Separation set distance for 2D Convolutional Codes

Abstract

In this paper we address the problem of extending the well-known notion of column distance of one-dimensional (1D) convolutional codes to the context of multidimensional (nD) convolutional codes. In particular, we treat the 2D case and propose a new and more general notion than the one previously introduced in this context. We derive upper bounds on the distances that lead to the novel notion of Maximum Separation Set Distance Profile 2D convolutional codes. This notion naturally extends the notion of Maximum Distance Profile 1D convolutional code. Characterizations in terms of the sliding paritycheck matrices are presented.