Data error control

A method for data error correction comprising:

• receiving encoded data, including receiving at least N channels of encoded data of N+M channels of encoded data that represent N channels of source data;
• and
• correcting errors in the received encoded data, including using the received at least N channels of encoded data to correct errors in at least m>M/2 other of the channels of encoded data;
• wherein each channel of the N+M channels of encoded data including a series of entries, the channels of encoded data satisfying parity equations such that each entry in at least some of the N+M channels of encoded data contributes to at least M independent parity equations.

A method for data error protection comprising:

• accepting source data;
• representing the source data as N channels of source data, each including a series of I entries;
• and
• encoding the N channels of source data to form N+M channels of encoded data, the channels of encoded data satisfying at least M×I independent parity equations, at least I entries of some of the channels of encoded data each being an argument to at least M of the parity equations.

Software stored on computer-readable media comprising instructions for causing a data processing system to:

• accept source data;
• represent the source data as N channels of source data, each including a series of I entries;
• and
• encode the N channels of source data to form N+M channels of encoded data, the channels of encoded data satisfying at least M×I independent parity equations, at least I entries of some of the channels of encoded data each being an argument to at least M of the parity equations.

A method for data error protection comprising:

• accepting source data;
• representing the source data as N channels of source data, each including a series of I entries;
• encoding the N channels of source data to form N+M channels of encoded data, the channels of encoded data satisfying at least M×I independent parity equations, at least I entries of some of the channels of encoded data each being an argument to at least M of the parity equations;
• and
• handling the N+M channels of encoded data;
• iteratively reconstructing entries in one or more channels of the N+M channels of encoded data, at each iteration applying one or more of the parity equations to received or reconstructed entries of the N+M channels of encoded data to reconstruct an entry in each of the one or more of the N+M channels;
• and
• recovering the source data using the reconstructed entries.

A method for data error control comprising:

• accepting source data;
• representing the source data as N channels of source data, each including a series of I entries;
• encoding the N channels of source data to form N+M channels of encoded data, the channels of encoded data satisfying at least M×I independent parity equations, at least I entries of some of the channels of encoded data each contributing to at least M of the parity equations;
• handling the N+M channels of encoded data, including introducing errors into at least m>M/2 of the N+M channels;
• and
• recovering the source data from the handled channels of encoded data.

A method for distributed storage of data comprising:

• accepting source data;
• representing the source data as N channels of source data, each including a series of I entries;
• encoding the N channels of source data to form N+M channels of encoded data, the channels of encoded data satisfying at least M×I independent parity equations, at least I entries of some of the channels of encoded data each being an argument to at least M of the parity equations;
• and
• distributing the N+M channels of encoded data to separate storages;
• retrieving at least some of the N+M channels of encoded data from the separate storages;
• iteratively reconstructing entries in one or more channels of the N+M channels of encoded data using the retrieved channels, at each iteration applying one or more of the parity equations to received or reconstructed entries of the N+M channels of encoded data to reconstruct an entry in each of the one or more of the N+M channels;
• and
• recovering the source data using the reconstructed entries.