On the Analytical Solution of Rank Problem in the Convolutional Code Identification Context

Abstract

The rank-based method is very effective to identify the convolutional code parameters in a non-cooperative context. This method cuts the received sequence up into vectors of length $l$ to form the rows of matrix $C^{(l)}$ . It is well known that there is a relationship between the code parameters and the rank behavior of $C^{(l)}$ . However, finding the general form of this relation is a challenging open problem. In this letter, we formulate and solve this problem for rate $\frac{k}{n}$ convolutional codes. Our analytical solution show that the rank behavior is highly dependent on the dual code constraint lengths. Moreover, it is proved that the applied experimental rank relation in prior works is true only for rate $\frac{n-1}{n}$ codes.