Jaekyun Moon

Maximum transition run codes for data storage systems

A new code is presented which improves the minimum distance properties of sequence detectors operating at high linear densities. This code, which is called the maximum transition run code, eliminates data patterns producing three or more consecutive transitions while imposing the usual k-constraint necessary for timing recovery. The code possesses the similar distance-gaining property of the (1,k) code, but can be implemented with considerably higher rates. Bit error rate simulations on fixed delay tree search with decision feedback and high order partial response maximum likelihood detectors confirm large coding gains over the conventional (0,k) code.

Performance comparison of detection methods in magnetic recording

Various detection schemes suitable for magnetic recording are compared in terms of their effective signal-to-noise ratios. It is shown that at high densities the performance of conventional detectors such as a peak detector, a threshold detector with partial response equalization, a decision feedback equalizer, and a Viterbi algorithm detector tuned to a linearly truncated channel fall far below the optimum performance that can be achieved by the maximum-likelihood sequence detector (MLSD). It is shown that while implementing the full MLSD is clearly out of the question for high densities with severe intersymbol interference (ISI), there exists an efficient detection scheme which achieves an excellent compromise between hardware complexity and detection performance. This scheme, which is called the fixed-delay tree search with decision feedback, combines a fast and efficient tree-search algorithm with a decision feedback equalizer to cancel out a portion of ISI without noise enhancement. It is well suited for run-length-limited systems and attains performance close to that of MLSD while maintaining reasonable implementation cost and processing requirements. >

Pattern-dependent noise prediction in signal-dependent noise

Maximum and near-maximum likelihood sequence detectors in signal-dependent noise are discussed. It is shown that the linear prediction viewpoint allows a very simple derivation of the branch metric expression that has previously been shown as optimum for signal-dependent Markov noise. The resulting detector architecture is viewed as a noise predictive maximum likelihood detector that operates on an expanded trellis and relies on computation of branch-specific, pattern-dependent noise predictor taps and predictor error variances. Comparison is made on the performance of various low-complexity structures using the positional-jitter/width-variation model for transition noise. It is shown that when medium noise dominates, a reasonably low complexity detector that incorporates pattern-dependent noise prediction achieves a significant signal-to-noise ratio gain relative to the extended class 4 partial response maximum likelihood detector. Soft-output detectors as well as the use of soft decision feedback are discussed in the context of signal-dependent noise.

Equalization for maximum likelihood detectors

In this paper, the minimum mean-square error (MMSE) technique has been used to equalize the recording channel in order to facilitate the application of the Viterbi detector. The resulting performance has been compared with that of the optimal equalization system which yields the minimum probability of error at the output of the Viterbi detector. The results indicate that depending on the constraint used in the MMSE design, the amount of noise correlation varies significantly at the equalizer output, which in turn makes a large difference in the performance of the Viterbi detector. In particular, in the jitter-dominant channel where unconditioned channel noise samples are highly correlated, the monic constraint on the equalizer target response tends to whiten the noise samples at the equalizer output. This results in a significant performance improvement of the monic constraint upon the fixed-energy constraint as well as the popular partial response targets of the form (1-D)(1+D)/sup n/. >

Discrete-time modeling of transition noise dominant channels and study of detection performance

Discrete-time modeling of transition-noise-dominant channels is considered which facilitates performance analysis of various sample-data detection schemes. Based on the proposed channel description method in the presence of transition noise, expressions for signal-to-total-noise-power ratios associated with a few selected detection schemes are derived. Under the assumption of a Lorentzian step response and perfect equalization, a comparison is made among different detectors based on the signal-to-noise ratio figure-of-merit evaluated as a function of linear density. >

Signal-to-noise ratio definition for magnetic recording channels with transition noise

This paper proposes a new signal-to-noise ratio (SNR) definition for magnetic recording channels with both additive and medium noise components. The proposed SNR is a generalized version of E/sub b//M/sub 0/, the information bit energy to noise spectral height ratio, widely used in average-power-constrained communication channels with additive white noise. The goal is to facilitate comparison of efficiencies of read channels that may operate at different symbol densities because of varying code rates.

A low-density generator matrix interpretation of parallel concatenated single bit parity codes

A coding scheme that concatenates, in parallel, multiple single bit parity check block codes is considered for use in high areal density magnetic recording. The coding scheme can be viewed as a low-density generator matrix and decoded as a low-density parity check code. Results are obtained using a Lorentzian channel model with and without transition noise that is modeled as first order position jitter. Results show SNR gains over uncoded EPR4 are nearly identical to those using low-density parity-check codes. Having demonstrated similar performance, the practical advantage of decreased encoding complexity and increased decoder architecture flexibility is emphasized.

Single-head/single-track detection in interfering tracks

Off-track interference (OTI) arises as a result of head misalignment and is likely to become the dominant source of errors in future magnetic storage systems with high track density. In this paper, using a two-track and single-head model for OTI, we compare two different equalization/detection techniques aiming at recovering data from only the main track. One is a conventional approach based on suppressing OTI by a linear equalizer and then performing partial response maximum-likelihood (PRML) detection of the main track data. The other views OTI as the response of the channel to an independent data sequence, simultaneously estimates the two data sequences by joint PRML detection, and then simply discards the adjacent track data at the end. We evaluate the detection performance in terms of effective detection signal-to-noise ratio, and provide bit-error-rate simulation results. We also discuss a technique to adaptively estimate the position of the head as well as compensate for the relative phase difference in the offtrack data.

Modeling the Lorentzian magnetic recording channel with transition noise

This paper derives closed-form expressions for modeling a magnetic recording channel with transition noise. The closed-form expressions assume matched filtering, a Lorentzian transition response, and a first-order position jitter and width variation model. The result is a model that is straightforward and easy to use for simulation and analytical purposes. From the model, equations are derived for partial response targets of constrained length that minimize mean squared error in the presence of transition noise. Simulation results for the resulting targets in various transition noise environments are also included, along with a discussion of the results.

Design of a rate 6/7 maximum transition run code

Maximum transition run (MTR) codes provide significant minimum distance gains when used with sequence detectors operating at high linear densities. A method for reducing the RLL k constraint associated with MTR block codes is presented. A block decodable, rate 4/5 MTR code with k=4 illustrates the technique. This reduction of k is combined with sliding-block decoding to develop a 97.8% efficient rate 6/7 MTR code with k=8.