Ara Patapoutian

On phase-locked loops and Kalman filters

Driessen (1994) and Christiansen (1994) independently showed that for a specific dynamic model, the proportional-integral phase-locked loop (PLL) has the same structure as the Kalman filter. In this paper, closed-form expressions of the corresponding Kalman gain values are derived both in acquisition and tracking modes of the PLL.

Punctured recursive convolutional encoders and their applications in turbo codes

Puncturing is the predominant strategy to construct high code rate convolutional encoders, and infinite impulse response convolutional encoders are an essential building block in turbo codes. In this paper various properties of convolutional encoders with these characteristics are developed. In particular, the closed form representation of a punctured convolutional encoder and its generator matrix are constructed, necessary and sufficient conditions are given such that the punctured encoders retain the infinite impulse response property, and various lower bounds on distance properties, such as effective free distance, are developed. Finally, necessary and sufficient conditions are given on the inverse puncturing problem: representing a known convolutional encoder as a punctured encoder.

Event error control codes and their applications

Burst error detection codes and cyclic redundancy check (CRC) codes are generalized to event-error detection codes, which are useful in various noisy channels. A systematic linear block code is constructed that detects any event error from an arbitrary list of event errors. The result is generalized to detection and correction of multiple event errors. Bounds are found on the minimum number of redundant bits needed to construct such codes. It is shown that, under certain conditions, the linear code construction is optimal. Various applications are discussed, where there is a Markov source or a Markov channel. It is argued that the codes described herein can be employed either as error detection codes, or as distance-enhancing codes when complete decoders are applied. Specific examples covered in this correspondence include hybrid automatic repeat request (ARQ) systems, intersymbol interference (ISI) channels, and Gilbert (1958) channels.

Performance of a signal-dependent autoregressive channel model

Recently, work has been published on a channel model that employs signal-dependent autoregressive filters to accurately and efficiently model signal nonlinearities and media noise characteristics, such as signal-dependence and correlation, which are common in magnetic recording signals. This paper evaluates the models performance using 42 sets of spin-stand data that cover a large range of head/media manufacturers and operating points.

Signal space analysis of head positioning formats

Head positioning formats or servo-bursts are used on disk drives to estimate the off-track position or the position error signal (PES) of the head with respect to a given track. In this paper the signal space technique is used to design estimators (demodulators) for different head positioning formats and to measure their performances. It will be shown that every format corresponds to a closed loop in the signal space and that the performance of a format is proportional to the circumference of the closed loop in signal space.

Optimal burst frequency derivation for head positioning

For a Lorentzian channel with a given fifty percent amplitude pulse width, we find closed form representation of the servo burst signal. We then derive the frequency of the servo burst signal that maximizes performance or signal to noise ratio. This optimal frequency depends on the estimation scheme used; that is, whether we estimate the amount of signal from peak, rectified area or matched filter estimator.

Getting the information in and out: The channel (invited)

Magnetic recording channels perform several signal processing tasks in the process of storing and retrieving data. Among them are precompensation, equalization, timing recovery, detection, and coding. A range of algorithms is available for each of these tasks with different levels of complexity and performance. We describe how each of these tasks is done today and indicate how they are likely to change as requirements and implementation technologies evolve.

Analog-to-digital converter algorithms for position error signal estimators

Algorithms are developed that utilize a single analog-to-digital converter in the read channel of a disk drive for dual purposes: for high-rate data detection and for high-resolution servo position error signal estimation. Iterative algorithms exploit the lower clock rate requirement of a servo field, while dithering takes advantage of the periodic characteristic of the servo position waveform.

The effect of a reread on data reliability

When a disk drive sector cannot be reliably decoded on a first try because of excessive errors, the sector may be read a second time. We analyze the effect of rereading the sector on data reliability. To this end, we separate noise sources into two classes: repeatable and nonrepeatable. We derive analytical expressions that predict the data reliability improvements due to reread. We show that, under reasonable assumptions, significant enhancements are achieved by a reread.

Servo-Burst Radial Period Optimization

We propose a performance metric to evaluate various servo-burst strategies. This metric generalizes a previous approach and enables the determination of the optimal servo-burst radial period. The results can be applied to servo-burst formats that can be projected on a two-dimensional signal space, including the quadrature servo-burst format. Here, we consider two estimators that trade complexity with performance