| US 7,581,156 B2 | ||
| Systems and methods for providing improved encoding and reconstruction of data | ||
| Mark Steven Manasse, San Francisco, Calif. (US) | ||
| Assigned to MIcrosoft Corporation, Redmond, Wash. (US) | ||
| Filed on Dec. 16, 2002, as Appl. No. 10/321,159. | ||
| Prior Publication US 2004/0117718 A1, Jun. 17, 2004 | ||
| Int. Cl. H03M 13/00 (2006.01) | ||
| U.S. Cl. 714—781 [714/786] | 12 Claims |
| 1. A method for efficient transmission of a data field when, prior to transmission, the data field includes a number of failures
less than or equal to three, comprising:
generating by at least one computer processor data representing a Vandermonde matrix over GF(2n) by:
generating an identity matrix portion;
generating an erasure coding portion comprising data values corresponding to a set of three rows having a property that each
minor of the set of three rows is invertible; and
computing a determinant of a submatrix of the erasure coding portion, wherein said computing includes ignoring columns from
the identity matrix portion, wherein said computing results in one of a 0 by 0, 1 by 1, 2 by 2 and 3 by 3 minor of the erasure
coding portion remaining;
using by the at least one computer processor the generated data representing the Vandermonde matrix to correct the failures
in the data field; and
in response to correcting the failures in the data field, transmitting by the at least one computer processor the data field
to a recipient, the transmitting being made more efficient by correcting the failures in the data field prior to performing
the transmitting.
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