Capacity Approaching Run-Length-Limited Codes for Multilevel Recording Systems

We propose two constructions for multilevel run-length-limited (RLL) block codes for which the rates are very close to the capacity. For each code construction, we propose a variation that has the advantage of low complexity of encoding and decoding. We conducted a simulation to see the combined effect of channel coding and our proposed RLL coding over an optical recording channel.     

Quasi-Cyclic LDPC Codes for the Magnetic Recording Channel: Code Design and VLSI Implementation

By implementing a field-programmable gate array (FPGA)-based simulator, we investigate the performance of randomly constructed high-rate quasi-cyclic (QC) low-density parity-check (LDPC) codes for the magnetic recording channel at very low block sector error rates. On the basis of extensive simulations, we conjecture guidelines for designing randomly constructed high-rate regular QC-LDPC codes with low error floor for the magnetic recording channel. Experimental results show that our high-rate regular QC-LDPC codes do not suffer from error floor, at least at block error rates of 10^-9, and can realize significant coding gains over Reed-Solomon codes that are used in current practice. Furthermore, we develop a QC-LDPC decoder hardware architecture that is well suited to achieving high decoding throughput. Finally, to evaluate the implementation feasibility of LDPC codes for the magnetic recording channel, using 0.13 mum standard cell and memory libraries, we designed a read channel signal processing datapath consisting of a parallel max-log-MAP detector and a QC-LDPC decoder, which can achieve a throughput up to 1.8 Gb/s     

Optimal code rates for concatenated codes on a PR4-equalizedmagnetic recording channel

At some nominal recording density, the read signal in digital magnetic recording resembles a Class IV partial response (PR4) signal and, hence, may be equalized to the PR4 shape with relatively little noise enhancement. When coding is added, for a fixed user density, the recording density must increase as a result of coding overhead, and the read signal will resemble PR4 to a lesser extent. Equalization to PR4 in this case will produce excessive noise enhancement. Thus, coding overhead (or rate) must be selected for optimum tradeoff between code strength and noise enhancement. Toward this end, we provide results for high-rate concatenated codes, assuming a Lorentzian recording channel model. In addition to examining optimal code rates, we compare parallel and serial concatenated code performance on the PR4 channel     

A study of PRML systems by write and read equalization

A new partial response (PR) channel which contains the write equalizer in addition to conventional PR channel is proposed. Our write equalizer outputs DC-free waveforms of two levels. Our read equalizer can reduce high-frequency noise, and what is more, it has little degradation of eye opening. The PR channels in combination with Viterbi decoder give partial response maximum-likelihood (PRML) systems which exhibit a good performance. The bit error rates for several PRML systems are obtained by computer simulation, where a Lorentzian channel with additive white Gaussian noise is assumed. The results shows that PR(1,1,-1,-1) system has an excellent performance in high density recording for a system in which the small transition spacings required by our write equalization is allowed     

Two-dimensional binary halftoned optical intensity channels [optical wireless communications]

The capacity of two-dimensional (2D) optical intensity channels in which transmit images are constrained to be binary-level has been considered. Examples of such links exist in holographic storage, page-oriented memories, optical interconnects, 2D barcodes as well as multiple-input/multiple-output wireless optical links. Data are transmitted by sending a series of time-varying binary-level optical intensity images from transmitter to receiver. Neither strict spatial alignment between transmitter and receiver nor independence among the spatial channels is required. The approach combines spatial discrete multitone modulation developed for spatially frequency selective channels with halftoning to produce a binary-level output image. Data are modulated in spatial frequency domain as dictated by a water pouring spectrum over the optical transfer function as well as channel and quantisation noise. A binary-level output image is produced by exploiting the excess spatial bandwidth available at the transmitter to shape quantisation noise out of band. A general mathematical framework has been presented, in which such systems can be analysed and designed. In a pixelated wireless optical channel application, halftoning achieves 99.8% of the capacity of an equivalent unconstrained continuous amplitude channel using lmegapixel arrays.     

