Compressive sampling of binary images

Compressive sampling is a novel framework that exploits sparsity of a signal in a transform domain to perform sampling below the Nyquist rate. In this paper, we apply compressive sampling to reduce the sampling rate of binary images. A system is proposed whereby the image is split into non-overlapping blocks of equal size and compressive sampling is performed on selected blocks only using the orthogonal matching pursuit technique. The remaining blocks are sampled fully. This way, the complexity and the required sampling time is reduced since the orthogonal matching pursuit operates on a smaller number of samples, and at the same time local sparsity within an image is exploited. Our simulation results show more than 20% saving in acquisition for several binary images

On practical design for joint distributed source and network coding

This paper considers the problem of communicating correlated information from multiple source nodes over a network of noiseless channels to multiple destination nodes, where each destination node wants to recover all sources. The problem involves a joint consideration of distributed compression and network information relaying. Although the optimal rate region has been theoretically characterized, it was not clear how to design practical communication schemes with low complexity. This work provides a partial solution to this problem by proposing a low-complexity scheme for the special case with two sources whose correlation is characterized by a binary symmetric channel. Our scheme is based on a careful combination of linear syndrome-based Slepian-Wolf coding and random linear mixing (network coding). It is in general suboptimal; however, its low complexity and robustness to network dynamics make it suitable for practical implementation

AN IMPROVED SPECTRAL CLASSIFICATION OF BOOLEAN FUNCTIONS BASED ON AN EXTENDED SET OF INVARIANT OPERATIONS

Boolean functions expressing some particular properties often appear in engineering practice. Therefore, a lot of research efforts are put into exploring different approaches towards classification of Boolean functions with respect to various criteria that are typically selected to serve some specific needs of the intended applications. A classification is considered to be strong if there is a reasonably small number of different classes for a given number of variables n and it it desir able that classificationrules are simple. A classification with respect to Walsh spectral coefficients, introduced formerly for digital system design purposes, appears to be useful in the context of Boolean functions used in cryptography, since it is ina way compatible with characterization of cryptographically interesting functions through Walsh spectral coefficients. This classification is performed in terms of certain spectral invariant operations. We show by introducing a new spectral invariant operation in the Walsh domain, that by starting from n≤5, some classes of Boolean functions can be merged which makes the classification stronger, and from the theoretical point of view resolves a problem raised already in seventies of the last century. Further, this new spectral invariant operation can be used in constructing bent functions from bent functions represented by quadratic forms