Anantha Raman Krishnan

Channel Models and Detectors for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) is a novel recording architecture intended to support densities beyond those of conventional recording systems. The gains from TDMR come primarily from more powerful coding and signal processing algorithms that allow the bits to be packed more tightly on the disk, and yet be retrieved with acceptable error rates. In this paper, we present some preliminary results for an advanced channel model based on micromagnetic simulations, coined the Grain Flipping Probability model. This model requires a one-time computationally complex characterization phase, but subsequently provides fast and accurate two-dimensional (2-D) readback waveforms that include effects captured from micromagnetic simulations and the statistical effects derived from the granularity of the recording medium. We also show the performance of several detectors over a pre-existing TDMR channel model directly as a function of channel density rather than the signal-to-noise ratio (SNR).

2-D Magnetic Recording: Read Channel Modeling and Detection

Two-dimensional magnetic recording (TDMR) is a novel storage architecture that, in theory, can achieve a density of up to 10 Tb/in2. It uniquely differs from other proposed next-generation architectures because of its reliance on sophisticated 2-D signal-processing algorithms. Recently, a number of contributions have been made in the development of read-channel models and detectors for TDMR systems. In this paper, we provide a detailed review on all important read-channel models under consideration. Our discussion focuses on the purpose of each model, placing a special emphasis on the suitability of the Voronoi model for the purpose of designing detectors. We also propose several detection schemes for TDMR based on the Voronoi model and present some numerical results.

LDPC codes which can correct three errors under iterative decoding

In this paper, we provide necessary and sufficient conditions for a column-weight-three LDPC code to correct all patterns up to three errors when decoded using Gallager A algorithm. We then provide a construction technique which results in a code satisfying the above conditions. We also provide numerical assessment of code performance via simulation results.

Read Channel Modeling for Detection in Two-Dimensional Magnetic Recording Systems

In this paper, we describe a read channel model for detector design for two-dimensional magnetic recording (TDMR) system, a novel strategy for recording at upto 10 Tb/in2. We describe a scheme for (1) modeling of the recording medium, (2) modeling of the write/readback process, and (3) an experimental method for the characterization of noise in the TDMR channel, occurring due to irregularities in the bit-boundaries in the recording medium, that can be used for detection purposes.

An Information Theoretic Approach to Constructing Robust Boolean Gene Regulatory Networks

We introduce a class of finite systems models of gene regulatory networks exhibiting behavior of the cell cycle. The network is an extension of a Boolean network model. The system spontaneously cycles through a finite set of internal states, tracking the increase of an external factor such as cell mass, and also exhibits checkpoints in which errors in gene expression levels due to cellular noise are automatically corrected. We present a 7-gene network based on Projective Geometry codes, which can correct, at every given time, one gene expression error. The topology of a network is highly symmetric and requires using only simple Boolean functions that can be synthesized using genes of various organisms. The attractor structure of the Boolean network contains a single cycle attractor. It is the smallest nontrivial network with such high robustness. The methodology allows construction of artificial gene regulatory networks with the number of phases larger than in natural cell cycle.

LDPC Decoding Strategies for Two-Dimensional Magnetic Recording

In this paper, we propose a linear programming (LP) decoding scheme for binary error-erasure channel for use in two-dimensional magnetic recording. We compare the performance of this decoding scheme with other decoding schemes like LP decoding for BSC and belief-propagation decoding. Also, we compare the effect of variance of grain-area in the medium on the bit-error rates of various decoding schemes.

Graph-based iterative reconstruction of sparse signals for compressed sensing

In this paper, we consider the problem of reconstruction of sparse signals in compressed sensing. In particular, we introduce a novel iterative algorithm based on graph-based decoding of low-density parity-check codes which possesses desirable properties like good performance, low complexity and running time, and ease of implementation. In this work, we outline the reconstruction algorithm, and analyze its performance on some measurement matrices. Furthermore, we also provide some initial results on the theoretical performance limits of this algorithm.

Coding for Correcting Insertions and Deletions in Bit-Patterned Media Recording

Bit-patterned media is a novel technology for magnetic data storage that is poised to increase recording density beyond 1 Tb/sq. in. However, a significant concern in BPMR is the stringent requirements for synchronization between write clock and island position, errors in which may manifest as insertions and deletions. In this paper, we introduce a method for compensating for synchronization errors by using conventional error-correcting codes. We present a numerical study that provides bounds on achievable coding rates. We also perform a simulation study to demonstrate the applicability of the proposed scheme in practical systems.

Polar codes for magnetic recording channels

Polar codes provably achieve the capacity of binary memoryless symmetric (BMS) channels with low complexity encoding and decoding algorithms, and their finite-length performance on these channels, when combined with suitable decoding algorithms (such as list decoding) and code modifications (such as a concatenated CRC code), has been shown in simulation to be competitive with that of LDPC codes. However, magnetic recording channels are generally modeled as binary-input intersymbol interference (ISI) channels, and the design of polar coding schemes for these channels remains an important open problem. Current magnetic hard disk drives use LDPC codes incorporated into a turbo-equalization (TE) architecture that combines a soft-output channel detector with a soft-input, soft-output sum-product algorithm (SPA) decoder. An interleaved coding scheme with a multistage decoding (MSD) architecture with LDPC codes as component codes has been proposed as an alternative to TE for ISI channels. In this work, we investigate the use of polar codes as component codes in the TE and MSD architectures. It is shown that the achievable rate of the MSD scheme converges to the symmetric information rate of the ISI channel when the number of interleaves is large. Simulations results comparing the performance of LDPC codes and polar codes in TE and MSD architectures are presented.

Constrained Coding for Optical Communication

The increase in speed of optical communication systems has brought new technical challenges to the fore. For example, combatting intrachannel cross-phase modulation (IXPM) and intrachannel four-wave mixing (IFWM) in high-speed time division multiplexing (TDM) systems has been a focus of considerable research [1, 2, 3]. IXPM and IFWM are interactions among neighboring bits (pulses) that are a result of fiber nonlinearities. They can limit system performance by causing energy transfer between interacting pulses, thereby resulting in the formation of ghost pulses or shadow pulses. Moreover, these interactions can also lead to timing and amplitude jitters in the system. Though ghost pulses occur due to interactions between pulses in varied positions, it has been observed that certain “resonance” positions lead to more energy transfers than others [2]. In particular, pulses at positions k, l, and m lead to ghost pulse at position \((k + l - m)\). Also, it has been observed that this interaction is the most for pulses that are close to each other. Figure 8.1 illustrates this phenomenon. The figure depicts the creation of a ghost pulse at position 0 as a result of pulses at positions − 1, 2, and 3.