Parameter Estimation of a Rate k/n Convolutional Code in Noisy Case

This paper studies the problem of the convolutional code parameters estimation in noisy scenario. Among the methods that have been proposed for this problem, the rank-based method has attracted most of the research. In this method, the receiver cuts the received sequence up into vectors of length l to form the rows of matrix C(l), for max 1, , ll . The code parameters are estimated based on the rank of these matrices. To this end, the relation between the code parameters and the rank of C(l) should be known. To do this, the previous works proposed an experimental relation; however, it is not established in the general case. This paper analytically computes the rank relation and proposes a method to extract the rate k/n convolutional code parameters. The method uses the Gaussian elimination with row pivoting (GERP) algorithm to estimate the rank and null space of C(l). The proposed algorithm is based on a threshold value. Hence, an appropriate threshold will be proposed based on the Minimax decision rule.