Noise Predictive Maximum Likelihood Research Articles

PR-NN: RNN-Based Detection for Coded Partial-Response Channels

In this paper, we investigate the use of recurrent neural network (RNN)-based detection of magnetic recording channels with inter-symbol interference (ISI). We refer to the proposed detection method, which is intended for recording channels with partial-response equalization, as Partial-Response Neural Network (PR-NN). We train bi-directional gated recurrent units (bi-GRUs) to recover the ISI channel inputs from noisy channel output sequences and evaluate the network performance when applied to continuous, streaming data. The computational complexity of PR-NN during the evaluation process is comparable to that of a Viterbi detector. The recording system on which the experiments were conducted uses a rate-2/3, (1,7) runlength-limited (RLL) code with an E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> PR4 partial-response channel target. Experimental results with ideal PR signals show that the performance of PR-NN detection approaches that of Viterbi detection in additive white gaussian noise (AWGN). Moreover, the PR-NN detector outperforms Viterbi detection and achieves the performance of Noise-Predictive Maximum Likelihood (NPML) detection in additive colored noise (ACN) at different channel densities. A PR-NN detector trained with both AWGN and ACN maintains the performance observed under separate training. Similarly, when trained with ACN corresponding to two different channel densities, PR-NN maintains its performance at both densities. Experiments confirm that this robustness is consistent over a wide range of signal-to-noise ratios (SNRs). Finally, PR-NN displays robust performance when applied to a more realistic magnetic recording channel with MMSE-equalized Lorentzian signals.

123 Gbit/in&lt;sup&gt;2&lt;/sup&gt; Recording Areal Density on Barium Ferrite Tape

The recording performance of a prototype magnetic tape based on perpendicularly oriented barium ferrite particles is investigated using an enhanced field tape write head and a 90 nm wide giant-magnetoresistive reader. A linear density of 680 kbits/in with a postdetection byte-error rate (BER) <;3.2e-2 is demonstrated based on recorded data processed by a software read channel with noise-predictive maximum likelihood detection. With this detector error rate, a user BER of <;1e-20 can be achieved by means of product error correction coding and iterative decoding. Several advances in the area of track-following servo control are also presented. Specifically, we describe a new timing-based servo pattern, which in combination with an optimized servo channel enables the generation of position estimates with nanoscale resolution and a high update rate. Track-following experiments are performed using an experimental low-noise tape transport, a prototype high-bandwidth actuator, and a set of speed-optimized H-infinity-based track-following controllers. Combining these technologies, we demonstrate a position-error signal (PES) with a standard deviation of 5.9 nm or less over a tape speed range of 1.23-4.08 m/s. This magnitude of PES in combination with a 90 nm wide reader allows operation with 140 nm wide tracks. Combined with a linear density of 680 kbits/in, this leads to an equivalent areal density of 123 Gbits/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Generalized Partial Response Equalization and Data-Dependent Noise Predictive Signal Detection Over Media Models for TDMR

Two-dimensional magnetic recording (2-D TDMR) is an emerging technology that aims to achieve areal densities as high as 10 Tb/in2 using sophisticated 2-D signal-processing algorithms. High areal densities are achieved by reducing the size of a bit to the order of the size of magnetic grains, resulting in severe 2-D intersymbol interference (ISI). Jitter noise due to irregular grain positions on the magnetic medium is more pronounced at these areal densities. Therefore, a viable read-channel architecture for TDMR requires 2-D signal-detection algorithms that can mitigate 2-D ISI and combat noise comprising jitter and electronic components. Partial response maximum likelihood (PRML) detection scheme allows controlled ISI as seen by the detector. With the controlled and reduced span of 2-D ISI, the PRML scheme overcomes practical difficulties such as Nyquist rate signaling required for full response 2-D equalization. As in the case of 1-D magnetic recording, jitter noise can be handled using a data-dependent noise-prediction (DDNP) filter bank within a 2-D signal-detection engine. The contributions of this paper are threefold: 1) we empirically study the jitter noise characteristics in TDMR as a function of grain density using a Voronoi-based granular media model; 2) we develop a 2-D DDNP algorithm to handle the media noise seen in TDMR; and 3) we also develop techniques to design 2-D separable and nonseparable targets for generalized partial response equalization for TDMR. This can be used along with a 2-D signal-detection algorithm. The DDNP algorithm is observed to give a 2.5 dB gain in SNR over uncoded data compared with the noise predictive maximum likelihood detection for the same choice of channel model parameters to achieve a channel bit density of 1.3 Tb/in2 with media grain center-to-center distance of 10 nm. The DDNP algorithm is observed to give $\sim$ 10% gain in areal density near 5 grains/bit. The proposed signal-processing framework can broadly scale to various TDMR realizations and areal density points.

