Locally Invertible Multidimensional Convolutional Encoders

A polynomial matrix is said to be locally invertible if it has an invertible subsequence map of equal size between its input and output sequence spaces. This paper examines the use of these matrices, which we call locally invertible encoders, for generating multidimensional convolutional codes. We discuss a novel method of encoding and inverting multidimensional sequences using the subsequence map. We also show that the overlapping symbols between consecutive input subsequences obtained during the sequence inversion can be used to determine if the received sequence is the same as the transmitted codeword.