Transform-based Distributed Data Gathering

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These transforms can be computed as data is routed towards the collection (or sink) node in the tree and exploit data correlation between nodes in the tree. Moreover, when used in wireless sensor networks, these transforms can also leverage data received at nodes via broadcast wireless communications. Various constructions of unidirectional transforms are also provided for use in data gathering in wireless sensor networks. New wavelet transforms are also proposed which provide significant improvements over existing unidirectional transforms

Optimal Error Rates for Interactive Coding I: Adaptivity and Other Settings

We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings. Most significantly, we explore adaptive interactive communication where the communicating parties decide who should speak next based on the history of the interaction. Braverman and Rao [STOC'11] show that non-adaptively one can code for any constant error rate below 1/4 but not more. They asked whether this bound could be improved using adaptivity. We answer this open question in the affirmative (with a slightly different collection of resources): Our adaptive coding scheme tolerates any error rate below 2/7 and we show that tolerating a higher error rate is impossible. We also show that in the setting of Franklin et al. [CRYPTO'13], where parties share randomness not known to the adversary, adaptivity increases the tolerable error rate from 1/2 to 2/3. For list-decodable interactive communications, where each party outputs a constant size list of possible outcomes, the tight tolerable error rate is 1/2. Our negative results hold even if the communication and computation are unbounded, whereas for our positive results communication and computation are polynomially bounded. Most prior work considered coding schemes with linear amount of communication, while allowing unbounded computations. We argue that studying tolerable error rates in this relaxed context helps to identify a setting's intrinsic optimal error rate. We set forward a strong working hypothesis which stipulates that for any setting the maximum tolerable error rate is independent of many computational and communication complexity measures. We believe this hypothesis to be a powerful guideline for the design of simple, natural, and efficient coding schemes and for understanding the (im)possibilities of coding for interactive communications

Burst-by-Burst Adaptive Decision Feedback Equalised TCM, TTCM and BICM for H.263-Assisted Wireless Video Telephony

Decision Feedback Equaliser (DFE) aided wideband Burst-by-Burst (BbB) Adaptive Trellis Coded Modulation (TCM), Turbo Trellis Coded Modulation (TTCM) and Bit-Interleaved Coded Modulation (BICM) assisted H.263-based video transceivers are proposed and characterised in performance terms when communicating over the COST 207 Typical Urban wideband fading channel. Specifically, four different modulation modes, namely 4QAM, 8PSK, 16QAM and 64QAM are invoked and protected by the above-mentioned coded modulation schemes. The TTCM assisted scheme was found to provide the best video performance, although at the cost of the highest complexity. A range of lower-complexity arrangements will also be characterised. Finally, in order to confirm these findings in an important practical environment, we have also investigated the adaptive TTCM scheme in the CDMA-based Universal Mobile Telecommunications System's (UMTS) Terrestrial Radio Access (UTRA) scenario and the good performance of adaptive TTCM scheme recorded when communicating over the COST 207 channels was retained in the UTRA environment

A Novel Predictive-Coding-Inspired Variational RNN Model for Online Prediction and Recognition

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.Comment: The paper is accepted in Neural Computatio

Linear MMSE-Optimal Turbo Equalization Using Context Trees

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin

A roadmap to integrate astrocytes into Systems Neuroscience.

Systems neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca2+ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in a time scale of subseconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, is, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca2+ and brain coding may represent a leap forward toward novel approaches in the study of astrocytes in health and disease