Abstract: Systems and methods, including computer software products, can be used to update or modify data stored in a memory. One or more variables are represented with one or more cell values in a memory. Each variable is associated with one or more of the cell values. Multiple states of the one or more variables are defined, and each defined state of the one or more variables includes a current store value for each variable and at least one previous store value for the variable. One or more single cell values influence the current store value and previous store value of at least one variable.

Abstract: We investigate a novel storage technology, Rank Modulation, for flash memories. In this scheme, a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The resulting scheme eliminates the need for discrete cell levels, and overshoot errors when programming cells (a serious problem that reduces the writing speed), as well as mitigate the problem of asymmetric errors. We present schemes for Gray codes, rewriting and joint coding in the rank modulation paradigm.

Abstract: We investigate error-correcting codes for a novel storage technology, which we call the rank-modulation scheme. In this scheme, a set of n cells stores information in the permutation induced by the different levels of the individual cells. The resulting scheme eliminates the need for discrete cell levels, and overshoot errors when programming cells (a serious problem that reduces the writing speed), as well as mitigates the problem of asymmetric errors. In this discussion, the properties of error correction in rank modulation codes are studied. We show that the adjacency graph of permutations is a subgraph of a multi-dimensional array of a special size, a property that enables code designs based on Lee-metric codes and L1-metric codes. We present a one-error-correcting code whose size is at least half of the optimal size. We also present additional error-correcting codes and some related bounds.

Abstract: Systems and methods, including computer software products, can be used to update or modify data stored in a memory. One or more variables are represented with one or more cell values in a memory. Each variable is associated with one or more of the cell values. Multiple states of the one or more variables are defined, and each defined state of the one or more variables includes a current store value for each variable and at least one previous store value for the variable. One or more single cell values influence the current store value and previous store value of at least one variable.

Abstract: Systems and methods, including computer software products, can be implemented for updating or modifying stored data. Multiple variables are represented by one or more cell values in a memory. Each variable is associated with one or more of the cell values and at least one single cell value influences a value of at least two of the variables. Multiple states of the multiple variables are defined. At least one of the multiple defined states of the multiple variables is associated with more than one set of cell values.

Abstract: Routing in a wireless network of communication devices that are located within a network boundary moves network traffic from a first communication device to a second communication device. A geometric indicator of network connectivity is constructed that identifies a curve on which network nodes are located and a network location for each node of the wireless network is determined, so that the network location of a node p identifies a node on the geometric indicator curve that is closest to the node p and indicates connectivity from the node p to the closest node of the geometric indicator curve. A routing scheme is determined, to route in the wireless network from the first communication device to the second communication device based on the respective determined network locations for the first and second communication devices.