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In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as the order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels. [ABSTRACT FROM AUTHOR]

The max-log-MAP (MLM) receiver is an approximated version of the well-known Bahl–Cocke–Jelinek-Raviv algorithm. The MLM algorithm is attractive due to its implementation simplicity. In practice, sliding-window implementations are preferred, whereby truncated signaling neighborhoods (around each transmission time instant) are considered. In this paper, we consider binary signaling sliding-window MLM receivers, where the MLM detector is truncated to a length-m signaling neighborhood. Here, truncation is used to ease the burden of analysis. For any number n of chosen times instants, we derive exact expressions for both 1) the joint distribution of the MLM symbol reliabilities, and 2) the joint probability of the erroneous MLM symbol detections. We show that the obtained expressions can be efficiently evaluated using Monte–Carlo techniques. The most computationally expensive operation (in each Monte–Carlo trial) is an eigenvalue decomposition of a size 2mn \times 2mn matrix. The proposed method handles various scenarios such as correlated noise distributions, modulation coding, etc. [ABSTRACT FROM PUBLISHER]

Noncontrollable finite-state channels (FSCs) are FSCs in which the channel inputs have no influence on the channel states, i.e., the channel states evolve freely. Since single-letter formulas for the channel capacities are rarely available for general noncontrollable FSCs, computable bounds are usually utilized to numerically bound the capacities. In this paper, we take the delayed channel state as part of the channel input and then define the directed information rate from the new channel input (including the source and the delayed channel state) sequence to the channel output sequence. With this technique, we derive a series of upper bounds on the capacities of noncontrollable FSCs with/without feedback. These upper bounds can be achieved by conditional Markov sources and computed by solving an average reward per stage stochastic control problem (ARSCP) with a compact state space and a compact action space. By showing that the ARSCP has a uniformly continuous reward function, we transform the original ARSCP into a finite-state and finite-action ARSCP that can be solved by a value iteration method. Under a mild assumption, the value iteration algorithm is convergent and delivers a near-optimal stationary policy and a numerical upper bound. [ABSTRACT FROM PUBLISHER]

Two-dimensional magnetic recording (TDMR) differs from traditional track recording in that the bit-size-to-grain-size ratio is drastically reduced so that the channel bits are roughly of the same sizes as those of the magnetic media grains. This is envisioned to be achieved by shingled writing, a write-process in which the corner-writer partially overwrites the previously written adjacent track, effectively writing very closely spaced narrow tracks with no guard bands. Since the tracks are very narrow, they can be read by an array of read-elements whose spacing is equal to the narrow track pitch, creating a two-dimensional (2-D) array of readback signals (the two dimensions being the cross-track and the down-track dimensions). In the absence of an array of read elements, the same 2-D readback can be obtained by progressive scans of a single read element that reads one narrow track at a time and stores the readback signal in a 2-D array. In this paper, we present simple magnetic grain media models and shingled-write process models that capture the essence of TDMR. We assume that the granular recording medium consists of randomly shaped tiles (each tile represents a grain), andomly covering the medium plane. We then derive a suitable 2-D read/write process model. Using proper information-theoretic inequalities and bounding techniques, we derive methods to bound the capacities of TDMR channels. The results reveal that information capacities in excess of 0.6 user bits per grain are possible to attain over TDMR channels. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of modeling the timing error process in magnetic recording systems. We propose a discrete- valued Markov model for the timing error process, and design two methods (data-aided and nondata-aided), based on the Baum-Welch algorithm, to extract the model parameters from the readback waveforms. The channel model we consider is an intersymbol interference (ISI) channel with additive Gaussian noise. The continuous-time readback signal at the output of the channel is sampled at baud-rate. Simulation results show that the estimated parameters are close to the actual values and the convergence is attained in a few iterations of the Baum-Welch algorithm. We also demonstrate the usefulness of the accurate model extraction by comparing a fine-tuned Markov timing recovery loop to the standard Mueller and Muller detector with a tuned second-order loop filter. [ABSTRACT FROM AUTHOR]

This is a semitutorial paper on trellis-based algorithms. We argue that most decoding/detection algorithms described on trellises can be formulated as path-partitioning algorithms, with proper definitions of mappings from subsets of paths to metrics of subsets. Thereby, the only two operations needed are path-concatenation and path-collection, which play the roles of multiplication and addition, respectively. Furthermore, we show that the trellis structure permits the path-partitioning algorithms to be formulated as forward-only algorithms (with structures resembling the Viterbi algorithm), thus eliminating the need for backward computations regardless of what task needs to be performed on the trellis. While all of the actual decoding/detection algorithms presented here are rederivations of variations of previously known methods, we believe that the exposition of the algorithms in a unified manner as forward-only path-partitioning algorithms is the most intuitive manner in which to generalize the Viterbi algorithm. We also believe that this approach may, in fact, influence the practical implementation of the algorithms as well as influence the construction of other forward-only algorithms (e.g., byte-wise forward-only detection algorithms). [ABSTRACT FROM AUTHOR]

Presents a study which examined the inversion of full matrices whose inverse are L-banded. Discussion on the banded matrix algebra; Representations of Gauss-Markov random processes; Summary.

