Cooperative Wireless Networks for Localization

This thesis adresses the problem of localization, and analyzes its crucial aspects, within the context of cooperative WSNs. The three main issues discussed in the following are: network synchronization, position estimate and tracking. Time synchronization is a fundamental requirement for every network. In this context, a new approach based on the estimation theory is proposed to evaluate the ultimate performance limit in network time synchronization. In particular the lower bound on the variance of the average synchronization error in a fully connected network is derived by taking into account the statistical characterization of the Message Delivering Time (MDT) . Sensor network localization algorithms estimate the locations of sensors with initially unknown location information by using knowledge of the absolute positions of a few sensors and inter-sensor measurements such as distance and bearing measurements. Concerning this issue, i.e. the position estimate problem, two main contributions are given. The first is a new Semidefinite Programming (SDP) framework to analyze and solve the problem of flip-ambiguity that afflicts range-based network localization algorithms with incomplete ranging information. The occurrence of flip-ambiguous nodes and errors due to flip ambiguity is studied, then with this information a new SDP formulation of the localization problem is built. Finally a flip-ambiguity-robust network localization algorithm is derived and its performance is studied by Monte-Carlo simulations. The second contribution in the field of position estimate is about multihop networks. A multihop network is a network with a low degree of connectivity, in which couples of given any nodes, in order to communicate, they have to rely on one or more intermediate nodes (hops). Two new distance-based source localization algorithms, highly robust to distance overestimates, typically present in multihop networks, are presented and studied. The last point of this thesis discuss a new low-complexity tracking algorithm, inspired by the Fano’s sequential decoding algorithm for the position tracking of a user in a WLAN-based indoor localization system.

Advanced receivers for next generation wireless communication systems

Despite extensive progress on the theoretical aspects of spectral efficient communication systems, hardware impairments, such as phase noise, are the key bottlenecks in next generation wireless communication systems. The presence of non-ideal oscillators at the transceiver introduces time varying phase noise and degrades the performance of the communication system. Significant research literature focuses on joint synchronization and decoding based on joint posterior distribution, which incorporate both the channel and code graph. These joint synchronization and decoding approaches operate on well designed sum-product algorithms, which involves calculating probabilistic messages iteratively passed between the channel statistical information and decoding information. Channel statistical information, generally entails a high computational complexity because its probabilistic model may involve continuous random variables. The detailed knowledge about the channel statistics for these algorithms make them an inadequate choice for real world applications due to power and computational limitations. In this thesis, novel phase estimation strategies are proposed, in which soft decision-directed iterative receivers for a separate A Posteriori Probability (APP)-based synchronization and decoding are proposed. These algorithms do not require any a priori statistical characterization of the phase noise process. The proposed approach relies on a Maximum A Posteriori (MAP)-based algorithm to perform phase noise estimation and does not depend on the considered modulation/coding scheme as it only exploits the APPs of the transmitted symbols. Different variants of APP-based phase estimation are considered. The proposed algorithm has significantly lower computational complexity with respect to joint synchronization/decoding approaches at the cost of slight performance degradation. With the aim to improve the robustness of the iterative receiver, we derive a new system model for an oversampled (more than one sample per symbol interval) phase noise channel. We extend the separate APP-based synchronization and decoding algorithm to a multi-sample receiver, which exploits the received information from the channel by exchanging the information in an iterative fashion to achieve robust convergence. Two algorithms based on sliding block-wise processing with soft ISI cancellation and detection are proposed, based on the use of reliable information from the channel decoder. Dually polarized systems provide a cost-and spatial-effective solution to increase spectral efficiency and are competitive candidates for next generation wireless communication systems. A novel soft decision-directed iterative receiver, for separate APP-based synchronization and decoding, is proposed. This algorithm relies on an Minimum Mean Square Error (MMSE)-based cancellation of the cross polarization interference (XPI) followed by phase estimation on the polarization of interest. This iterative receiver structure is motivated from Master/Slave Phase Estimation (M/S-PE), where M-PE corresponds to the polarization of interest. The operational principle of a M/S-PE block is to improve the phase tracking performance of both polarization branches: more precisely, the M-PE block tracks the co-polar phase and the S-PE block reduces the residual phase error on the cross-polar branch. Two variants of MMSE-based phase estimation are considered; BW and PLP.

