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 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: 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.