Stokes Vector Modulation of Optical Signals; Coherence, Noise, and Digital Signal Processing

Stokes vector modulation (SVM) is a method of encoding information onto an optical wave by controlling its amplitude and its state of polarization (SOP). SVM offers the potential to achieve the high spectral efficiency of multi-dimensional symbols using a power-efficient, direct-detection receiver. Combining the two independent degrees of freedom representing polarization with one representing amplitude, SVM symbols are defined in a 3-D space of Stokes vectors, where vector length represents the amplitude and altitude/azimuth angles represent the SOP. The recoverable information content is fundamentally limited by the noise on the received signal, which may include shot noise due to photon-counting, electrical circuit noise, amplified spontaneous emission due to optical amplifiers, and self-interference of low-coherence light sources. Some of these noise terms do not obey the usual approximation of additive white Gaussian noise, and some may not be isotropic in Stokes space. Taking these complexities into account, I will theoretically analyze and compare several recently-proposed SVM receiver designs under different conditions of source coherence and channel impairments. For the most promising options, I will design symbol constellations and receiver decision strategies suitable for maximal data throughput. Construction and operation of apparatus to experimentally verify bit-error performance up to at least 10 Gsym/s with different sources, constellations, fiber spans, and receivers will be an essential component of the work. Possible extensions may include simultaneous modulation of the degree of polarization, to create a 4-D symbol space. Further, I will develop and characterize a system based on a cubic constellation for 8-SVM, using an off-the-shelf integrated modulator driven with simple bias points and data waveforms. Symbol error rates (SER) and bit error rates BER) are measured up to 30 Gb/s, and analysis of the symbol errors reveals a significant effect of inter-symbol interference. Finally, I will theoretically and experimentally demonstrate a novel adaptation of independent component analysis (ICA) for compensation of both cross-polarization and inter-symbol interference in a direct-detection link using Stokes vector modulation (SVM). SVM systems suffer from multiple simultaneous impairments that can be difficult to resolve with conventional optical channel DSP techniques. The proposed method is based on a six-dimensional adaptation of ICA that simultaneously derotates the SVM constellation, corrects distortion of constellation shape, and mitigates inter-symbol interference (ISI) at high symbol rates. Experimental results at 7.5 Gb/s and 15Gb/s show that the newly-developed ICA-based equalizer achieves power penalties below ~1 dB, compared to the ideal theoretical bit-error rate (BER) curves. At 30-Gb/s, where ISI is more severe, ICA still enables polarization de-rotation and BE

Faster Correlation Attack on Bluetooth Keystream Generator E0

Abstract. We study both distinguishing and key-recovery attacks against E0, the keystream generator used in Bluetooth by means of correlation. First, a powerful computation method of correlations is formulated by a recursive expression, which makes it easier to calculate correlations of the finite state machine output sequences up to 26 bits for E0 and allows us to verify the two known correlations to be the largest for the first time. Second, we apply the concept of convolution to the analysis of the distinguisher based on all correlations, and propose an efficient distinguisher due to the linear dependency of the largest correlations. Last, we propose a novel maximum likelihood decoding algorithm based on fast Walsh transform to recover the closest codeword for any linear code of dimension L and length n. It requires time O(n + L · 2 L) and memory min(n, 2 L). This can speed up many attacks such as fast correlation attacks. We apply it to E0, and our best key-recovery attack works in 2 39 time given 2 39 consecutive bits after O(2 37) precomputation. This is the best known attack against E0 so far.

Kernel methods in genomics and computational biology

Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems, from the classification of tumors to the automatic annotation of proteins. Their ability to work in high dimension, to process non-vectorial data, and the natural framework they provide to integrate heterogeneous data are particularly relevant to various problems arising in computational biology. In this chapter we survey some of the most prominent applications published so far, highlighting the particular developments in kernel methods triggered by problems in biology, and mention a few promising research directions likely to expand in the future