85.9 Gb/in&lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$^{ {2}}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; Recording Areal Density on Barium Ferrite Tape

The recording performance of a new magnetic tape based on perpendicularly oriented barium ferrite particles was investigated using a 90-nm-wide giant-magnetoresistive reader and a prototype enhanced-field write head. A linear density of 600 kb/in with a postdetection byte-error rate <;3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> was demonstrated based on measured recording data and a software read channel that used a noise-predictive maximum likelihood detection scheme. Using a new iterative decoding architecture, a user bit-error rate of <;1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-20</sup> can be achieved at this operating point. To facilitate aggressive scaling of the track density, we made several advances in the area of the track-following servo. First, we developed an experimental low-noise tape transport. Second, we implemented an optimized servo channel that together with an experimental timing-based servo pattern enables the generation of position estimates with nanoscale resolution at a high update rate. Third, we developed a field-programmable gate array-based prototyping platform in which we have implemented the servo channel and an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -based track-following controller, enabling real-time closed-loop track-following experiments. Combining these technologies, we achieved a position-error signal (PES) with a standard deviation of 10.3 nm. This magnitude of PES in combination with a 90-nm-wide reader allows the writing and reading of 177-nm-wide tracks at 600 kb/in, for an equivalent areal density of 85.9 Gb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This paper clearly demonstrates the continued scaling potential of tape technologies based on low-cost particulate media.

Performance evaluation of signal dependent noise predictive maximum likelihood detector for two-dimensional magnetic recording read/write channel

Two-dimensional magnetic recording is affected by the inter-track interference (ITI) from the adjacent tracks. We investigate the improvement of partial response maximum likelihood (PRML) systems with signal dependent noise predictor (SDNP) in the bit error rate performance. The systems reduce the influence of ITI by two dimensional finite impulse response filter using the waveforms reproduced by triple readers from the adjacent tracks. The results show that the SDNP provides larger improvement to PR(2,6,1)ML system compare with PR1ML system.

40 Gb/s Operation of SOA-REAM in Single-Feeder WDM-PON [Invited

The integrated semiconductor optical amplifier (SOA) with a reflective electro-absorption modulator (REAM) is a promising candidate for the colorless optical network unit in a wavelength-division-multiplexed passive optical network (WDM-PON), due to its low chirp and wide bandwidth. However, 40&#x00A0;Gb/s operation of REAMs (bandwidth &#x2264; 20&#x00A0;GHz) still encounters severe intersymbol interference. Furthermore, Rayleigh backscattering (RB) and discrete reflections cause strong beat noise in WDM-PONs with single-fiber loopback configuration. In this paper, we present two novel techniques based on electrical equalization for a 40-Gb/s single-feeder WDM-PON based on SOA-REAM. The first method is to employ partial-response (PR) signaling and a noise predictive maximum likelihood (NPML) equalizer at the upstream receiver. The other one combines correlative level (CL) pre-coding with partial-response maximum likelihood (PRML) equalization. We experimentally demonstrate a 40-Gb/s uplink of 20&#x00A0;km using a 20-GHz SOA-REAM in a WDM-PON by both PR-NPML and CL-PRML. The results also verify the superiority of PR-NPML over the previously reported equalizers. Moreover, compared with PR-NPML, CL-PRML further improves the system performance. Experiments prove that the tolerance to beat noise and the receiver sensitivity are enhanced by 4&#x00A0;dB and 0.8&#x00A0;dB, respectively, at a bit error ratio of 2&#x00D7;10&#x2212;4.

