DISTRIBUTED COMPUTATION OF LINEAR COMBINATIONS IN A NETWORK

摘要

A first source node transmits a first transmission vector formed by multiplying a vector of input values and an inverse of a transfer matrix that relates vectors transmitted from the first source node via a plurality of intermediate nodes to vectors received at a plurality of destination nodes. Each of the intermediate nodes transmits a vector formed by a linear operation performed on received vectors. The linear operation may be determined based on linear combinations of the first transmission vector and one or more second transmission vectors transmitted by second source nodes. The linear combinations are to be received at the destination nodes. The linear operation is chosen so that propagation of the first transmission vector through the intermediate nodes produces, at the destination nodes, predetermined linear combinations of the first transmission vector and one or more second transmission vectors transmitted by one or more second source nodes.

主权项

1. A method comprising:
transmitting, from a first source node, a first transmission vector formed by multiplying a vector of input values and an inverse of a transfer matrix that relates vectors transmitted from the first source node via a plurality of intermediate nodes to vectors received at a plurality of destination nodes, wherein each of the intermediate nodes transmits a vector formed by a linear operation performed on received vectors, and wherein the linear operation is chosen so that propagation of the first transmission vector through the plurality of intermediate nodes produces, at the plurality of destination nodes, predetermined linear combinations of the first transmission vector and at least one second transmission vector transmitted by at least a second source node.