Error-correcting code on a cactus:A solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.

Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

Statistical physics of error-correcting codes

In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

On the Automorphism Groups of some AG-Codes Based on Ca;b Curves

*Partially supported by NATO.

Multi-Pattern Viterbi Algorithm for joint decoding of multiple speech patterns

Joint decoding of multiple speech patterns so as to improve speech recognition performance is important, especially in the presence of noise. In this paper, we propose a Multi-Pattern Viterbi algorithm (MPVA) to jointly decode and recognize multiple speech patterns for automatic speech recognition (ASR). The MPVA is a generalization of the Viterbi Algorithm to jointly decode multiple patterns given a Hidden Markov Model (HMM). Unlike the previously proposed two stage Constrained Multi-Pattern Viterbi Algorithm (CMPVA),the MPVA is a single stage algorithm. MPVA has the advantage that it cart be extended to connected word recognition (CWR) and continuous speech recognition (CSR) problems. MPVA is shown to provide better speech recognition performance than the earlier techniques: using only two repetitions of noisy speech patterns (-5 dB SNR, 10% burst noise), the word error rate using MPVA decreased by 28.5%, when compared to using individual decoding. (C) 2010 Elsevier B.V. All rights reserved.

Brain decoding based on functional magnetic resonance imaging using machine learning : a comparative study

Brain decoding of functional Magnetic Resonance Imaging data is a pattern analysis task that links brain activity patterns to the experimental conditions. Classifiers predict the neural states from the spatial and temporal pattern of brain activity extracted from multiple voxels in the functional images in a certain period of time. The prediction results offer insight into the nature of neural representations and cognitive mechanisms and the classification accuracy determines our confidence in understanding the relationship between brain activity and stimuli. In this paper, we compared the efficacy of three machine learning algorithms: neural network, support vector machines, and conditional random field to decode the visual stimuli or neural cognitive states from functional Magnetic Resonance data. Leave-one-out cross validation was performed to quantify the generalization accuracy of each algorithm on unseen data. The results indicated support vector machine and conditional random field have comparable performance and the potential of the latter is worthy of further investigation.

Algebraic distributed space-time codes with low ML decoding complexity

"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic constructions of full diversity Distributed Space-Time Codes (DSTCs) are provided for any power of two number of relays. The left regular matrix representation has been shown to naturally result in space-time codes meeting the additional constraints required for DSTCs. The DSTCs so constructed have the salient feature of reduced Maximum Likelihood (ML) decoding complexity. In particular, the ML decoding of these codes can be performed by applying the lattice decoder algorithm on a lattice of four times lesser dimension than what is required in general. Moreover these codes have a uniform distribution of power among the relays and in time, thus leading to a low Peak to Average Power Ratio at the relays.

Joint decoding of multiple speech patterns for robust speech recognition

We are addressing a new problem of improving automatic speech recognition performance, given multiple utterances of patterns from the same class. We have formulated the problem of jointly decoding K multiple patterns given a single Hidden Markov Model. It is shown that such a solution is possible by aligning the K patterns using the proposed Multi Pattern Dynamic Time Warping algorithm followed by the Constrained Multi Pattern Viterbi Algorithm The new formulation is tested in the context of speaker independent isolated word recognition for both clean and noisy patterns. When 10 percent of speech is affected by a burst noise at -5 dB Signal to Noise Ratio (local), it is shown that joint decoding using only two noisy patterns reduces the noisy speech recognition error rate to about 51 percent, when compared to the single pattern decoding using the Viterbi Algorithm. In contrast a simple maximization of individual pattern likelihoods, provides only about 7 percent reduction in error rate.

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

Non-orthogonal space-time block codes (STBC) with large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having largedimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 X 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10(-3) uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme.