Abstract: A method for encoding data comprises choosing a sequence of pivot candidate positions for a sequence of g encoding vectors to encode a block of g data symbols in a round of coded packets by: providing a set of g pivot candidate positions; choosing a pivot candidate position for the sequence from the set of pivot candidate positions; removing the chosen pivot candidate position from the set of pivot candidate positions; and repeating until the set of pivot candidate positions is empty and the sequence of chosen pivot candidate positions for the round is non-linear. A set of encoding vectors is generated based on the chosen sequence of pivot candidate positions, each encoding vector comprising zero valued coefficients for positions within the encoding vector before the pivot candidate position for the encoding vector and a non-zero valued coefficient for at least the pivot candidate position.

Abstract: A method for use in a distributed storage system having a plurality of nodes, the method including receiving, at a source node, original data, encoding the original data into plurality of coded fragments using a linear code, transmitting at least a first one of the coded fragments from the source node to a first sink node. The method further includes receiving, at the source node, modified data, calculating, at the source node, a coded difference between the original data and the modified data, transmitting the coded difference from the source node to the first sink node; and recovering, at the first sink node, at least a first portion of the modified data using the coded difference and the at least a first one of the coded fragments.

Abstract: Fulcrum network codes, which are a network coding framework, achieve three objectives: (i) to reduce the overhead per coded packet to almost 1 bit per source packet; (ii) to operate the network using only low field size operations at intermediate nodes, dramatically reducing complexity in the network; and (iii) to deliver an end-to-end performance that is close to that of a high field size network coding system for high-end receivers while simultaneously catering to low-end ones that can only decode in a lower field size. Sources may encode using a high field size expansion to increase the number of dimensions seen by the network using a linear mapping. Receivers can tradeoff computational effort with network delay, decoding in the high field size, the low field size, or a combination thereof.

Abstract: Described herein are systems and processes to provide file updating for distributed storage performed using linear codes, such as network codes and random linear network coding (RLNC). The processes enable efficiently updating coded file fragments without requiring a full upload of a new coded fragments. Separate processes for modifying, deleting, and adding data elements are described.

Abstract: Fulcrum network codes, which are a network coding framework, achieve three objectives: (i) to reduce the overhead per coded packet to almost 1 bit per source packet; (ii) to operate the network using only low field size operations at intermediate nodes, dramatically reducing complexity in the network; and (iii) to deliver an end-to-end performance that is close to that of a high field size network coding system for high-end receivers while simultaneously catering to low-end ones that can only decode in a lower field size. Sources may encode using a high field size expansion to increase the number of dimensions seen by the network using a linear mapping. Receivers can tradeoff computational effort with network delay, decoding in the high field size, the low field size, or a combination thereof.