Richard D. Barndt

A simple statistical model of partial erasure in thin film disk recording systems

A simple statistical model of the partial erasure effect in metallic thin-film recording is given. Experimental data are shown and used to determine a fundamental parameter of the micromagnetic structure of the medium. This single parameter determines the extent of erasure at any transition separation. Since it has no (first-order) dependence on the rate of zigzags, it is anticipated that it will be relatively independent of the transition noise amplitude of the medium. >

Experimental studies of nonlinearities in high density disk recording

Nonlinear amplitude reduction in high-density disk recording has been studied. Dibit responses were measured at two flying heights, and disks with varying coercivity, magnetic moment, and substantially different noise levels were used. It is shown that the nonlinear amplitude loss is reduced substantially at lower flying heights. Increasing coercivity or decreasing magnetic moment similarly reduces this loss. Measurements of disks with different noise levels indicate more reduction for the low-noise medium only at the lower flying height. By deconvolving isolated pulses, transition lengths for single transitions were determined at each flying height. It is also found that the nonlinear amplitude reduction curves scale with transition length at a fixed flying height, indicating a universal curve. >

Media selection for high density recording channels

The implementation of high-density partial response channels in disk drives has been hampered by nonlinear interactions between transitions occurring in the write process. It is shown that the degree of nonlinearity is not characterized by the density relative to the isolated transition pulse width, but rather by the transition spacing in relation to the transition width. Factors that determine the transition width are examined. In particular, the potential gains from using low moment media are investigated. A nonlinear model of the disk channel is discussed. The dependence of partial response signaling on linear superposition is discussed. Eye patterns are shown revealing the effects of nonlinearities on a partial response system. >

Nonlinear effects in high-density tape recording

Nonlinearities in high-density tape recording have been studied. Dibit responses were measured versus recording density and write current. The dibit responses were then compared to the linear superposition of isolated transitions. It is shown that nonlinear bit shift and transition width changes are required to explain the differences. These nonlinear effects can be parameterized for signal processing purposes using the pulse response by including a timing shift and a time scaling for the second pulse response in a dibit. These parameters explain the observed difference between square-wave spectral response and isolated pulse FFT. A simple technique for obtaining head efficiency, the effective head-medium spacing, and the depth of recording is presented. >

Error Floor Estimation of Long LDPC Codes on Partial Response Channels

The presence of error floor in low density parity check (LDPC) codes is of great concern for potential applications of LDPC codes to data storage channels, which require the error correcting code (ECC) to maintain the near-capacity error correcting performance at frame error rate as low as 10-12. In order to investigate the error floor of LDPC codes under partial response channels used in data storage systems, we propose a new estimation method combining analytical tools and simulation, based on the concept of trapping sets. The definition of trapping sets is based on the dominant error patterns observed in the decoding process. The goal is to accurately estimate the error rate in the error floor region for certain types of LDPC codes under the partial response channel and further extend the frame error rate down to 10-14 or lower. Towards this goal, we first use field programmable gate array (FPGA) hardware simulation to find the trapping sets that cause the decoding failure in the error floor region. For each trapping set, we extract the parameters which are key to the decoding failure rate caused by this trapping set. Then we use a much simpler in situ hardware simulation with these parameters to obtain the conditional decoding failure rate. By considering all the trapping sets we find, we obtain the overall frame error rate in the error floor region. The estimation results for a length -4623 QC-LDPC code under the EPR4 channel are within 0.3 dB of the direct simulation results. In addition, this method allows us to estimate the frame error rate of a LDPC code down to 10-14 or lower.

Nonlinear intersymbol destruction versus linear intersymbol interference on high density disk drives

The nonlinear behavior of the hard disk recording channel is described using a simple theoretical model. According to this model, linear superposition applies only when the transition spacing is greater than about 3.5a, where a is the transition width parameter. Two methods to increase density are examined. First, the system variables determining the transition width are identified. Of these the magnetic moment is unique in that its value is not fixed by the level of technology; that is, it can be chosen to optimize channel characteristics. Second, an advanced model is described that abandons linearity in favor of a simple nonlinear channel model. This model applies when the transition spacing is greater than 2.5a. Both of these techniques result in more severe signal roll-off than a hypothetical linear superposition channel.<<ETX>>

Read Level Profiling Algorithms for NAND Based SSD Flash

In a NAND flash memory, optimal read levels for minimizing bit error rate (BER) can be determined as offsets from a default read level. In general, memory would be allocated to store all the offset values for each of the 128 word-lines in a block using three or more different read levels per word-line. Fluctuations occur in optimal read levels from word-line to word- line but nevertheless demonstrate a behavior that allows a compression of the number of read level offsets to be stored. It is desirable to reduce the memory required to store the offsets and to smooth the noisy estimates. We present three read level profiling algorithms with two optimization criteria to reduce the number of read level offsets that needs to be stored while minimizing the degradation in BER. The read level profiling algorithms cluster the word-lines into groups in which the word-lines belonging to the same group have the same read level offset value. These algorithms are tested on lab data and it has been shown that with a moderate number of groups, no significant BER degradation occurs that would increase decoding errors.