The Dispersion of Nearest-Neighbor Decoding for Additive Non-Gaussian Channels

We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor (NN) decoding over a power-limited stationary memoryless additive non-Gaussian noise channel. We show that the dispersion term depends on the non-Gaussian noise only through its second and fourth moments, thus complementing the capacity result (Lapidoth, 1996), which depends only on the second moment. Furthermore, we characterize the second-order asymptotics of point-to-point codes over $K$-sender interference networks with non-Gaussian additive noise. Specifically, we assume that each user's codebook is Gaussian and that NN decoding is employed, i.e., that interference from the $K-1$ unintended users (Gaussian interfering signals) is treated as noise at each decoder. We show that while the first-order term in the asymptotic expansion of the maximum number of messages depends on the power of the interferring codewords only through their sum, this does not hold for the second-order term.Comment: 12 pages, 3 figures, IEEE Transactions on Information Theor

Optimal Detection for Diffusion-Based Molecular Timing Channels

This work studies optimal detection for communication over diffusion-based molecular timing (DBMT) channels. The transmitter simultaneously releases multiple information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is modeled as an additive noise channel. For a DBMT channel without flow, this noise follows the L\'evy distribution. Under this channel model, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is also shown that under ML detection, releasing multiple particles improves performance, while for any additive channel with $\alpha$-stable noise where $\alpha<1$ (such as the DBMT channel), under linear processing at the receiver, releasing multiple particles degrades performance relative to releasing a single particle. Hence, a new low-complexity detector, which is based on the first arrival (FA) among all the transmitted particles, is proposed. It is shown that for a small number of released particles, the performance of the FA detector is very close to that of the ML detector. On the other hand, error exponent analysis shows that the performance of the two detectors differ when the number of released particles is large.Comment: 16 pages, 9 figures. Submitted for publicatio

Sensor Deployment for Network-like Environments

This paper considers the problem of optimally deploying omnidirectional sensors, with potentially limited sensing radius, in a network-like environment. This model provides a compact and effective description of complex environments as well as a proper representation of road or river networks. We present a two-step procedure based on a discrete-time gradient ascent algorithm to find a local optimum for this problem. The first step performs a coarse optimization where sensors are allowed to move in the plane, to vary their sensing radius and to make use of a reduced model of the environment called collapsed network. It is made up of a finite discrete set of points, barycenters, produced by collapsing network edges. Sensors can be also clustered to reduce the complexity of this phase. The sensors' positions found in the first step are then projected on the network and used in the second finer optimization, where sensors are constrained to move only on the network. The second step can be performed on-line, in a distributed fashion, by sensors moving in the real environment, and can make use of the full network as well as of the collapsed one. The adoption of a less constrained initial optimization has the merit of reducing the negative impact of the presence of a large number of local optima. The effectiveness of the presented procedure is illustrated by a simulated deployment problem in an airport environment

Naïve Learning in Social Networks: Convergence, Influence and Wisdom of Crowds

We study learning and influence in a setting where agents communicate according to an arbitrary social network and naïvely update their beliefs by repeatedly taking weighted averages of their neighbors’ opinions. A focus is on conditions under which beliefs of all agents in large societies converge to the truth, despite their naïve updating. We show that this happens if and only if the influence of the most influential agent in the society is vanishing as the society grows. Using simple examples, we identify two main obstructions which can prevent this. By ruling out these obstructions, we provide general structural conditions on the social network that are sufficient for convergence to truth. In addition, we show how social influence changes when some agents redistribute their trust, and we provide a complete characterization of the social networks for which there is a convergence of beliefs. Finally, we survey some recent structural results on the speed of convergence and relate these to issues of segregation, polarization and propaganda.Social Networks, Learning, Diffusion, Bounded Rationality