Recursive Convolutional Codes for Time-Invariant LDPC Convolutional Codes

In this paper we present an attractive alternative to construct time-invariant Low-Density Parity-Check Convolutional Codes (LDPC-CC) of coding rate-b/c from a simple recursive systematic convolutional encoder design. The proposed Recursive Convolutional Doubly-Orthogonal (RCDO) encoders have a corresponding Tanner graph for which the girth is controlled by the doubly-orthogonal conditions that are imposed onto the set of generators that represent the encoder. Therefore, RCDO encoders can be decoded using simply a cascade of the same threshold decoder. The convergence behavior of the iterative decoder is then controlled by the position and by the number of forward and feedback connections that constitute the encoder. RCDO encoders give rise to a class of capacity approaching codes that use simple encoder and decoder structures.