Presents information on a study which described the Viterbi algorithm for channels with intersymbol interference (ISI) and correlated signal-dependent noise. Error performance of ISI channels; Gaussian statistics and branch metrics; Error analysis of the Viterbi sequence decoder.

Studies the statistics of zig-zag transition walls in digital magnetic recording and their relationship to transition noise defining quantities. Brief review of triangle zig-zag transition (TZ-ZT) model and other proposed stochastic zig-zag transition models; Statistical relationship of zig-zag patterns to measurable media or recording quantities.

A method is developed to determine the optimal bit aspect ratio of a recording system which maximizes the information density per unit area of the recording medium. The areal information density is computed as the achievable mutual information rate divided by the area of each binary symbol on the medium. A data-dependent autoregressive noise model is fitted to the recording channel and the achievable information rate of the recording channel is estimated by computing the achievable information rate of the channel model. [ABSTRACT FROM AUTHOR]

Presents a study that developed a cycle-slip detector (CSD) for the binary intersymbol interference channel that uses the channel soft-output information as its input. Features of the channel-timing model; Information on a CSD-aided iterative timing recovery algorithm; Details of the CSD for intersymbol interference channels.

Provides information on a study which developed a signal-dependent decision feedback equalizer for magnetic recording. Details on the feed-forward equalizer; Simulation results; Conclusion.

Explores the accuracy of the triangle zig-zag transition (TZ-ZT) model by comparing it to the data obtained through spin-stand measurements. Most attractive feature of the stochastic zig-zag models; Model validation procedure and results; Conclusion.

Proposes the triangle zig-zag transition (TZ-ZT) model as a faster alternative to micromagnetic media modeling. Equations that relate the statistics of the TZ-ZT model to recording process parameters; Simulation results.

Shingled magnetic recording is a promising option to sustain the historical areal density growth of hard disk drives while retaining conventional heads and media. Nevertheless, highly scaled shingled magnetic recording is subject to severe intertrack interference (ITI), fewer grains per channel bit and therefore lower signal-to-noise ratio (SNR). This naturally demands 2-D read channel signal processing, which has an inherently large spectrum of detection performance versus computational complexity tradeoff. By concurrently detecting multitrack readback signals from a read head array, joint 2-D signal detection can fully utilize the 2-D interference to maximize the detection performance at the penalty of the highest computational complexity. Multitrack joint 2-D detection has not been thoroughly studied from either the detection performance or silicon implementation perspective because of the justifiable concern on its practical feasibility. To fill this missing link, this paper presents a comprehensive study of multitrack joint 2-D signal detection performance and silicon implementation cost. We further present an interleaved pipelining strategy to reduce joint 2-D signal detector silicon consumption. By carrying out comprehensive simulations and application-specific integrated circuit (ASIC) design, this paper shows that multitrack joint 2-D signal detection is a practically attractive option with superior detection performance and affordable silicon cost, especially when considering projected CMOS technology scaling toward 16 nm and below. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach to magnetic recording based on shingled writing and two-dimensional readback and signal- processing. This approach continues the use of conventional granular media but proposes techniques such that a substantial fraction of one bit of information is stored on each grain. Theoretically, areal-densities of the order of 10 Terabits per square inch maybe achievable. In this paper we examine the feasibility of this two-dimensional magnetic recording (TDMR) and identify the significant challenges that must be overcome to achieve this vision. [ABSTRACT FROM AUTHOR]

We establish area theorems for iterative detection and decoding (or simply, iterative detection) over coded linear systems, including multiple-input multiple-output channels, intersymbol interference channels, and orthogonal frequency-division multiplexing systems. We propose a linear precoding technique that asymptotically ensures the Gaussianness of the messages passed in iterative detection, as the transmission block length tends to infinity. Area theorems are established to characterize the behavior of the iterative receiver. We show that, for unconstrained signaling, the proposed single-code scheme with linear precoding and iterative linear minimum mean-square error (LMMSE) detection is potentially information lossless, under various assumptions on the availability of the channel state information at the transmitter. We further show that, for constrained signaling, our proposed single-code scheme considerably outperforms the conventional multicode parallel transmission scheme based on singular value decomposition and water-filling power allocation. Numerical results are provided to verify our analysis. [ABSTRACT FROM PUBLISHER]

We propose to use various trellis structures to characterize different types of insertion and deletion channels. We start with binary independent and identically distributed (i.i.d.) insertion or deletion channels, propose a trellis representation and develop a simulation based algorithm to estimate the corresponding information rates with independent and uniformly distributed inputs. This approach is then generalized to other cases, including channels with additive white Gaussian noise, channels with both insertions and deletions, and channels with intersymbol interference (ISI) where the latter model is motivated by the recent developments on bit-patterned media recording. We demonstrate that the proposed algorithm is an efficient and flexible technique to closely estimate the achievable information rates for channels with insertions and/or deletions with or without intersymbol interference when i.i.d. inputs are employed while we also provide some notes on the achievable information rates when Markov inputs are used. We emphasize that our method is useful for evaluating information rates for channels with insertion/deletions with additional impairments where there does not seem to be a hope of obtaining fully analytical results. [ABSTRACT FROM AUTHOR]