Algebraic approach to reduce the number of delay elements in the realization of multidimensional convolutional code

Given an m-D convolutional code with a generator matrix G, the goal is to find an equivalent generator matrix G´ (which generates the same code) that requires the fewest number of delay elements to implement in the canonical form. The technique proposed earlier is based on the sequential search which is not suitable for large generator matrices. It has been inspected that the number of delay elements required for implementation depends greatly on the maximum total degree of each row vector of the generator matrix. In this paper, the algebraic approach based on the usage of Grobner basis theory and the row reduction technique is proposed in the form of an iterative algorithm for row-wise reducing the maximum total degree and thus decreasing the total number of delay elements.