A new fast generalized sphere decoding algorithm in MIMO systems

A new generalized sphere decoding algorithm is proposed for underdetermined MIMO systems with fewer receive antennas N than transmit antennas M. The proposed algorithm is significantly faster than the existing generalized sphere decoding algorithms. The basic idea is to partition the transmitted signal vector into two subvectors x and x with N - 1 and M - N + 1 elements respectively. After some simple transformations, an outer layer Sphere Decoder (SD) can be used to choose proper x and then use an inner layer SD to decide x, thus the whole transmitted signal vector is obtained. Simulation results show that Double Layer Sphere Decoding (DLSD) has far less complexity than the existing Generalized Sphere Decoding (GSDs).

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

Progression of auditory discrimination based on neural decoding predicts awakening from coma.

Auditory evoked potentials are informative of intact cortical functions of comatose patients. The integrity of auditory functions evaluated using mismatch negativity paradigms has been associated with their chances of survival. However, because auditory discrimination is assessed at various delays after coma onset, it is still unclear whether this impairment depends on the time of the recording. We hypothesized that impairment in auditory discrimination capabilities is indicative of coma progression, rather than of the comatose state itself and that rudimentary auditory discrimination remains intact during acute stages of coma. We studied 30 post-anoxic comatose patients resuscitated from cardiac arrest and five healthy, age-matched controls. Using a mismatch negativity paradigm, we performed two electroencephalography recordings with a standard 19-channel clinical montage: the first within 24 h after coma onset and under mild therapeutic hypothermia, and the second after 1 day and under normothermic conditions. We analysed electroencephalography responses based on a multivariate decoding algorithm that automatically quantifies neural discrimination at the single patient level. Results showed high average decoding accuracy in discriminating sounds both for control subjects and comatose patients. Importantly, accurate decoding was largely independent of patients' chance of survival. However, the progression of auditory discrimination between the first and second recordings was informative of a patient's chance of survival. A deterioration of auditory discrimination was observed in all non-survivors (equivalent to 100% positive predictive value for survivors). We show, for the first time, evidence of intact auditory processing even in comatose patients who do not survive and that progression of sound discrimination over time is informative of a patient's chance of survival. Tracking auditory discrimination in comatose patients could provide new insight to the chance of awakening in a quantitative and automatic fashion during early stages of coma.

Decoding sequence learning from single-trial intracranial EEG in humans.

We propose and validate a multivariate classification algorithm for characterizing changes in human intracranial electroencephalographic data (iEEG) after learning motor sequences. The algorithm is based on a Hidden Markov Model (HMM) that captures spatio-temporal properties of the iEEG at the level of single trials. Continuous intracranial iEEG was acquired during two sessions (one before and one after a night of sleep) in two patients with depth electrodes implanted in several brain areas. They performed a visuomotor sequence (serial reaction time task, SRTT) using the fingers of their non-dominant hand. Our results show that the decoding algorithm correctly classified single iEEG trials from the trained sequence as belonging to either the initial training phase (day 1, before sleep) or a later consolidated phase (day 2, after sleep), whereas it failed to do so for trials belonging to a control condition (pseudo-random sequence). Accurate single-trial classification was achieved by taking advantage of the distributed pattern of neural activity. However, across all the contacts the hippocampus contributed most significantly to the classification accuracy for both patients, and one fronto-striatal contact for one patient. Together, these human intracranial findings demonstrate that a multivariate decoding approach can detect learning-related changes at the level of single-trial iEEG. Because it allows an unbiased identification of brain sites contributing to a behavioral effect (or experimental condition) at the level of single subject, this approach could be usefully applied to assess the neural correlates of other complex cognitive functions in patients implanted with multiple electrodes.

