Yuan Xing Lee

Decoding of parallel Reed-Solomon codes with applications to product and concatenated codes

An approach to decode parallel RS codes, based on the multisequence shift-register synthesis algorithm, is considered. The applications include decoding of product and concatenated codes.

Error propagation evaluation for RLL-constrained DFE read channels

Decision feedback equalization (DFE) is a promising low-cost solution for signal detection in magnetic recording channels. In terms of the bit error rate after detection, (0,k)-DFE and MDFE (Multilevel Decision Feedback Equalization) are comparable to (0,k)-PR4ML. Error propagation, however, is one of the major concerns for all DFE approaches. In this paper, an analysis of error propagation for RLL-constrained DFE at all stages of data processing, including RLL decoder and error correction, is performed. To evaluate error propagation, a Markov chain is constructed that explicitly models any type of RLL constraints. From this model, a Markov chain, describing the error distribution inside the bursts, is derived and a relation between these chains and error propagation decay rate is established. Performance of interleaved ECC (Error Correction Code) is also evaluated. The results obtained are compared with those from simulation. By using the newly developed model, a special technique of equalizer design, aimed to reduce error propagation, is analyzed. The comparison between (0,k)-DFE and MDFE in terms of the bit error rate after ECC is also provided.

Performance comparison of a class of (1,7) DFE detectors

At high recording densities, it becomes necessary to use constrained codes for spacing the transitions further apart on the medium to reduce non-linear distortion. In this paper, we present the performance comparison of a class of rate 2/3 (1,7) coded DFE (decision feedback equalization) detectors (conventional DFE, dual DFE, FDTS/DF (fixed delay tree-search with decision feedback), MDFE (multi-level DFE) and M2DFE). M2DFE is a new detector that is a modified version of MDFE incorporating two critical loops for making delayed decisions on marginal samples. Results show that MSDFE outperforms the other detectors, thereby proving to be the best choice for (1,7) coded channels. Further, it (as in MDFE) has the additional advantage of being able to operate at half the user data rate while the other detectors need to operate at 1.5 times the user rate.

Performance comparison of modified multilevel decision feedback equalization detectors

Multilevel decision feedback equalization (MDFE) is a detection scheme that was developed for (1,k) coded recording channels. The user signal-to-noise ratio required to achieve a chosen bit error rate (BER) of 1e-6 has been shown to be about 1.9 dB more than that of the maximum likelihood lower bound for a Lorentzian channel at user density 2.5. Recently, an advanced version of MDFE, called M2DFE, was proposed. By using computer simulations, the BER of M2DFE has been shown to improve by about 1 dB compared to MDFE. In this paper, we first discuss the various aspects of M2DFE design and then present its theoretical analysis. Using the analysis, we show how the two critical parameters in the design are to be chosen for optimum performance. We also propose a modified M2DFE detector, which exploits the noise correlation at the slicer input, to improve the BER performance as well as reduce error propagation considerably. These MDFE detectors are then compared for their BERs and error propagation performances.

Error propagation evaluation for MDFE detection

Multilevel decision feedback equalization (MDFE) provides a simple and effective approach to equalization and detection for high recording densities with bit error rate comparable to PRML. However, in contrast to PRML it has, like any other DFE detector, a significant error propagation. To study this effect, the Markov chain analysis is applied. We will evaluate the performance of MDFE read channel on all subsequent stages of data processing including MDFE detector, run-length limited decoder and error correction decoder. A simple constraint on the feedback equalizer is examined, that may be useful in restricting the resulting error propagation.

DFE timing acquisition: analysis and a new approach for fast acquisition

The problem of timing acquisition in decision feedback equalization (DFE) detectors for magnetic recording channels, in particular the multi-level DFE (MDFE), is considered. We first address the issue of the optimal choice of preamble pattern for timing acquisition and show that a 6T periodic pattern (T being the bit period) is optimum for medium to high user densities. Next, we show that the MDFE timing-error detector using the 6T-pattern is near optimum for acquisition. Finally, we propose a novel threshold-based fast acquisition scheme that can eliminate false lock and effectively prevent hang up problems.

