In previous work, we presented a method for constructing dynamic input-output models for real-time state estimation in correlated dynamic fields using wireless sensor networks (WSNs). The input signals correspond to the sensors on the boundary of the physical space under study, reflecting the assumption there are no independent sources in the interior of the region. In this paper, we present a method to identify sensors not on the boundary that should be used as inputs in the dynamic models when there are inner sources, i.e., sources inside the physical space. We extend concepts from the behavioral model theory of Jan Willems to handle noisy time series. We construct a block-Hankel structured matrix based on the sensor data, and then calculate as an independence indicator the angle between each row of the matrix and the subspace determined by the span of the preceding rows. The inner sources are identified based on these angle values. Experimental results with real temperature data collected with a WSN, and including heat sources as inner sources, illustrate the proposed method.

In many sensor networks applications, sensors collect correlated measurements of a physical field, e.g., temperature field in a building or in a data center. However, the locations of the sensors are usually inconsistent with the application requirements. In this paper, we consider the problem of estimating the field at arbitrary positions of interest, where there are possibly no sensors, from the irregularly placed sensors. We map this sensor network on a graph, and, by introducing the concepts of interconnection matrices, system digraphs, and cut point sets, we can pose sensor network tradeoffs and derive real-time field estimation algorithms. The results of temperature field estimation, obtained from simulations and real world experiments, show that the methodology presented in this paper can successfully predict the field values at arbitrary locations, including others than the ones with sensors.

In this paper we construct three types of low-density parity-check codes with column weight j = 3 based on geometries in graphical models. Low-density parity-check codes with j > 2 are desired because their minimum distance improves linearly with the code block length n. The codes we present here have girth 8 and girth 10. All codes are regular and well-structured. These codes have flexible block lengths and code rates, and may be used in the area of communications and data storage. Our simulation results show that they have better bit-error-rate decoding performance and lower error floors in additive white Gaussian noise channels than randomly constructed low-density parity-check codes.

The paper introduces three new classes of structured regular (n, 2, k) LDPC codes with girth 12, 16, and 20, respectively. These codes are systematically constructed, well structured, and have uniform row and column weights, which make them able to simplify greatly the implementation of LDPC coders. Their large girth improves their decoding performance. Simulation results compare their bit error rate (BER) performance over additive white Gaussian noise (AWGN) channels with randomly constructed LDPC codes. When concatenated with error-correcting codes such as Reed-Solomon codes, LDPC codes with j=2 are promising for data storage and other applications.