Abstract: A method for finding a valid codeword based on a near codeword trapping in a low-density parity-check decoding process includes identifying trapping set configurations and applying corrections to produce trapping sets with a limited number of invalid checks. Trapping set configurations are corrected in order to produce a trapping set in a table of trapping sets, the table associating each corrected trapping set with a valid codeword.

Abstract: A method for finding a valid codeword based on a near codeword trapping in a low-density parity-check decoding process includes identifying trapping set configurations and applying corrections to produce trapping sets with a limited number of invalid checks. Trapping set configurations are corrected in order to produce a trapping set in a table of trapping sets, the table associating each corrected trapping set with a valid codeword.

Abstract: The present invention is directed to a method and apparatus to find an optimal unification substitution for formulas in a technology library. In an exemplary aspect of the present invention, a method for finding an optimal unification substitution for formulas in a technology library during integrated circuit design may include the following steps: (a) receiving input including a list L of pairs of formulas in standard form, a set S of substitutions for variables, a right part e(x1, . . . , xp) of an identity, and an information I={t, h, r, a, p} on best application; (b) when the list L is not empty, extracting and removing first pair (ƒ?(A?1, . . . , A?n?), g?(B?1, . . . , B?m?)) from the list L; (c) removing head inverters and buffers from formulas ƒ?(A?1, . . . , A?n?) and g?(B?1, . . . , B?m?)) and obtaining a pair (ƒ(A1, . . . , An), g(B1, . . . , Bm)); (d) when the ƒ is a commutative operation but neither a variable nor constant, and when heads of the formulas ƒ(A1, . . . , An) and g(B1, . . .

Abstract: Integrated circuits are designed having optimal signal timing between and among cells. A set of identities are generated corresponding to logic operations and to library cells in technology basis. A resynthesis window is created for the identities having less than a predetermined depth of critical variables. Logic equations of the resynthesis window are transformed using the identities, and the resynthesized window area is optimized.

Abstract: The present invention includes methods for optimizing integrated circuit design by identifying a buffer tree in the integrated circuit design, the buffer tree having a plurality of vertices, each representing one of a buffer and an inverter, and also having branches, between the vertices, each representing an electrical connection. A plurality of optimization devices are applied in a random sequence to the vertices of the buffer tree. Such devices can include, for example, cell type modification; insertion of one buffer; insertion of several buffers; interchange of two grandchildren; making a grandchild into a child; making a child a grandchild; interchanging a child and a grandchild; eliminating two inverters; removing one buffer; removing more than one buffer; and removing two inverters.

Abstract: The present invention is a method for searching an identity base for identities that can be applied to a given formula. The method includes transforming the formulas from an identity base into a standard form, creating a set of code words for said identity base, constructing a lexicographical tree of a code word set of said identity base, and outputting a list of formula numbers from said identity base.

Abstract: The present invention comprises method for optimizing an integrated circuit design that includes computing of capacities and delays of an integrated circuit design, resynthesizing said integrated circuit design utilizing a plurality of local optimization procedures, and removing overlap the local optimization procedures can include a local resynthesis of logic trees procedure that utilizes multiple cost functions, a dynamic buffer and inverter tree optimization procedure, and a cell resizing procedure. Generally, faster local optimization procedures are applied first and slower, more thorough procedures are applied to areas where the faster procedures have not solved the optimization tasks.

Abstract: Provided are systems and techniques for optimizing an integrated circuit design, in which a critical zone is identified in an integrated circuit design and a plurality of alternative identities are applied in the critical zone in order to obtain a corresponding plurality of outcomes. Alternative representations are then identified as those of the plurality of outcomes pursuant to which at least one of ramptime and timing are improved, and a best one of the alternative representations is selected to replace into the critical zone based on specified priorities which include: (i) selecting based on reduction in ramptime violation; (ii) selecting from among alternative representations that preserve cell area based on timing improvement; and (iii) if all alternative representations increase cell area, selecting based on an evaluation of a relationship between timing decrement and area increment.

Abstract: The present invention selects parts of an integrated circuit description for resynthesis and then prepares those parts for resynthesis. Initially, a resynthesis goal is input, with the resynthesis goal having been selected from a set of possible resynthesis goals. Plural buffer and/or logic trees in the integrated circuit description are then selected based on the resynthesis goal, and information for each of the selected trees is obtained and stored. The tree information includes: (i) a description of each tree cell, including cell types, cell coordinates, and flips and angles of the tree cell, (ii) a description of each input net, (iii) a signal arrival time for each input net as a function of a capacity of such input net, (iv) coordinates of each pin driving each input net, and (v) a maximum capacity of each input net that will prevent such input net from having a timing violation.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arraingement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60°. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arraingement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60°. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: A process for designing an integrated circuit chip includes specifying a set of cells, a set of wiring nets for interconnecting the cells, and a set of regions on the chip in which the cells are to be placed. An assignment of the cells of the set to the regions is generated, and the set of cells is randomly divided into a first subset of cells which remain in the assignment, and a second subset of cells which are removed from the assignment. Penalties are computed for assigning the cells of the second subset to the regions respectively, and the cells of the second subset are assigned to the regions such that a total penalty thereof is minimized. The process is repeated iteratively with the size of the second subset being progressively reduced relative to the size of the first subset until an end criterion is reached.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arraingement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60.degree.. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arraingement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60.degree.. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: A process for implementation on a programmed digital computer includes providing a placement of clusters of cells which are assigned to regions on an integrated circuit chip, and combining the regions to form region groups. The region groups collectively constitute a "jiggle" which resembles a sieve. The clusters in each region group are re-assigned to the regions in the region group. The regions are recombined to form different region groups (a different jiggle), and the clusters in each different region group are re-assigned to the regions in the different region group. These steps are repeated using at least two, preferably four different jiggles, until an end criterion is reached. Then, the regions and clusters are hierarchically subdivided, and the process is repeated for each hierarchical level until the clusters have been reduced to individual cells.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arraingement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60.degree.. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arrangement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60.degree.. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arrangement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60.degree.. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.

Abstract: An initial placement of cells, and a routing including wires interconnecting the cells, is provided for a microelectronic integrated circuit. A grid is defined as including a plurality of first gridlines that extend parallel to a first axis, and a plurality of second gridlines that extend parallel to a second axis that is angularly displaced from the first axis. The cells are represented as vertices located at intersections of first and second gridlines, and the wires are represented as edges that extend along the first and second gridlines. Clusters of vertices are created such that each cluster includes vertices located on a respective first gridline. A "cover" is computed as including a minimum block of clusters that are connected to all other clusters by wires extending along the second gridlines. Clusters outside the cover are spatially reordered along the second axis away from the cover in descending order of numbers of wires extending from the clusters along the second gridlines.

Abstract: Several inventions are disclosed. A cell architecture using hexagonal shaped cells is disclosed. The architecture is not limited to hexagonal shaped cells. Cells may be defined by clusters of two or more hexagons, by triangles, by parallelograms, and by other polygons enabling a variety of cell shapes to be accommodated. Polydirectional non-orthogonal three layer metal routing is disclosed. The architecture may be combined with the tri-directional routing for a particularly advantageous design. In the tri-directional routing arrangement, electrical conductors for interconnecting terminals of microelectronic cells of an integrated circuit preferrably extend in three directions that are angularly displaced from each other by 60.degree.. The conductors that extend in the three directions are preferrably formed in three different layers. A method of minimizing wire length in a semiconductor device is disclosed. A method of minimizing intermetal capacitance in a semiconductor device is disclosed.