Decoding noisy messages: a method that just shouldn't work

Abstract

This paper is about receiving text messages through a noisy and costly line. Because the line is noisy we need redundancy, but because it is costly we can afford very little of it. I start by using well-known machinery for decoding noisy messages (compressed sensing), then I attempt to reduce the redundancy (using random projections), until I get to a point where I use more orthogonal vectors than the space dimension allows. Instead of grinding to a halt or spurting out noise, this method is still able to decode messages correctly or almost correctly. I have no idea why the method works: this is my first reason for writing this paper using a narrative instead of formal scientific style (the second one is that I am tired of writing semi-formal prose, and long for a change).