Demonstration of 40-Gb/s WDM-PON System Using SOA-REAM and Equalization

The wavelength-division-multiplexed passive optical network (WDM-PON) has been widely considered as the ultimate solution for future bandwidth-hungry access networks. However, in WDM-PON, the necessity of colorless operation and low cost constrains the choice of upstream transmitter and thus limits the achievable data rate. The integrated semiconductor optical amplifier-reflective electro-absorption modulator (SOA-REAM) is a promising candidate for uplink transmitter, because of its wide modulation bandwidth and low chirp. In this letter, a novel equalization technique based on noise predictive maximum likelihood (NPML) and partial response (PR) signaling is proposed to enable SOA-REAM-based 40-Gb/s WDM-PON. We experimentally demonstrate a 40-Gb/s error-free transmission over 20-km, using a 20-GHz SOA-REAM. Moreover, the performance of the proposed PR-NPML equalizer is compared with that of other common equalizers in both the transmission and the reflection studies.

29.5-$\hbox{Gb/in}^{2}$ Recording Areal Density on Barium Ferrite Tape

The recording performance of a new magnetic tape based on ultra-fine, perpendicularly-oriented BaFe particles was investigated. Specifically, using a low lateral tape motion demonstration platform, a new servo pattern written on the advanced perpendicularly oriented BaFe medium, a new low friction head technology, a novel synchronous servo channel design, and advanced servo control concepts, we were able to demonstrate a record closed-loop track-follow performance with a 23.4 nm standard deviation of position-error signal, roughly one order of magnitude better than in current tape products. In addition, using read back waveforms captured on the same advanced perpendicularly oriented BaFe medium with a 0.2-μm -wide data reader, we demonstrated write/read performance at 518 kbpi using advanced noise-predictive maximum likelihood (NPML) detection schemes. Combining these two results, we estimate that the new medium can support an areal recording density of up to 29.5 Gb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This result demonstrates the scalability and extendability of tape technology using low-cost particulate media.

High Recording Density Tape Using Fine Barium-Ferrite Particles With Improved Thermal Stability

The effects of reducing barium-ferrite magnetic particle volume have been studied. We optimized barium-ferrite substitution elements and their amount and demonstrated thermal stability for very fine particles of the size 1.5 × 103 nm3. Using a giant magnetoresistive (GMR) head with a 0.2 ?m read track width, test tape containing these fine particles exhibited a bit error rate of 1.5 ×10-4 at a linear density of 360 kbpi using a noise predictive maximum likelihood (NPML) detection for nonstationary noise sources, i.e., data-dependent noise. This corresponds to a 15 Gb/in2 areal recording density in linear tape application.

Performance evaluation of detectors for perpendicular recording systems

This paper evaluates the performance of detectors with d = 1 constraint for perpendicular recording systems under assumptions of nonlinear distortion. Nonlinear distortions considered are transition jitter and DC-offset. Detectors used in this study are the partial response maximum likelihood (PRML), noise-predictive maximum likelihood (NPML), fixed delay tree search with decision feedback (FDTS/DF), dual decision feedback equalizer (DDFE) and multilevel decision feedback equalizer (MDFE). Their performances are discussed in terms of mean squared error (MSE) and noise power spectra of equalizer at discrimination point and similarity of frequency response between overall system and partial response (PR) target polynomial.