Constrained multitrack RLL codes for the storage channel

Multitrack codes that have recently been proposed for the magnetic storage channel promise larger capacities than conventional run-length limited (RLL) single-track codes. We propose two additional constraints that allow the design of efficient multitrack RLL codes, while incorporating more tolerance to timing and synchronization failures. The effect on the capacity is minimal     

Low-Density Parity-Check Coded Recording Systems With Run-Length-Limited Constraints

We propose two techniques for the low-density parity-check (LDPC) coded partial response channel with run-length-limited (RLL) constraints. The first is a modification of the selective flipping technique so that side information is not needed. The second is based on the estimation of flipped bits for the selective flipping technique. The second technique can achieve significant performance improvement over the simple selective flipping technique either with side information or without side information. We also incorporate these two techniques into a known technique to design LDPC coded recording systems that can meet strict RLL constraints without performance degradation.      

Time interval analysis errors in measuring recording mediatransition jitter

Media transition position jitter noise can be a dominant signal-to-noise ratio (SNR) issue in magnetic recording systems with magnetoresistive (MR) heads and (0,k) PRML channels, since the high MR head “gain” emphasizes media jitter noise over electronic noise, and (0,k) codes are sensitive to dibit jitter. Time interval analyzer (TIA) instruments are useful for measuring transition jitter (write jitter), since they can separate write jitter from electronic noise (read jitter) with minimal synchronization and speed variation difficulties. This paper analyzes TIA errors due to read channel intersymbol interference (ISI), which occurs even though TIA measurements are made with periodic LF or HF bit patterns at equal bit intervals “T”, which should be unchanged by ISI. Theory and data show that TIA measurements underestimate jitter by as much as 40% at low channel bit density D_c≡P₅₀/T≈1.5-1.8, and overstate jitter at high density. Even though typical TIA jitter measurements are made between nonadjacent pattern pulses, these errors still occur due to ISI by unmeasured neighbor pulses. It is shown that similar errors occur with TIA electronic read jitter noise measurements. At channel densities above D_c≈2.6, channel amplification of transition jitter occurs, which may be a factor in PRML channel bit density limits     

Multitrack Digital Data Storage: A Reduced Complexity Architecture

We describe a low-complexity noniterative detector for magnetic and optical multitrack high-density data storage. The detector is based on the M-algorithm architecture. It performs limited breadth-first detection on the equivalent one-dimensional (1-D) channel obtained by column-by-column helical unwinding of the two-dimensional (2-D) channel. The detection performance is optimized by the use of a specific 2-D minimum-phase factorization of the channel impulse response by the equalizer. An optimized path selection scheme maintains the complexity close to practical 1-D Viterbi. This scheme is based on an approximate path metric parallel sort network, taking advantage of the metrics' residual ordering from previous M-algorithm iterations. Such an architecture approaches maximum-likelihood performance on a high areal density uncoded channel for a practical number of retained paths M and bit error rate (BER) below 10^-4. The performance of the system is evaluated when the channel is encoded with multi-parity check (MPC) block inner code and an outer interleaved Reed-Solomon code. The inner code enhances the minimum error distance of the equalized channel and reduces the correct path losses of the M-algorithm path buffer. The decoding is performed noniteratively. Here, we compare the performance of the system to the soft iterative joint decoding of the read channels for data pages encoded with low-density parity check (LDPC) codes with comparable rates and block length. We provide an approximation of the 2-D channel capacity to further assess the performance of the system     

Finite-Length Extrinsic Information Transfer (EXIT) Analysis for Coded and Precoded ISI Channels

In this paper, we consider the classic problem of accessing coded and precoded intersymbol interference (ISI) channels, and particularly partial response (PR) channels, which are widely used in modeling magnetic recording systems. Previous work has either treated the binary precoder as an exclusive function of the channel characteristics, disregarding possible impact from the channel code, or, in performing the iterative analysis of this concatenated system, assumed an unbounded length. Our approach here is to extend the conventional infinite-length extrinsic information transfer (EXIT) charts to ISI systems of limited lengths, and to explicitly account for the effect of the channel nonergodicity. We found that short-length channel codes may exhibit distinctively different EXIT behaviors in different rate regions, and it is important to couple the precoder and the channel code. We show that infinite- and finite-length EXIT behaviors do not always agree, and hence the results obtained from the infinite-length analysis may not hold for practical short-length systems.     