A novel interpolation approach for reducing clock-rate in multilevel decision feedback equalization detectors

The multilevel decision feedback equalization (MxDFE) family of detectors provides excellent performance over (1, 7)-coded magnetic recording channels, while being simple in structure. However, the reduced code-rate of 2/3 increases the channel data rate by 50% compared to the user data rate. Although this is not a problem for the write heads because of the reduced bandwidth of the (1, 7) writing signal [compared with (0, k) codes], it becomes an issue at the detector side for high-data-rate applications. We propose a novel interpolation approach for reducing the detector clock rate. Performance simulations of MDFE and M2DFE detectors, carried out over different user densities, channel models, and equalizer configurations, show that the proposed scheme can reduce the detector clock rate to the user rate with negligible impact on performance. We also present a timing recovery scheme for acquisition and tracking of the reduced-rate clock.

Modulation codes for precoded partial response channels

[d, k] Modulation codes for 1/(1/spl oplus/D/sup 2/) precoded PR4 channels (PPR4) and 1/(1/spl oplus/D/spl oplus/D/sup 2//spl oplus/D/sup 3/) precoded EPR4 channels (PEPR4) are proposed in this paper. They differ from conventional (d, k) constrained codes in the sense that they provide PPR with a direct control over separation between transitions during writing and the number of consecutive zero-samples during reading. Their Finite State Machines (FSM), which have the same Shannon Capacity as their counterparts of (d, k) codes, are constructed. For comparison with the 2/3 (1;7) code, a 2/3 [1, 6] code for PPR4 and a 2/3 [1, 5] code for PEPR4 are designed. They have a 5-state encoder and 8-bit decoding window, and an 8-state encoder and 9-bit decoding window, respectively. Their power spectra are calculated. As an example, error rate performances of (1, 7) PR4ML, (1, 7) PPR4ML, and [1, 6] PPR4ML are simulated under the Lorentzian model with both medium and electronic noises at various channel recording density. The result shows that the [1, 6] PPR4ML outperforms both the (1, 7) PR4ML and the (1, 7) PPR4ML consistently. More importantly, the [d, k] precoded PR (PPR) prevents error propagation which (1, 7) PR may suffer from, and deals with non-linearity more effectively than (1, 7) PPR. The technique presented in this paper is applicable to other extended PPR or precoded generalized PR (PGPR).

An on-the-fly decoding technique for Reed-Solomon codes

An on-the-fly error correction technique for double-byte-error-correction (DBEC) and triple-byte-error-detection (TBED) Reed-Solomon (RS) codes is presented in this paper. This new algorithm finds number of byte-errors (single byte-error, double-byte errors, and triple-byte errors) by simply testing the values of a few syndrome functions, and locates and corrects the byte-errors directly without using the standard iterative algorithms for finding the error location polynomial. More importantly, it neither suffers from malfunctions incurred in Deng-Costello algorithm (1987), nor requires syndrome re-calculation as in Koksal-Yucels modification (1992). It is also much more simpler and faster than the original Deng-Costello algorithm. It has found applications in high-end disk drives where powerful on-the-fly correction is necessary.

A new class of codes in Lee metric and their application to error-correcting modulation codes

A new class of t-error-correcting codes in Lee metric is proposed. For the new codes, unlike the BCH codes in Lee metric, the Galois field characteristic may be chosen independently of t and metric parameter Q. The proposed codes are applied for the bitshift error detection/correction in (d,k)-encoded binary data. The resulting fixed-length error-correcting/modulation code have a regular encoding and can be used for the constraints, imposed by any given FSTD. The 2-shift correcting codes are specially studied. It is shown that both for the finite lengths case and asymptotically these codes outperform the construction based on BCH codes.