Space–Time Block Codes and the Complexity of Sphere Decoding

In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Maximum-likelihood noncoherent lattice decoding of QAM

We present a novel, maximum-likelihood (ML), lattice-decoding algorithm for noncoherent block detection of QAM signals. The computational complexity is polynomial in the block length; making it feasible for implementation compared with the exhaustive search ML detector. The algorithm works by enumerating the nearest neighbor regions for a plane defined by the received vector; in a conceptually similar manner to sphere decoding. Simulations show that the new algorithm significantly outperforms existing approaches

Augmented LDPC Graph for Distributed Video Coding with Multiple Side Information

The advances made in channel-capacity codes, such as turbo codes and low-density parity-check (LDPC) codes, have played a major role in the emerging distributed source coding paradigm. LDPC codes can be easily adapted to new source coding strategies due to their natural representation as bipartite graphs and the use of quasi-optimal decoding algorithms, such as belief propagation. This paper tackles a relevant scenario in distributedvideo coding: lossy source coding when multiple side information (SI) hypotheses are available at the decoder, each one correlated with the source according to different correlation noise channels. Thus, it is proposed to exploit multiple SI hypotheses through an efficient joint decoding technique withmultiple LDPC syndrome decoders that exchange information to obtain coding efficiency improvements. At the decoder side, the multiple SI hypotheses are created with motion compensated frame interpolation and fused together in a novel iterative LDPC based Slepian-Wolf decoding algorithm. With the creation of multiple SI hypotheses and the proposed decoding algorithm, bitrate savings up to 8.0% are obtained for similar decoded quality.

Robust discrimination between EEG responses to categories of environmental sounds in early coma.

Humans can recognize categories of environmental sounds, including vocalizations produced by humans and animals and the sounds of man-made objects. Most neuroimaging investigations of environmental sound discrimination have studied subjects while consciously perceiving and often explicitly recognizing the stimuli. Consequently, it remains unclear to what extent auditory object processing occurs independently of task demands and consciousness. Studies in animal models have shown that environmental sound discrimination at a neural level persists even in anesthetized preparations, whereas data from anesthetized humans has thus far provided null results. Here, we studied comatose patients as a model of environmental sound discrimination capacities during unconsciousness. We included 19 comatose patients treated with therapeutic hypothermia (TH) during the first 2 days of coma, while recording nineteen-channel electroencephalography (EEG). At the level of each individual patient, we applied a decoding algorithm to quantify the differential EEG responses to human vs. animal vocalizations as well as to sounds of living vocalizations vs. man-made objects. Discrimination between vocalization types was accurate in 11 patients and discrimination between sounds from living and man-made sources in 10 patients. At the group level, the results were significant only for the comparison between vocalization types. These results lay the groundwork for disentangling truly preferential activations in response to auditory categories, and the contribution of awareness to auditory category discrimination.

Silver space-time trellis-coded modulation

Silver Code (SilC) was originally discovered in [1–4] for 2×2 multiple-input multiple-output (MIMO) transmission. It has non-vanishing minimum determinant 1/7, slightly lower than Golden code, but is fast-decodable, i.e., it allows reduced-complexity maximum likelihood decoding [5–7]. In this paper, we present a multidimensional trellis-coded modulation scheme for MIMO systems [11] based on set partitioning of the Silver Code, named Silver Space-Time Trellis Coded Modulation (SST-TCM). This lattice set partitioning is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions. Viterbi algorithm is applied for trellis decoding, while the branch metrics are computed by using a sphere-decoding algorithm. It is shown that the proposed SST-TCM performs very closely to the Golden Space-Time Trellis Coded Modulation (GST-TCM) scheme, yetwith a much reduced decoding complexity thanks to its fast-decoding property.

Applications of Linear Programming to Coding Theory

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem. In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such vectors are known as pseudocodewords. In this work, we completely classify the set of linear programming pseudocodewords for the family of cycle codes. For the case of the binary symmetric channel, another approximation of maximum-likelihood decoding was introduced by Omura in 1972. This decoder employs an iterative algorithm whose behavior closely mimics that of the simplex algorithm. We generalize Omura's decoder to operate on any binary-input memoryless channel, thus obtaining a soft-decision decoding algorithm. Further, we prove that the probability of the generalized algorithm returning the maximum-likelihood codeword approaches 1 as the number of iterations goes to infinity.

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.