Adaptive noise-predictive maximum-likelihood (NPML) data detection for magnetic tape storage systems

Advanced data detection will be one of the key enablers to achieving the very high areal recording densities of future tape storage systems. Departing from the partial-response maximum-likelihood (PRML)-based read channel design traditionally used in tape systems, this paper describes noise-predictive maximum-likelihood (NPML) detection, which is a technique that has been known for many years in the hard-disk-drive industry but has been introduced for the first time in the tape storage industry in IBM tape drives. In the NPML read channel design, the readback signals are conditioned prior to data detection so that their noise components are statistically decorrelated and reduced in power. This paper describes the basic principles of NPML detection and its application to tape systems in the form of a 16-state detector. It is argued that, because of the inherent variability of the recording channel characteristics in tape drives, fully adaptive NPML detection needs to be realized in order to optimize detection performance. Actual readback waveforms of data recorded on metal particulate as well as barium-ferrite particulate tape media are used to illustrate the error rate performance achieved by 16-state and 32-state NPML detectors. It is shown that, under realistic worst-case channel conditions, a 16-state NPML detector could offer an improvement in error rate after an error-correcting code of approximately two orders of magnitude.

Performance of Advanced Data-Detection Schemes on Barium-Ferrite Particulate Media

Noise-predictive maximum likelihood (NPML) detection has become state of the art in modern hard-disk drive (HDD) systems. Tape drive systems, in contrast, have typically adopted a traditional partial-response maximum likelihood detection approach, a fact that mainly reflects the large disparity in areal recording density between tape drives and HDDs. However, tape drive systems maintain a growth rate in areal recording density that is similar to that of HDDs, which implies that in future tape storage systems also advanced detection schemes need to be employed. This paper investigates the performance achieved by NPML, in particular, data-dependent NPML for data detection on barium-ferrite (BaFe) particulate tape media. Using actual readback waveforms, it is found that these advanced detection techniques are fairly efficient in improving the bit-error-rate performance of the read channel. Therefore, they enable, in combination with the BaFe media, a significant increase in linear recording density over that of state-of-the-art tape systems.

Partial-response coding, maximum-likelihood decoding: capitalizing on the analogy between communication and recording [History of Communications

Signal processing and coding technology for digital magnetic recording is the core technology of the channel electronics module in a hard disk drive (HDD) that processes signals read from magnetic media. In this historical review I focus on what is now widely known as partial-response, maximum-likelihood (PRML) technology, which takes advantage of the inherent redundancy that exists in signals read out of magnetic media; its theoretical foundation goes back to 1970, and it capitalizes on the analogy between high-speed data transmission and high-density digital recording, and that between a convolutional code and a partial-response signal. The first PRML-based product was introduced by IBM in 1990, and PRML technology soon became the industry standard for all digital magnetic recording products, ranging from computers' HDDs and tape drives to micro hard discs used in PCs, mobile phones, and MP3 players; use of the PRML principle has recently been extended to optical recording products such as CDs and DVDs. Its improved version, called NPML (noise-predictive, maximum-likelihood), and variants have been adopted by the HDD industry since 2000. Today, a large number of communication and information theory researchers are investigating use of advanced techniques such as turbo coding/decoding to further improve the density and reliability of both magnetic and optical recording systems.

Message-passing iterative decoding between detector and RSC code decoder for PMR channel

For higher density perpendicular magnetic recording (PMR) systems, it is difficult to expect an improvement in performance when only partial response maximum likelihood (PRML) or noise predictive maximum likelihood (NPML) detection is used. Hence, we consider a system that performs better than either PRML or NPML. We concatenate a channel detector using a recursive systematic convolutional (RSC) code decoder and a message-passing algorithm. The RSC code itself is simple but its performance is inferior to other iterative decoding methods. Therefore, we used channel iteration between the channel detector and the RSC decoder in order to improve performance. We also used a precoding and random interleaver. We evaluated the performance on the PMR channel with jitter noise.

