Multi Coding Rates Nested Recursive Convolutional Doubly-Orthogonal Codes

This article presents a class of multi-coding rates time-invariant Recursive Convolutional Doubly-Orthogonal codes (RCDO). The Nested-RCDO (N-RCDO) codes are generated from their RCDO mother code which has a Tanner graph with a girth equal to 10 due to the doubly-orthogonal conditions imposed onto the connections positions of the mother recursive convolutional encoder. This implies that the girths of the N-RCDO codes are also equals to 10. Moreover, results are showing that regular (3, dρ) N-RCDO codes nearly achieve their asymptotic decoding limits for all the desired coding rates obtained from the regular mother RCDO code. These codes also offer a substantial additional coding gain as compared to the non-recursive multi coding rates CDO codes.