Methods for compression of multivariate correlated data for multi-channel communication

A non-transitory computer-readable medium storing instructions for compressively encoding two correlated data vectors, wherein the instructions, when executed by one or more processors of a computing system, cause the one or more processors to:

• obtain a first data vector and a second data vector;
• transform the first data vector into a first canonical vector, wherein the first canonical vector includes:
• a first component indicative of information in the first data vector and information in the second data vector, and
• a second component indicative of information in the first data vector and substantially exclusive of information in the second data vector,
• transform the second data vector into a second canonical vector, wherein the second canonical vector includes:
• a first component indicative of information in the first data vector and information in the second data vector, and
• a second component indicative of information in the second data vector and substantially exclusive of information in the first data vector,
• generate:
• (i) a common information vector based on the first component of the first canonical vector and the first component of the second canonical vector,
• (ii) a first private vector based on the first canonical vector and the common information vector, and
• (iii) a second private vector based on the second canonical vector and the common information vector;
• compress the first private vector at a first private rate to generate a first digital message;
• compress the second private vector at a second private rate to generate a second digital message;
• compute an amount of common information included in the common information vector;
• based on the amount of common information, compute a third rate;
• compress the common information vector at the third rate to generate a third digital message;
• route the first digital message via a first channel, the second digital message via a second channel and the third digital message via a third channel.