6.7 ${\hbox{Gb/in}}^{2}$ Recording Areal Density on Barium Ferrite Tape

We investigated the performance of a barium ferrite tape medium in linear tape recording, using a giant-magnetoresistive read head of 0.5 mum track width. A linear density of 400 kbpi with an error rate of 6 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> was demonstrated based on measured recording data and a simulated channel with advanced noise predictive maximum likelihood detection schemes. Using a timing-based servo format that reduces the position error signal (PES) due to medium jitter and servo-writer velocity variations, we achieved a PES of 0.07 mum standard deviation and a maximum PES (in a 10-s interval) of 0.35 mum. This PES magnitude allows the writing and reading of 1.5-mum tracks at 400 kbpi, for an equivalent areal density of 6.7 Gb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Adaptive noise-predictive maximum likelihood detection using tentative decision and partial path selection

We present a noise-predictive maximum likelihood (NPML) detection scheme considering both low complexity and effective adaptation. First, for achieving low complexity, we exploit the modified Viterbi decoding method that partially selects the survival paths. The partial path selection method limits the number of selected paths among all survival paths at the Viterbi trellis and selects a path with minimum metric among the selected paths while the original Viterbi algorithm considers all paths and decides the best path. Next, for effective adaptation, we propose an adaptive NPML scheme exploiting a tentative decision value of the Viterbi decoding process.

A simplified noise-predictive partial response maximum likelihood detection using M-algorithm for perpendicular magnetic recording channels

We propose a simplified noise-predictive partial response maximum likelihood (NPML) system in conjunction with M-algorithm for dual-layered perpendicular magnetic recording channels. The complexity, which is increased by the construction of noise prediction filter, can be reduced through the M-algorithm. Despite the complexity of the proposed scheme (M=4) is decreased to 1/4 than one of the full NP(12321)ML system, two systems maintain almost the same bit-error rate and the detection performance of the noise-predictive maximum likelihood is better than that of the conventional PRML.

Noise-Predictive Viterbi Detector with Pattern-Dependent Distortion Canceller for High-Density Optical Recording

We propose noise-predictive maximum-likelihood (NPML) detection with a pattern-dependent distortion canceller (PDDC) to cancel nonlinear distortion. NPML detection and NPML/PDDC detection were applied to a Blu-ray disc with a capacity of 27 Gbytes. The detection performance was investigated. And the results are reported. Both the NPML detector and the NPML/PDDC detector lower bit error rate (BER), and improve the radial-tilt margin and spherical-aberration margin. Only the NPML/PDDC detector could improve tangential-tilt margin, however.

A dual noise-predictive partial response decision-feedback equalizer for RLL(1,x) coded perpendicular magnetic recording channels

Partial response maximum likelihood (PRML) is a powerful and indispensable detection scheme for perpendicular magnetic recording channels. The performance of PRML can be improved by incorporating a noise prediction scheme into branch metric computations of the Viterbi algorithm (VA). However, the systems constructed by VA have shortcomings in the form of high complexity and cost. In this connection, a new simple detection scheme is proposed by exploiting the minimum run-length parameter d=1 and is extended to dual-detection scheme for improving the bit-error rate (BER) performance. Simulation results show that the proposed scheme has a comparable performance to noise-predictive maximum likelihood detector with less complexity when the partial response (PR) target is (1,2,1).

A novel fast approach for estimating error propagation in decision feedback detectors

The study of error-burst statistics is important for all detection systems, and more so for the decision feedback class. In data storage applications, many detection systems use decision feedback in one form or another. Fixed-delay tree search with decision feedback (FDTS/DF) and decision feedback equalization (DFE) are the direct forms, whereas the partial response detectors such as the reduced state sequence estimator (RSSE) and noise predictive maximum likelihood (NPML) detectors are the other forms. Although DF reduces the system complexity, it is inevitably linked with error propagation (EP), which can be quantified using error-burst statistics. Analytical evaluation of these statistics is difficult, if not impossible, because of the complexity of the problem. Hence, the usual practice is to use computer simulations. However, the computational time in traditional bit-by-bit simulations can be prohibitive at meaningful signal-to-noise ratios. In this paper, we propose a novel approach for fast estimation of error-burst statistics in FDTS/DF detectors, which is also applicable to other detection systems. In this approach, error events are initiated more frequently than natural by artificially injecting noise samples. These noise samples are generated using a transformation that results in significant reduction in computational complexity. Simulation studies show that the EP performance obtained by the proposed method matches closely with those obtained by bit-by-bit simulations, while saving as much as 99% of simulation time.