Joint design of optimum partial response target and equalizer for recording channels with jitter noise

We address joint design of optimum generalized partial response (GPR) target and equalizer for perpendicular recording channels with jitter noise. We develop a new cost function which accounts for the data-dependent nature of jitter noise based on the minimum mean square error (MMSE) criterion. Using the step-response-based channel model, we derive expressions for the statistics required to compute the optimum equalizer and target in the presence of jitter noise. We also derive a bit-response-based model for the jitter noise channel. We present an approach for doing simulations as well as analytical computations for the jitter noise channel without resorting to the widely used Taylor series approximations. Our computational and simulation results show that, while the targets designed without accounting for the jitter lead to error-floor effect in the bit-error-rate performance, the targets designed by our approach give significant performance improvement under high jitter conditions, with no sign of error-floor effect for the range of signal-to-noise ratios considered.     

Evaluation of the capabilities of several ions to sensitize Nd in the laser material LNA (La0.9Nd0.1MgAl11O19)

In the hexaaluminate laser material La_0.9Nd_0.1MgAl₁₁O₁₉ also known as LMA:Nd the Nd³⁺ fluorescence can be enhanced by codoping the matrix with rare-earth (REⁿ⁺) or transition metal (TM^m+) ions. A large number of potential donor ions D (D = Mn²⁺, Dy³⁺, Tb³⁺, Eu²⁺, Eu³⁺ and Ti³⁺) are studied in the hexaaluminate host. The D→Nd³⁺ energy transfer, t he, luminescent efficiency as well as the back-transfer strongly depend on the overlap of the D emission and Nd³⁺ absorption, the concentration of the two ions and their localization in the crystal host. In this paper the optical properties — absorption and emission — of the D and Nd³⁺ ions as well as the D→Nd³⁺ interactions are considered using a Forster-Dexter's approach, to compare the capabilities of the different donors in the Nd³⁺-doped hexaaluminate host. The C_DNd and R₀ parameters are estimated in each case, and the results discussed in terms of the localization of the donor ions, their absorption and emission as well as their lifetime properties.     

Service differentiated drop code unit for metro ring optical networks

The authors demonstrate using both simulation and experiment, a drop code unit for metro ring optical networks with service differentiation capability. This is achieved by means of a spectral amplitude coding technique whereby the code weight in a particular channel is varied to provide different signal quality levels. Transmission of three channels with different weights operating at 10 Gbps per channel was simulated over a 68 km unamplified and 185 km amplified links of dispersion compensated fibre. Services are perfectly dropped at bit error rates from 10^-9 to 10^{-3, leaving the through service free from accumulated noise. The authors also present a 2.5 Gbps per channel proof-of-concept experiment over 40 km of single-mode fibre (SMF).}     

Rate 8/9 sliding block distance-enhancing code with stationarydetector

A new distance-enhancing code for partial-response magnetic recording channels eliminates most frequent errors, while keeping the two-step code trellis time invariant. Recently, published trellis codes either have lower code rates or result in time-varying trellises with a period of nine, thus requiring a higher complexity of detectors and code synchronization. The new code introduces dependency between code words in order to achieve the same coding constraints as the 8/9 time-varying maximum transition runlength (TMTR) code, with the same code rate, but resulting in a trellis that has a period of 2. This code has been applied to the E²PR4 and a 32-state generalized partial response (GPR) ISI target. The resulting two-step trellises have 14 and 28 states, respectively. Coding gain is demonstrated for both targets in additive white Gaussian noise     

Application of MTR soft-decision decoding in multiple-head magnetic recording systems

Application of a simple approach for the soft-decision decoding of Maximum-Transition-Run (MTR) codes has been presented in this paper. A lowdemanded hardware realization have been proposed for soft-decision decoding in MTR basic AND, OR and XOR logic circuits. The suggested approach is explored over the two-track, two-head E²PR4 partial response magnetic recording system. The overall two-track channel detection complexity reduction of 41·9% is offered in simulation scheme, encoded by Low-Density Parity-Check (LDPC) code, serially concatenated with inner MTR. The 1·9 dB coding gain has been obtained, comparing to uncoded channel and assuming the AWGN noise presence.     

