Patrick J. Lee

Neural net equalization for a magnetic recording channel

In this paper, we summarize some recent results on the use of neural net equalization in a magnetic recording channel using partial response signaling. Specifically, we compare the performance of various neural net equalizers to the performance of more conventional equalizer designs. The results, which were based on experimentally measured data (includes both known and unknown nonlinear channel characteristics), show that with respect to a mean square error performance metric, the neural net equalizer has significantly better performance than conventional designs.<<ETX>>

Polar codes for magnetic recording channels

Polar codes provably achieve the capacity of binary memoryless symmetric (BMS) channels with low complexity encoding and decoding algorithms, and their finite-length performance on these channels, when combined with suitable decoding algorithms (such as list decoding) and code modifications (such as a concatenated CRC code), has been shown in simulation to be competitive with that of LDPC codes. However, magnetic recording channels are generally modeled as binary-input intersymbol interference (ISI) channels, and the design of polar coding schemes for these channels remains an important open problem. Current magnetic hard disk drives use LDPC codes incorporated into a turbo-equalization (TE) architecture that combines a soft-output channel detector with a soft-input, soft-output sum-product algorithm (SPA) decoder. An interleaved coding scheme with a multistage decoding (MSD) architecture with LDPC codes as component codes has been proposed as an alternative to TE for ISI channels. In this work, we investigate the use of polar codes as component codes in the TE and MSD architectures. It is shown that the achievable rate of the MSD scheme converges to the symmetric information rate of the ISI channel when the number of interleaves is large. Simulations results comparing the performance of LDPC codes and polar codes in TE and MSD architectures are presented.

Post-Error Correcting Code Modeling of Burst Channels Using Hidden Markov Models With Applications to Magnetic Recording

We present two approaches for modeling burst channels using hidden Markov models (HMMs). The first method is based on the maximum-likelihood approach and improves on the computational efficiency of earlier methods. We present new algorithms for scaling and for determining the model parameters by using smart search techniques. We then generalize a gap length analysis and apply it to modeling HMMs. The algorithms are low-complexity and memory-efficient. Finally, we present simulation results for modeling errors in magnetic storage channels and show how this can be used for evaluating decoder failure rates by using Wolfs method, from real observed data

One-pairs codes for partial response magnetic recording

We consider a new constraint on stored data in partial response digital magnetic recording. The one-pairs constraint is an upper bound on the maximum number of symbols between pairs of ones in a coded sequence and can be considered as an alternative to the widely used (0, G/I) constraint. The constraint limits quasi-catastrophic error propagation and guarantees the occurrence of superior timing corrections in partial response class IV (PR4) and extended PR4 (EPR4) magnetic recording systems. In this paper we give low complexity rate 8/9, 16/17, and 24/25 block codes, derive the capacity of this constraint, and compute the power spectral density for maxentropic codes. The codes achieve greater than 95% of channel capacity and the 24/25 code has smaller than expected error propagation.

Post-ECC Modeling of Magnetic Recording Channels using Hidden Markov Models

In this paper, we present maximum-likelihood modeling of burst errors in magnetic recording channels using hidden Markov models (HMM). We derive low-complexity and memory efficient algorithms for computing the log-likelihood function for burst sequences, and use this algorithm to optimally determine the model parameters using smart search techniques. Finally, we illustrate a modeling example from real observed data collected from hard disks, and show how the model can be applied for evaluating decoder failure rates using Wolfs method [5].

On the Probability of Undetected Error for Over-Extended Reed-Solomon Codes

We derive upper and lower bounds on the weight distribution of Over-Extended Reed-Solomon (OERS) codes. Using these bounds, we obtain tight upper and lower bounds on the probability of undetected error for OERS codes on q-ary symmetric channels.

Codes for improved timing recovery in PR4 and EPR4 magnetic recording

We consider an alternative to the widely-used (0,G/I) constraint in partial response digital magnetic recording systems. The new one-pairs constraint is an upper bound on the maximum number of symbols between pairs of ones in a coded sequence. Codes for the one-pairs constraint can be used to limit quasi-catastrophic error propagation and improve timing recovery in Class-IV partial response (PR4) and Extended PR4 (EPR4) magnetic recording systems. Rate 4:5, 8:9, 16:17, and 24:25 block and finite state codes are discussed and compared with well-known rate 8:9 and 16:17 block codes. The new codes have improved one pairs statistics, low complexity, and for the 24:25 code, reduced error propagation.

Capacity, power spectral density, and codes for the one-pairs constraint

We consider a new constraint for improved timing recovery in partial response digital magnetic recording. The one-pairs constraint is an upper bound on the maximum number of symbols between pairs of ones in a coded sequence and can be considered as an alternative to the widely-used (0,G/I) constraint. We derive the capacity of this constraint, compute the power spectral density for maxentropic one-pairs constrained codes and give rate 16/17 and 24/25 block codes for this constraint.

Parallel error-trapping and error-detection decoding

The authors present a parallel decoding method for a concatenated outer (nearest the channel) error-correcting code (ECC) and inner (nearest the user) error-detecting code (EDC). This method can be used if (1) both the ECC and EDC are linear codes, (2) the ECC decoder can be implemented as an error-trapping decoder, and (3) the EDC decoder is realized by a polynomial division circuit. The parallel decoding algorithm is described when the received codeword is corrected by both a forward and a backward error-trapping ECC decoder. A mathematical justification for the algorithm is presented.<<ETX>>