Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among processes. By extending the results by Chow and Liu on dependence tree approximations, we show that the best causal dependence tree approximation is the one which maximizes the sum of directed informations on its edges, where best is defined in terms of minimizing the KL-divergence between the original and the approximate distribution. Moreover, we describe a low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure

Artificial Intelligence Approach to the Determination of Physical Properties of Eclipsing Binaries. I. The EBAI Project

Achieving maximum scientific results from the overwhelming volume of astronomical data to be acquired over the next few decades will demand novel, fully automatic methods of data analysis. Artificial intelligence approaches hold great promise in contributing to this goal. Here we apply neural network learning technology to the specific domain of eclipsing binary (EB) stars, of which only some hundreds have been rigorously analyzed, but whose numbers will reach millions in a decade. Well-analyzed EBs are a prime source of astrophysical information whose growth rate is at present limited by the need for human interaction with each EB data-set, principally in determining a starting solution for subsequent rigorous analysis. We describe the artificial neural network (ANN) approach which is able to surmount this human bottleneck and permit EB-based astrophysical information to keep pace with future data rates. The ANN, following training on a sample of 33,235 model light curves, outputs a set of approximate model parameters (T2/T1, (R1+R2)/a, e sin(omega), e cos(omega), and sin i) for each input light curve data-set. The whole sample is processed in just a few seconds on a single 2GHz CPU. The obtained parameters can then be readily passed to sophisticated modeling engines. We also describe a novel method polyfit for pre-processing observational light curves before inputting their data to the ANN and present the results and analysis of testing the approach on synthetic data and on real data including fifty binaries from the Catalog and Atlas of Eclipsing Binaries (CALEB) database and 2580 light curves from OGLE survey data. [abridged]Comment: 52 pages, accepted to Ap

Improving the tolerance of stochastic LDPC decoders to overclocking-induced timing errors: a tutorial and design example

Channel codes such as Low-Density Parity-Check (LDPC) codes may be employed in wireless communication schemes for correcting transmission errors. This tolerance to channel-induced transmission errors allows the communication schemes to achieve higher transmission throughputs, at the cost of requiring additional processing for performing LDPC decoding. However, this LDPC decoding operation is associated with a potentially inadequate processing throughput, which may constrain the attainable transmission throughput. In order to increase the processing throughput, the clock period may be reduced, albeit this is at the cost of potentially introducing timing errors. Previous research efforts have considered a paucity of solutions for mitigating the occurrence of timing errors in channel decoders, by employing additional circuitry for detecting and correcting these overclocking-induced timing errors. Against this background, in this paper we demonstrate that stochastic LDPC decoders (LDPC-SDs) are capable of exploiting their inherent error correction capability for correcting not only transmission errors, but also timing errors, even without the requirement for additional circuitry. Motivated by this, we provide the first comprehensive tutorial on LDPC-SDs. We also propose a novel design flow for timing-error-tolerant LDPC decoders. We use this to develop a timing error model for LDPC-SDs and investigate how their overall error correction performance is affected by overclocking. Drawing upon our findings, we propose a modified LDPC-SD, having an improved timing error tolerance. In a particular practical scenario, this modification eliminates the approximately 1 dB performance degradation that is suffered by an overclocked LDPC-SD without our modification, enabling the processing throughput to be increased by up to 69.4%, which is achieved without compromising the error correction capability or processing energy consumption of the LDPC-SD

Hardness results for decoding the surface code with Pauli noise

Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding algorithms take into account this prior information about the specific noise present. This motivates us to consider the complexity of surface code decoding where the input to the decoding problem is not only the syndrome-measurement results, but also a noise model in the form of probabilities of single-qubit Pauli errors for every qubit. In this setting, we show that Maximum Probability Error (MPE) decoding and Maximum Likelihood (ML) decoding for the surface code are NP-hard and #P-hard, respectively. We reduce directly from SAT for MPE decoding, and from #SAT for ML decoding, by showing how to transform a boolean formula into a qubit-dependent Pauli noise model and set of syndromes that encode the satisfiability properties of the formula. We also give hardness of approximation results for MPE and ML decoding. These are worst-case hardness results that do not contradict the empirical fact that many efficient surface code decoders are correct in the average case (i.e., for most sets of syndromes and for most reasonable noise models). These hardness results are nicely analogous with the known hardness results for MPE and ML decoding of arbitrary stabilizer codes with independent $X$ and $Z$ noise.Comment: 37 pages, 18 figures. 26 pages, 12 figures in main tex

Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications

Communication systems to date primarily aim at reliably communicating bit sequences. Such an approach provides efficient engineering designs that are agnostic to the meanings of the messages or to the goal that the message exchange aims to achieve. Next generation systems, however, can be potentially enriched by folding message semantics and goals of communication into their design. Further, these systems can be made cognizant of the context in which communication exchange takes place, providing avenues for novel design insights. This tutorial summarizes the efforts to date, starting from its early adaptations, semantic-aware and task-oriented communications, covering the foundations, algorithms and potential implementations. The focus is on approaches that utilize information theory to provide the foundations, as well as the significant role of learning in semantics and task-aware communications.Comment: 28 pages, 14 figure

Simultaneous ranging and self-positioning in unsynchronized wireless acoustic sensor networks

Automatic ranging and self-positioning is a very desirable property in wireless acoustic sensor networks (WASNs) where nodes have at least one microphone and one loudspeaker. However, due to environmental noise, interference and multipath effects, audio-based ranging is a challenging task. This paper presents a fast ranging and positioning strategy that makes use of the correlation properties of pseudo-noise (PN) sequences for estimating simultaneously relative time-of-arrivals (TOAs) from multiple acoustic nodes. To this end, a proper test signal design adapted to the acoustic node transducers is proposed. In addition, a novel self-interference reduction method and a peak matching algorithm are introduced, allowing for increased accuracy in indoor environments. Synchronization issues are removed by following a BeepBeep strategy, providing range estimates that are converted to absolute node positions by means of multidimensional scaling (MDS). The proposed approach is evaluated both with simulated and real experiments under different acoustical conditions. The results using a real network of smartphones and laptops confirm the validity of the proposed approach, reaching an average ranging accuracy below 1 centimeter.This work was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2015-70202-P, TEC2012-37945-C02-02 and FEDER funds

Smoothing of binary codes, uniform distributions, and applications

The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a lattice in the Euclidean space. We aim to characterize the cases when the output distribution is close to the uniform distribution on the space, as measured by R{\'e}nyi divergence of order $\alpha \in [1,\infty]$. A version of this question is known as the channel resolvability problem in information theory, and it has implications for security guarantees in wiretap channels, error correction, discrepancy, worst-to-average case complexity reductions, and many other problems. Our work quantifies the requirements for asymptotic uniformity (perfect smoothing) and identifies explicit code families that achieve it under the action of the Bernoulli and ball noise operators on the code. We derive expressions for the minimum rate of codes required to attain asymptotically perfect smoothing. In proving our results, we leverage recent results from harmonic analysis of functions on the Hamming space. Another result pertains to the use of code families in Wyner's transmission scheme on the binary wiretap channel. We identify explicit families that guarantee strong secrecy when applied in this scheme, showing that nested Reed-Muller codes can transmit messages reliably and securely over a binary symmetric wiretap channel with a positive rate. Finally, we establish a connection between smoothing and error correction in the binary symmetric channel