Forward error correcting codes characterization based on rank properties

In this paper we deal with the error correcting code reverse engineering problem. We take the point of view of an adversary who eavesdrops communications without any a priori knowledge and who wants to recover the error correcting code parameters. For this, we propose a detailed analysis of the central criterion which is the origin of all state of the art reconstruction techniques. This criterion, also called the rank criterion, consists in observing the variation of the rank of a particular matrix built with the intercepted bit stream to deduce the parameters of the code. We also propose new equations to reconstruct turbo codes. Our analysis is confirmed by experimental results.