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

TL;DR

This paper explores a surprising decoding method for noisy, costly communication channels that maintains accuracy even when using seemingly impossible levels of redundancy, challenging conventional understanding.

Contribution

It introduces an unconventional decoding approach combining compressed sensing and random projections that works beyond traditional limits, with unclear theoretical justification.

Findings

Method successfully decodes messages with excessive orthogonal vectors

Decoding accuracy remains high despite high redundancy levels

Challenges existing assumptions about decoding limits

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).