In this paper, the development of an eye-tracking-based human–computer interface for real-time applications is presented. To identify the most appropriate pupil detection algorithm for the proposed interface, we analyzed the performance of eight algorithms, six of which we developed based on the most representative pupil center detection techniques. The accuracy of each algorithm was evaluated for different eye images from four representative databases and for video eye images using a new testing protocol for a scene image. For all video recordings, we determined the detection rate within a circular target 50-pixel area placed in different positions in the scene image, cursor controllability and stability on the user screen, and running time. The experimental results for a set of 30 subjects show a detection rate over 84% at 50 pixels for all proposed algorithms, and the best result (91.39%) was obtained with the circular Hough transform approach. Finally, this algorithm was implemented in the proposed interface to develop an eye typing application based on a virtual keyboard. The mean typing speed of the subjects who tested the system was higher than 20 characters per minute.

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This paper proposes and proves a theorem which stipulates sufficient conditions the coefficients of two quadratic permutation polynomials (QPP) must satisfy, so that the permutations generated by them are identical. The result is used to reduce the search time of QPP interleavers with lengths given by Long Term Evolution (LTE) standard up to 512, by improving the distance spectrum over the set of polynomials with the largest spreading factor. Polynomials that lead to better performance compared to LTE standard are found for several lengths. Simulations show that 0.5 dB coding gains can be obtained compared to LTE standard.

Quadratic permutation polynomials (QPPs) have been widely studied and used as interleavers in turbo codes. However, less attention has been given to cubic permutation polynomials (CPPs). This paper proves a theorem which states sufficient and necessary conditions for a cubic permutation polynomial to be a null permutation polynomial. The result is used to reduce the search complexity of CPP interleavers for short lengths (multiples of 8, between 40 and 352), by improving the distance spectrum over the set of polynomials with the largest spreading factor. The comparison with QPP interleavers is made in terms of search complexity and upper bounds of the bit error rate (BER) and frame error rate (FER) for AWGN and for independent fading Rayleigh channels. Cubic permutation polynomials leading to better performance than quadratic permutation polynomials are found for some lengths.

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