Charles Warren Cox DeceasedAptos, CA

6345376, Feb 5, 2002

Jul 18, 2000

09/618414

Charles Edwin Cox - San Jose CA
Myron Dale Flickner - San Jose CA
James Lee Hafner - San Jose CA
Martin Aureliano Hassner - Palo Alto CA
Barry Marshall Trager - Yorktown Heights NY
Shmuel Winograd - Scarsdale NY

International Business Machines Corporation - Armonk NY

H03M 1300

714785, 714781

A computationally efficient, machine-implementable method and means for detecting and correcting errors in received codewords on-the-fly within the capacity of a linear cyclic code using ultra-fast error location processing. Each error locator polynomial of degree t over a finite Galois field derived from a codeword syndrome is mapped into a matrix representative of a system of linear simultaneous equations related to the polynomial coefficients. Roots indicative of error locations within the codeword are extracted from the matrix by a modified Gaussian Elimination process for all the roots where t5 and at least one root plus a subset of candidate roots from the finite field for iterative substitution where t 5. Corrected values are separately determined and correction is secured by logically combining the corrected values with the codeword values in error at the error locations represented by the roots.

6405339, Jun 11, 2002

Aug 31, 1999

09/387665

Charles Edwin Cox - San Jose CA
Martin Aureliano Hassner - Mountain View CA

International Business Machines Corporation - Armonk NY

G06F 1110

714756, 714784

A composite encoder/syndrome generating device that both computes check symbols over counterpart data symbol strings to form codewords, and derives syndromes from codewords indicative of their error state. The multistage device provides recursive processing paths at each stage of depth corresponding to the number of symbols concurrently applied to the device. The device is adapted as an encoder when the feed-forward paths between stages are enabled; it is adapted as a syndrome generator upon their disablement. The number of symbols concurrently processed may be varied from clock cycle to clock cycle by conforming the recursion paths per stage to the number of symbols applied as input to the device.

6438724, Aug 20, 2002

Mar 16, 1999

09/270069

Charles Edwin Cox - San Jose CA
James Lee Hafner - San Jose CA
Martin Aureliano Hassner - Palo Alto CA
Ralph Koetter - Urbana IL
Arvind Motibhai Patel - San Jose CA

International Business Machines Corporation - Armonk NY

H03M 1315

714758

A method and apparatus for ensuring the integrity of data that can detect errors that remain when the data correction scheme fails to correct at least some of the errors, or has added additional errors. Reed-Solomon check symbols are used for error correction and cyclic redundancy check symbols are used to detect the remaining errors. The roots of the generator polynomials used to generate the Reed-Solomon check symbols and the cyclic redundancy check symbols meet a selected subset of a plurality of conditions. The roots are further selected so that the necessary exponentiation may be performed by a combination of exponentiations by powers of two and multiplications. The Reed-Solomon check symbols are generated based on the data portion of the data block. A deterministically altered data stream is generated based on the data portion of the data block and the cyclic redundancy check symbols are generated based on the deterministically altered data stream. The deterministically altered data stream is generated by performing an operation on a symbol of the data portion based on a position of the symbol within a Reed-Solomon codeword.

6446234, Sep 3, 2002

Mar 16, 1999

09/269000

Charles Edwin Cox - San Jose CA
James Lee Hafner - San Jose CA
Martin Aureliano Hassner - Palo Alto CA
Ralph Koetter - Urbana IL
Arvind Motibhai Patel - San Jose CA

International Business Machines Corporation - Armonk NY

H03M 1315

714758

A method and apparatus for ensuring the integrity of data that can detect errors that remain when the data correction scheme fails to correct at least some of the errors, or has added additional errors. Reed-Solomon check symbols are used for error correction and cyclic redundancy check symbols are used to detect the remaining errors. The roots of the generator polynomials used to generate the Reed-Solomon check symbols and the cyclic redundancy check symbols meet a selected subset of a plurality of conditions. The roots are further selected so that the necessary exponentiation may be performed by a combination of exponentiations by powers of two and multiplications. The Reed-Solomon check symbols are generated based on the data portion of the data block. A deterministically altered data stream is generated based on the data portion of the data block and the cyclic redundancy check symbols are generated based on the deterministically altered data stream. The deterministically altered data stream is generated by performing an operation on a symbol of the data portion based on a position of the symbol within a Reed-Solomon codeword.

