Luciana De Micco

FPGA implementation of a chaotic oscillator using RK4 method

The dual deterministic-stochastic behavior of chaotic systems (CS) makes them extremely interesting in electronic engineering as CS may replace noise sources in different applications. Consequently it is convenient to have hardware implementations for both, analog and digital versions. Discrete components, Micro Controllers, Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGAs) are possible choices.

Complexity of Simple, Switched and Skipped Chaotic Maps in Finite Precision

In this paper we investigate the degradation of the statistic properties of chaotic maps as consequence of their implementation in a digital media such as Digital Signal Processors (DSP), Field Programmable Gate Arrays (FPGA) or Application-Specific Integrated Circuits (ASIC). In these systems, binary floating- and fixed-point are the numerical representations available. Fixed-point representation is preferred over floating-point when speed, low power and/or small circuit area are necessary. Then, in this paper we compare the degradation of fixed-point binary precision version of chaotic maps with the one obtained by using floating point 754-IEEE standard, to evaluate the feasibility of their FPGA implementation. The specific period that every fixed-point precision produces was investigated in previous reports. Statistical characteristics are also relevant, it has been recently shown that it is convenient to describe the statistical characteristic using both, causal and non-causal quantifiers. In this paper we complement the period analysis by characterizing the behavior of these maps from an statistical point of view using cuantifiers from information theory. Here, rather than reproducing an exact replica of the real system, the aim is to meet certain conditions related to the statistics of systems.

Ro-based PRNG: FPGA implementation and stochastic analysis

This paper deals with the use of Ring Oscillators (ROs) as pseudo random number generators (PRNG). The design, made for ALTERA Cyclone III ©, using low level primitives is explained. Two relevant characteristics of a PRNG are considered to validate the design: 1) the equiprobability of all possible outcomes and 2) the statistical independence of consecutive values. In this work these properties are measured via Information Theory Quantifiers. A dual entropy plane is used to represent the time series and easily visualize the results obtained with different configurations. The quality is also compared with other available PRNGs by means of the dual entropy plane. Our method constitutes an effective reduction of the complete analysis made with test suites like DIEHARD or NIST.

Randomness of finite-state sequence machine over GF(4) and quality of hopping turbo codes

In this study, the authors study a turbo-coding (TC) scheme, whose constituent codes are designed using convolutional encoders. These encoders are finite-state sequence machines (FSSMs) operating over the Galois Field, GF(4). The scheme includes encryption polynomials whose coefficients are selected every L steps, from the set of optimal polynomials of GF(4). Two cases are considered for the polynomial selection: periodical and random. This kind of encoder was studied in a previous study and a correspondence between the randomness of the encoded sequence and performance of the TC was conjectured. The main contribution of this study is to systematically confirm this correspondence, by analysing the randomness of the output and performance of the TC using several randomness quantifiers. Three of the quantifiers are defined on the basis of recurrence plots. Other two quantifiers are defined on the basis of the information theory. All the quantifiers allow one to justify why the proposed TC works better with random selection of the optimal polynomials and with small values of L . In summary, it is shown that a random selection of polynomials and a small L produce FSSMs with enhanced randomness properties and it is also shown that they produce the best quality of the TC, measured by means of the corresponding bit error rate.