Guest Editorial: Nonlinear Optimization of Communication Systems

Linear programming and other classical optimization techniques have found important applications in communication systems for many decades. Recently, there has been a surge in research activities that utilize the latest developments in nonlinear optimization to tackle a much wider scope of work in the analysis and design of communication systems. These activities involve every “layer” of the protocol stack and the principles of layered network architecture itself, and have made intellectual and practical impacts significantly beyond the established frameworks of optimization of communication systems in the early 1990s. These recent results are driven by new demands in the areas of communications and networking, as well as new tools emerging from optimization theory. Such tools include the powerful theories and highly efficient computational algorithms for nonlinear convex optimization, together with global solution methods and relaxation techniques for nonconvex optimization

On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling

This paper investigates the information rate loss in analog channels when the sampler is designed to operate independent of the instantaneous channel occupancy. Specifically, a multiband linear time-invariant Gaussian channel under universal sub-Nyquist sampling is considered. The entire channel bandwidth is divided into $n$ subbands of equal bandwidth. At each time only $k$ constant-gain subbands are active, where the instantaneous subband occupancy is not known at the receiver and the sampler. We study the information loss through a capacity loss metric, that is, the capacity gap caused by the lack of instantaneous subband occupancy information. We characterize the minimax capacity loss for the entire sub-Nyquist rate regime, provided that the number $n$ of subbands and the SNR are both large. The minimax limits depend almost solely on the band sparsity factor and the undersampling factor, modulo some residual terms that vanish as $n$ and SNR grow. Our results highlight the power of randomized sampling methods (i.e. the samplers that consist of random periodic modulation and low-pass filters), which are able to approach the minimax capacity loss with exponentially high probability.Comment: accepted to IEEE Transactions on Information Theory. It has been presented in part at the IEEE International Symposium on Information Theory (ISIT) 201

The Faculty Notebook, April 2003

The Faculty Notebook is published periodically by the Office of the Provost at Gettysburg College to bring to the attention of the campus community accomplishments and activities of academic interest. Faculty are encouraged to submit materials for consideration for publication to the Associate Provost for Faculty Development. Copies of this publication are available at the Office of the Provost

Channel Capacity under Sub-Nyquist Nonuniform Sampling

This paper investigates the effect of sub-Nyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear time-invariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of right-invertible time-preserving sampling methods which include irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal-to-noise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while typically complicated to realize, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.Comment: accepted to IEEE Transactions on Information Theory, 201

Low-complexity Multiclass Encryption by Compressed Sensing

The idea that compressed sensing may be used to encrypt information from unauthorised receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analysed: firstly, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.Comment: IEEE Transactions on Signal Processing, accepted for publication. Article in pres