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: Described are network coding (NC) systems and techniques which utilize multiple composite extension finite fields to reduce complexity at various nodes in a network and also reduce overhead due to signal coding coefficients. A coding design uses a series of finite fields where increasingly larger fields are based on a previous smaller field. Techniques disclosed herein can be applied to existing systems using Random Linear Network Coding (RLNC) or Fulcrum codes.

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: Network coding (NC) systems and techniques utilize multiple composite extension finite fields to reduce complexity at various nodes in a network and also reduce overhead due to signal coding coefficients. A coding design uses a series of finite fields where increasingly larger fields are based on a previous smaller field. For example, the design of a field with 256 elements ? 2 2 2 2 is based on polynomial arithmetic over a field with 16 elements ? 2 2 2 , in turn based on a field with 4 elements 22. Techniques disclosed herein can be applied to existing systems using Random Linear Network Coding (RLNC) or Fulcrum codes. A new coding design is also disclosed.

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.

Abstract: Network coding by beam forming in networks, for example, in single frequency networks, can provide aid in increasing spectral efficiency. When network coding by beam forming and user cooperation are combined, spectral efficiency gains may be achieved. According to certain embodiments, a method includes operating a user equipment of a plurality of user equipment in a network comprising a plurality of access points. The method also includes the user equipment forming a beam. The method further receives processing received signals from at least one of the plurality of access points at the user equipment. The forming the beam is configured to let different user equipment of the plurality of user equipment to receive different signals from the plurality of access points to achieve diversity by using different beams amongst the plurality of user equipment. The method additionally includes cooperating with the plurality of user equipment to decode the received data.

Abstract: Network coding by beam forming in networks, for example, in single frequency networks, can provide aid in increasing spectral efficiency. When network coding by beam forming and user cooperation are combined, spectral efficiency gains may be achieved. According to certain embodiments, a method includes operating a user equipment of a plurality of user equipment in a network comprising a plurality of access points. The method also includes the user equipment forming a beam. The method further receives processing received signals from at least one of the plurality of access points at the user equipment. The forming the beam is configured to let different user equipment of the plurality of user equipment to receive different signals from the plurality of access points to achieve diversity by using different beams amongst the plurality of user equipment. The method additionally includes cooperating with the plurality of user equipment to decode the received data.