Raman Venkataramani

Optimal sub-Nyquist nonuniform sampling and reconstruction for multiband signals

We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support /spl Fscr/ that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landaus (1967) lower bound equal to the measure of /spl Fscr/. For signals with sparse /spl Fscr/, this rate can be much smaller than the Nyquist rate. Unfortunately the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a previous study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with /spl Fscr/ that tiles under translation. For signals with nontiling /spl Fscr/, which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate.

A new construction of 16-QAM Golay complementary sequences

We present a new construction of 16-QAM Golay sequences of length n = 2/sup m/. The number of constructed sequences is (14 + 12m)(m!/2)4/sup m+1/. When employed as a code in an orthogonal frequency-division multiplexing (OFDM) system; this set of sequences has a peak-to-mean envelope power ratio (PMEPR) of 3.6. By considering two specific subsets of these sequences, we obtain new codes with PMEPR bounds of 2.0 and 2.8 and respective code sizes of (2 + 2m)(m!/2)4/sup m+1/ and (4 + 4m)(m!/2)4/sup m+1/. These are larger than previously known codes for the same PMEPR bounds.

Further results on spectrum blind sampling of 2D signals

We address the problem of sampling of 2D signals with sparse multi-band spectral structure. We show that the signal can be sampled at a fraction of the its Nyquist density determined by the occupancy of the signal in its frequency domain, but without explicit knowledge of its spectral structure. We find that such a signal can almost surely be reconstructed from its multi-coset samples provided that a universal pattern is used. Also, the scheme can attain the Landau-Nyquist minimum density asymptotically. The spectrum blind feature of our reconstruction scheme has potential applications in Fourier imaging. We apply the sampling scheme on a test image to demonstrate its performance.

Sub-Nyquist sampling of multiband signals: perfect reconstruction and bounds on aliasing error

We consider the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. We derive the conditions for exact reconstruction and find an explicit reconstruction formula. Key features of this method are that the sampling rate can be made arbitrarily close to the minimum (Landau) rate and that it can handle classes of multiband signals that are not packable. We compute various bounds on the aliasing error due to mismodeling the spectral support and examine the performance in the presence of additive white sample noise. Finally we provide optimal designs for the reconstruction system.

Bounds on the achievable region for certain multiple description coding problems

An achievable region for the L-channel multiple description coding problem is presented. This region generalizes previous two-channel results of El Gamal and Cover (1982) and of Zhang and Berger (1987). New outer bounds on the rate distortion region for memoryless Gaussian sources with mean-squared error distortion are also derived. For the Gaussian source, the achievable region meets the outer bound at certain points.

Successive refinement on trees: a special case of a new MD coding region

New achievability results for the L-stage successive refinement problem with L>2 are presented. These are derived from a recent achievability result for the more general problem of multiple description (MD) coding with L>2 channels. It is shown that successive refinability on chains implies successive refinability on trees and that memoryless Gaussian sources are successively refinable on chains and trees.

Dimension Reduction for Systems with Slow Relaxation: In Memory of Leo P. Kadanoff

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize ‘optimal’ model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.

MAP-Based Timing Recovery for Magnetic Recording

We consider the problem of timing recovery in magnetic recording channels based on MAP estimation of the timing information. The read and write clocks are modeled as random walk processes that allow for slowly varying phase and frequency offsets of the clocks. We propose a new timing error detector (TED) that provides sufficient statistics about the instantaneous timing error. Using the clock models and the new TED, the MAP estimates of the sampling times are derived. This method is shown to be more robust than the conventional algorithm based on the Mueller and Muller TED and easily implementable for a small additional complexity.

Macroscopic and Microscopic Approaches in Sector Failure Rate Estimation

The sector failure rate (SFR) is extremely small at normal operating conditions of hard disk drives. In practice, it cannot be obtained by counting as that would require prohibitively large simulation times. Therefore, appropriate statistical models characterizing the distribution of error symbols are used in order to estimate the SFR. In this paper, we look at the underlying philosophy of existing estimation methods and classify them into macroscopic and microscopic types. We observe that the microscopic approach is well suited for certain iterative channels.

Trellis-Based Optimal Baud-Rate Timing Recovery Loops for Magnetic Recording Systems

The advent of iteratively decodable codes has allowed a decrease in tolerable signal-to-noise ratios (SNRs) in magnetic recording systems, which typically translates into an increase in the recording densities. However, at such low SNRs, conventional timing recovery loops suffer from frequent cycle slips. Typical timing recovery loops in magnetic recording applications perform data detection, timing error detection, and loop filtering in a sequential manner. This sequence of operations in the timing recovery loop performs well if the timing error is a small fraction of the bit interval. However, in the cycle-slip regions, the timing error is comparable to the bit interval, and the loop fails. In this paper, we represent the timing error in magnetic recording systems by using a Markov model that does not confine the timing error to only small fractions of the bit interval. By utilizing such a model, we give a trellis representation of the timing error process. The trellis representation permits the formulations of two optimal baud-rate timing recovery loops, according to two optimality criteria. We prove that both optimality criteria lead to solutions similar to the classical first-order phase-locked loop. The new loops do not perform data detection, timing error detection, and loop filtering in a sequential manner. Instead, the loops perform data detection and timing error detection jointly on a trellis, without the need for a loop filter. Simulation results show that the new timing recovery loops outperform the standard second-order baud-rate Mueller and Muller phase-locked loop with fine-tuned loop parameters. This performance gain is substantial if the timing error process is extremely noisy or if there is residual frequency offset resulting from inaccurate acquisition from the sector preamble on a disk drive.