A Graph Approach to the Structural Analysis of Simplified Convolutional Self-Doubly-Orthogonal Codes

A graph approach to the structural analysis of simplified convolutional self-doubly-orthogonal codes is presented. Using difference sets and computation tree, it is shown that the code simplification leads to a reduction of the number of independent observations over two successive decoding iterations, and yields only an increase of the number of cycles of length eight in the Tanner graphs for the codes. This analysis provides a theoretical explanation on the nature of the code simplification and helps improving the search algorithms for these new codes.