Multi-level decision feedback equalization for saturation recording

An impediment to the practical use of fixed-delay tree search with decision feedback (FDTS/DF) for retrieving data from hard disk drives is that four additions and one multiplications must be evaluated in one clock cycle. It is shown here that on recording channels using 2/3(1,7) run-length-limited (RLL) coding, a detector achieving the performance of FDTS/DG can be implemented with a two-tap transversal filter. The feedback loop can be rearranged so that this transversal filter no longer resides in the forward path of the feedback loop. Instead, its transfer function is incorporated into the specification of the forward and backward equalizers. This modification leads to a simpler equalizer architecture in which the slicer performs binary decisions on a multilevel signal. Implementation issues pertaining to phase detection, gain detection, DC detection and adaptive equalization using a least-mean-squared (LMS) technique are addressed. Simulation results are given     

Magnetooptics, lasers, and memory systems

The field of magnetooptics is reviewed and the application of a magnetic memory system as a readout technique is discussed. A review and comparison of the fundamental magneto-optic effects and their utility in a system is presented. It is shown for a longitudinal Kerr readout system that laser and shot noise limit wide-band (1 MHz) signal-to-noise ratios to about 40 dB. Media noise problems are reviewed. The limitations to packing density are discussed, and it is concluded that packing densities greater than 10⁷bit/in²(including suitable guardbands) are practical. The various techniques for optico-thermal recording are surveyed. A discussion of related hardware components (such as optical modulators and lasers) is presented. It is concluded that a viable magnetooptic detection-laser beam memory system is practical. No suitable nonmechanical scanning system has yet been developed.     

3 Gb/in2 recording demonstration with dual element headsand thin film disks

We have successfully demonstrated magnetic recording at an areal density of 3 Gb/in² with narrow track inductive-write MR-read dual element heads on low noise Co alloy thin film disks. In this demonstration, the write head is a ten turn thin film inductive head with thick and narrow P2 pole-tips. The read head is a shielded ~1 μm trackwidth MR sensor soft-film biased in the read region for linearization and exchange-biased at the tail regions for magnetic stabilization. During recording tests, the heads were flown over low noise Co-alloy media at a clearance similar to that in the previous 1 Gb/in² recording experiment. Results showed good writability from the narrow track write head in terms of overwrite and hard transition shift. Readback yields symmetrical signals as large as 600 μV (p-p) and rolloff measurements showed 50% densities as high as 5000 fc/mm. Track profile and microtrack profile measurements showed the write and read trackwidths to be ~1.4 μm and ~1.1 μm respectively, with tight side-writing and side-reading characteristics. An overall assessment of the parametric recording results suggested areal density feasibility up to as high as 3 Gb/in². This projection was confirmed by error rate performance testing using a PRML channel with a digital filter and write precompensation. At a data rate of 4-5 Mb/s and at very low ontrack error, a linear density as high as 185 Kbpi and an optimized track pitch as narrow as 1.5 μm were achieved, corresponding to an areal recording density of ~3.1 Gb/in²     

Detection techniques for high-density magnetic recording

In this paper, we present techniques for improving the performance of Viterbi detector in the presence of channel nonlinearities and media noise, which are the dominant source of errors in high density magnetic recording channels. Instead of treating these distortions separately, we combine them into a "high-density (HD) noise", which is signal dependent and correlated in nature. To compensate for signal-dependent mean and correlation of HD noise, we modify the branch metrics by subtracting an estimate of the mean from the signals on each branch and optimize the equalization target by minimizing the dominant error event probability, respectively. Simulation results show that these modifications yield significant performance gains.     

A photoluminescence study of vanadium-related defects in n-type, semi-insulating and p-type Cd(Zn)Te

A photoluminescence (PL) study of vanadium-related defects in semi-insulating and co-doped p-type and n-type CdTe:V crystals gives evidence of the presence of the V²⁺–Zn complex. In addition to the ³T₂(F)→³A₂(F) emission of V³⁺ near 0.5 eV and the ⁴T₂(F)→⁴T₁(F) transition of V²⁺ near 0.45 eV, two further luminescence bands are detected at higher energies. The first emission band (I), peaking around 0.8 eV, is correlated to the V²⁺–Zn complex and the second one (II), peaking around 0.6 eV, is attributed to the acceptor level introduced by the cadmium vacancies. Varying the zinc concentration in CdTe, we analyse the behaviour of the vanadium impurity charge state. We show that the V²⁺ internal transition decreases with zinc alloying due to the formation of the V²⁺–Zn complex. The emission bands related to isolated V_Cd are present with high intensity only in the p-type crystals, in which all the vanadium content is in the V³⁺ oxidation state, whereas, in the semi-insulating and n-type crystals, the PL spectrum is dominated by Emission I related to the V²⁺–Zn complex. The presence of this complex in the semi-insulating crystals used in photorefractive (PR) applications and the dominance of this complex over the optical properties of Cd(Zn)Te:V imply the contribution of this complex to the PR processes.