Blind Deconvolution Using Convex Programming

This talk will consider the problem of decoding a message that has passed through an unknown channel. To protect against the channel uncertainty, we encode the message by embedding it into a high dimensional space before transmission using the same random matrices used in compressive sensing. We show that if the code length is sufficiently large, then both the message and the channel response can be recovered from the output of the channel by solving a rank minimization program.