We derive the capacities of a class of channels, either memoryless or indecomposable finite-state, that also suffer from bursts of erasures. For such channels, we analyze the performances of low-density parity-check (LDPC) codes and code ensembles under belief propagation (BP) decoding, using density evolution (DE) techniques. Although known LDPC codes perform well in non-erasure-affected channels, their performances are far from the capacities when both random errors and erasures are present. We show that enhancing the codes' erasure handling using published methods beats, in some instances, the BP thresholds. However, to achieve capacity, codes must be constructed to tackle both effects simultaneously.

We consider the problem of channel shortening equalization to perform reduced complexity detection for MIMO channels with intersymbol interference and additive Gaussian noise, the problem is to find a MIMO equalizer and a partial response MIMO target filter such that the combination produces the best detection performance. We show the existence of an infinite family of optimal equalizers and targets that satisfy the a posteriori equivalence condition. Furthermore, these solutions are intimately related to MIMO decision feedback equalizers designed with the "monk determinant" constraint on the feedback filter. These results generalize some recent results on channel shortening based on a posteriori equivalence to the MIMO setting.

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.

We present a family of equalizers and targets for certain inter-symbol interference (ISI) channels with the property that the performance of a maximum-likelihood (ML) or maximum a posteriori (MAP) based detector for the target channel is also simultaneously optimal for the equalized channel. In particular, the MMSE Decision feedback equalizer (DFE) belongs to this family of filters. Although, these solutions are infinite impulse response (IIR) filters, we can achieve good performance using finite impulse response (FIR) filters. We present an algorithm for designing equalizers and FIR targets that minimize the probability of sequence detection error.

Timing recovery is crucial for magnetic recording systems. A conventional timing recovery loop (also known as the phase-locked loop) consists of a timing error detector (TED), a loop filter, and a voltage controlled oscillator (VCO), all of which process the samples 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 using a discrete Markov model that does not confine the timing error to only small fractions of the bit interval. By utilizing such a model, we derive an optimal baud-rate processing unit that does not perform tasks in sequence, but jointly. The derived unit has a similar structure as the classical first-order phase-locked loop (PLL). Simulation results show that the new detector outperforms the standard Mueller and Muller phase-locked loop. This performance gain is substantial if the timing error process is extremely noisy or if there is residual frequency-offset. For moderately low-noise timing errors without residual frequency-offset, the improvement over the Mueller and Müller phase-locked loop is just marginal.

We consider the problem of multiple-input multiple-output (MIMO) sampling of multiband signals. In this problem, a set of input signals is passed through a MIMO channel modeled as a known linear time-invariant system. The inputs are modeled as multiband signals whose spectral supports are sets of finite measure and the channel outputs are sampled on nonuniform sampling sets. The aim is to reconstruct the inputs from the output samples. This sampling scheme is quite general and it encompasses various others including Papoulis' generalized sampling and nonuniform sampling as special cases. We introduce notions of joint upper and lower densities for collections of sampling sets and then derive necessary conditions on these densities for stable sampling and consistent reconstruction of the channel inputs from the sampled outputs. These results generalize classical density results for stable sampling and interpolation due to Landau.

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.

An achievable region for the L-channel multiple description coding problem is presented. This region generalizes two-channel results of El Gamal and Cover (1982) and of Zhang and Berger (1987). It further generalizes three-channel results of Gray and Wyner (1974) and of Zhang and Berger. A source that is successively refinable on chains is shown to be successively refinable on trees. A new outer bound on the rate-distortion (RD) region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.

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.

We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class /spl Bscr/(/spl Fscr/) of multiband signals with spectral support /spl Fscr/, at rates arbitrarily close to the Landau (1969) minimum rate equal to the Lebesgue measure of /spl Fscr/, even when /spl Fscr/ does not tile R under translation. Using the conditions for exact reconstruction, we derive an explicit reconstruction formula. We compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band-limited to the "span of /spl Fscr/" (the smallest interval containing /spl Fscr/) which is a bigger class than the valid signals /spl Bscr/(/spl Fscr/), band-limited to /spl Fscr/. We also examine the performance of the reconstruction system when the input contains additive sample noise.

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.

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 nd 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. 1.