Block Structured Adaptive Mesh and Time Refinement for Hybrid, Hyperbolic + N-body Systems

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov's method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.Comment: 40 pages, 10 figures, JPC in press. Extended the code test section, new convergence tests, several typos corrected. Full resolution version available at http://www.exp-astro.phys.ethz.ch/miniati/charm.pd

Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories

Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by ℓ. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation

Rewriting Codes for Joint Information Storage in Flash Memories

Memories whose storage cells transit irreversibly between states have been common since the start of the data storage technology. In recent years, flash memories have become a very important family of such memories. A flash memory cell has q states—state 0.1.....q-1 - and can only transit from a lower state to a higher state before the expensive erasure operation takes place. We study rewriting codes that enable the data stored in a group of cells to be rewritten by only shifting the cells to higher states. Since the considered state transitions are irreversible, the number of rewrites is bounded. Our objective is to maximize the number of times the data can be rewritten. We focus on the joint storage of data in flash memories, and study two rewriting codes for two different scenarios. The first code, called floating code, is for the joint storage of multiple variables, where every rewrite changes one variable. The second code, called buffer code, is for remembering the most recent data in a data stream. Many of the codes presented here are either optimal or asymptotically optimal. We also present bounds to the performance of general codes. The results show that rewriting codes can integrate a flash memory’s rewriting capabilities for different variables to a high degree

Using Short Synchronous WOM Codes to Make WOM Codes Decodable

In the framework of write-once memory (WOM) codes, it is important to distinguish between codes that can be decoded directly and those that require that the decoder knows the current generation to successfully decode the state of the memory. A widely used approach to construct WOM codes is to design first nondecodable codes that approach the boundaries of the capacity region, and then make them decodable by appending additional cells that store the current generation, at an expense of a rate loss. In this paper, we propose an alternative method to make nondecodable WOM codes decodable by appending cells that also store some additional data. The key idea is to append to the original (nondecodable) code a short synchronous WOM code and write generations of the original code and of the synchronous code simultaneously. We consider both the binary and the nonbinary case. Furthermore, we propose a construction of synchronous WOM codes, which are then used to make nondecodable codes decodable. For short-to-moderate block lengths, the proposed method significantly reduces the rate loss as compared to the standard method.Comment: To appear in IEEE Transactions on Communications. The material in this paper was presented in part at the 2012 IEEE International Symposium on Information Theory, Cambridge, MA, July 201

Increasing Flash Memory Lifetime by Dynamic Voltage Allocation for Constant Mutual Information

The read channel in Flash memory systems degrades over time because the Fowler-Nordheim tunneling used to apply charge to the floating gate eventually compromises the integrity of the cell because of tunnel oxide degradation. While degradation is commonly measured in the number of program/erase cycles experienced by a cell, the degradation is proportional to the number of electrons forced into the floating gate and later released by the erasing process. By managing the amount of charge written to the floating gate to maintain a constant read-channel mutual information, Flash lifetime can be extended. This paper proposes an overall system approach based on information theory to extend the lifetime of a flash memory device. Using the instantaneous storage capacity of a noisy flash memory channel, our approach allocates the read voltage of flash cell dynamically as it wears out gradually over time. A practical estimation of the instantaneous capacity is also proposed based on soft information via multiple reads of the memory cells.Comment: 5 pages. 5 figure