Multidimensional convolutional code: progresses and bottlenecks

Multidimensional (m-D, m≥2) finite support convolutional code has become a new area of research in the multidimensional system and signal processing. While the one-dimensional convolutional code and its variants have been thoroughly understood, the m-D counterpart still lacks unified notation and practical implementation. In this document, the issues related to equivalent encoder, syndrome decoder and the realization of m-D convolutional code are discussed. The application of Grobner basis theory for finding a syndrome decoder matrix is given. In addition, the formulations of optimal realization problem and m-D convolutional code design problem is stated. Recent development and one open-problem are also reported.