results in the uncorrelated Rayleigh (K=0) fast flat fading channel with CSI:

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Pairwiseerror

probability

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.

One possibility: puncturing?

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bn

cn

dn

xnConvolutional

encoder InterleaverChaos-based

codedmodulator

Chaos-basedcoded

modulator

Interleaver

bn

cn

x1n

x2n

To channel

Chaos-basedcoded

modulator

Puncture to achieve up to 1 bit/s/Hz

2. Traveling towards efficiency

Promising preliminary results for both kinds of systems.

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Parallel: keeps properties in fading Serial: converges in AWGN

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:

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

●Code debugging●Remove & optimize loops●Optimal use of instruction pipeline●Optimal use of DSP registry●Data types trade-offs●Operational trade-offs (LUTs)●….........

3. Coping with implementation

One advantage on the side of chaos-based systems:➤ Much better behavior in uncorrelated fast flat fading channels.

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Getting insight onthe trade-offs

As channel degrades,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 “let's 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!).

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5. Previous work

1. 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