6671850, Dec 30, 2003

May 1, 2000

09/562575

Charles Edwin Cox - San Jose CA
Martin Aureliano Hassner - Mountain View CA
Barry Marshall Trager - Yorktown Heights NY
Shmuel Winograd - Scarsdale NY

International Business Machines Corporation - Armonk NY

H03M 1300

714781, 714764, 360 48, 708492

An on-the-fly algebraic error correction system and corresponding method for reducing error location search are presented. The method transforms an error locator polynomial into two transformed polynomials whose roots are elements in a smaller subfield, in order to significantly simplify the complexity, and to reduce the latency of the error correcting system hardware implementation. More specifically, if the error locator polynomial is over a finite field of (2 ) elements, the transformed polynomial is over a finite subfield of (2 ) elements. Thus, the problem of locating the roots of the error locator polynomial is reduced to locating the roots of the transformed polynomials. Assuming the error locator polynomial is of degree m, the present method requires at most (m /2) evaluations of polynomials over the Galois field GF(2 ) and (2 ) evaluations over the subfield GF(2 ) or root finding of two polynomials of at most a degree m over the subfield GF(2 ).

6792569, Sep 14, 2004

Apr 24, 2001

09/842244

Charles Edwin Cox - San Jose CA
Martin Aureliano Hassner - Palo Alto CA
Barry Marshall Trager - Yorktown Heights NY
Shmuel Winograd - Scarsdale NY

International Business Machines Corporation - Armonk NY

H03M 1300

714781

An error correction algebraic decoder uses a key equation solver for calculating the roots of finite field polynomial equations of degree up to six, and lends itself to efficient hardware implementation and low latency direction calculation. The decoder generally uses a two-step process. The first step is the conversion of quintic equations into sextic equations, and the second step is the adoption of an invertible Tschirnhausen transformation to reduce the sextic equations by eliminating the degree 5 term. The application of the Tschirnhausen transformation considerably decreases the complexity of the operations required in the transformation of the polynomial equation into a matrix. The second step defines a specific Gaussian elimination that separates the problem of solving quintic and sextic polynomial equations into a simpler problem of finding roots of a quadratic equation and a quartic equation.

7380053, May 27, 2008

Mar 17, 2005

11/083209

Charles Edwin Cox - San Jose CA, US
Jimmy Lee Reaves - San Jose CA, US

International Business Machines Corporation - Armonk NY

G06F 12/00

711108, 711104

A method and system for emulating content-addressable memory (CAM) primitives (e. g. , a read operation) is disclosed. According to one embodiment, a method is provided for emulating a read operation on a plurality of CAM elements utilizing a read input including match input data and a CAM element selection index. In the described method, match reference data is distributed among a plurality of random-access memory (RAM) elements by storing match reference data corresponding to each of the plurality of CAM elements within a first RAM element of the plurality. Thereafter, a first record is identified within the first RAM element utilizing a first portion of the match input data and the CAM element selection index. A read operation result is then generated utilizing the first record.

2008027, Nov 6, 2008

Feb 27, 2008

12/038009

Charles Edwin Cox - San Jose CA, US
Jimmy Lee Reaves - San Jose CA, US

G06F 12/00

711108, 711E12001

A method and system for emulating content-addressable memory (CAM) primitives (e.g., a read operation) is disclosed. According to one embodiment, a method is provided for emulating a read operation on a plurality of CAM elements utilizing a read input including match input data and a CAM element selection index. In the described method, match reference data is distributed among a plurality of random-access memory (RAM) elements by storing match reference data corresponding to each of the plurality of CAM elements within a first RAM element of the plurality. Thereafter, a first record is identified within the first RAM element utilizing a first portion of the match input data and the CAM element selection index. A read operation result is then generated utilizing the first record.