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

Abstract: 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 . 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.