Codes Detecting and Correcting Solid Burst Errors

This paper studies linear codes capable of detecting and correcting solid burst error of length b or less. The lower and upper bounds on the number of parity-check digits required for such codes are obtained. Illustrations of codes for detecting as well as correcting such errors are provided

Low-Complexity Codes for Random and Clustered High-Order Failures in Storage Arrays

RC (Random/Clustered) codes are a new efficient array-code family for recovering from 4-erasures. RC codes correct most 4-erasures, and essentially all 4-erasures that are clustered. Clustered erasures are introduced as a new erasure model for storage arrays. This model draws its motivation from correlated device failures, that are caused by physical proximity of devices, or by age proximity of endurance-limited solid-state drives. The reliability of storage arrays that employ RC codes is analyzed and compared to known codes. The new RC code is significantly more efficient, in all practical implementation factors, than the best known 4-erasure correcting MDS code. These factors include: small-write update-complexity, full-device update-complexity, decoding complexity and number of supported devices in the array

Strategy for implementing stabilizer-based codes on solid-state qubits

We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions. Using pulse sequences, we show how to induce the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and energy-nonconserving errors caused by the environment.Comment: 5 pages, 1 figur

Ludwig: A parallel Lattice-Boltzmann code for complex fluids

This paper describes `Ludwig', a versatile code for the simulation of Lattice-Boltzmann (LB) models in 3-D on cubic lattices. In fact `Ludwig' is not a single code, but a set of codes that share certain common routines, such as I/O and communications. If `Ludwig' is used as intended, a variety of complex fluid models with different equilibrium free energies are simple to code, so that the user may concentrate on the physics of the problem, rather than on parallel computing issues. Thus far, `Ludwig''s main application has been to symmetric binary fluid mixtures. We first explain the philosophy and structure of `Ludwig' which is argued to be a very effective way of developing large codes for academic consortia. Next we elaborate on some parallel implementation issues such as parallel I/O, and the use of MPI to achieve full portability and good efficiency on both MPP and SMP systems. Finally, we describe how to implement generic solid boundaries, and look in detail at the particular case of a symmetric binary fluid mixture near a solid wall. We present a novel scheme for the thermodynamically consistent simulation of wetting phenomena, in the presence of static and moving solid boundaries, and check its performance.Comment: Submitted to Computer Physics Communication

On lower bounds of various dominating codes for locating vertices in cubic graphs

Self-identifying codes, self-locating dominating codes and solid-locating dominating codes are three subsets of vertices of a graph G to locate vertices. The optimal size of them is denoted by γSID (G),γSLD (G) and γDLD (G). In the master thesis, we mainly discuss their lower bound problem in families of graphs. In the first section, we briefly describe the background of the study and some related questions. In the second, third and fourth section, we show some basic definitions, concepts and examples related to self-identifying codes (SID), self-locating dominating codes (SLD) and solid-locating dominating codes (DLD) in rook’s graphs. In the fifth section, we first introduce some known results of lower bounds of open-locating dominating codes in cubic graphs and then in the sixth section we present some new results about the lower bounds of self-identifying codes, self-locating dominating codes and solid-locating dominating codes in cubic graphs

Computer modeling of the mineralogy of the Martian surface, as modified by aqueous alteration

Mineralogical constraints can be placed on the Martian surface by assuming chemical equilibria among the surface rocks, atmosphere and hypothesized percolating groundwater. A study was made of possible Martian surface mineralogy, as modified by the action of aqueous alteration, using the EQ3/6 computer codes. These codes calculate gas fugacities, aqueous speciation, ionic strength, pH, Eh and concentration and degree of mineral saturation for complex aqueous systems. Thus, these codes are also able to consider mineralogical solid solutions. These codes are able to predict the likely alteration phases which will occur as the result of weathering on the Martian surface. Knowledge of the stability conditions of these phases will then assist in the definition of the specifications for the sample canister of the proposed Martian sample return mission. The model and its results are discussed