Information theory

(content prepared by Yanne Chembo)

Liquid state machine computation

LSM The leading paradigm in computation today is the Turing machine. Information is first digitalized in a stream of bits, and then processed in computers or communcation networks. The Turing machine has already proved the extent and ubiquity of its power, and has enabled the prodigious leap into the on-going information era. However, the most performant computer, the human brain, is not a Turing machine. Its processeing capabilities can be approximated with the paradigm of Liquid State machine (LSM). whose archetype is the plane surface of quiet liquid volume. If an object is thrown into a quiet lake from one edge , "an Intelligence" (in the sense of Laplace, i.e., with an infinite computation power) located at the other edge could analyze the induced surface waves and extract informations about the object in question: its volume, shape, velocity, etc. This kind of processing is perfomed in real-time, and it does not involve any storage of information; moreover, the liquid comes back to its initial quiet state after the excitation. This type of computing is strinkingly similar to the operating mode of living being brains, that process information in real-time from external stimulii.

As displayed by the figure, the "liquid" is considered as a reservoir, yielding a given outputs depending on the input data. The reservoir can therefore be "trained" to perform a given task (pattern recognition, mainly) by optimizing the output relativele the expected result. LSMs have been extensively investigated in the community of cognitive sciences and neuronal systems. We are actually involved at the FEMTO-ST Institute in research activities whose objective is to achieve ultra-fast LSM computation with optoelectronic systems.

Random number generation

RNG By definition, truely random variables physically originate from probabilistic physical phenomena, such as random decay or thermal noise. Those generated with computational methods are in fact only pseudo-random numbers because they are deterministic outputs of nonlinear functions, that can satisfy some stringent statistical properties. These (pseudo-)random numbers are useful in several applications ranging from real-time random sampling to hardware crypto-graphic applications. Generating (tens of) billions of such pseudo-random numbers is in fact a very difficult task. Achieving this objective by the way of photonic solutions is the focus of dedicated research activities in several laboratories worldwide.

We are actually exploring the idea of generating pseudo-random number with optoelectronic systems. As shown in the figure, the output of these systems is a continuous chaotic (and then, pseudo-random) signal whose probability density function converges towards a Gaussian curve. The bandwidth of such signals can be as high as 10 GHz, and nothing theoretically prevents an increase to significantly higher frequencies.