Cycle and Distance Properties of Structured LDPC Codes Based on Circulant Permutation Matrices

This paper investigates cycle and distance properties of structured Low Density Parity Check (LDPC) codes based on circulant permutation matrices. A very simple algorithm to detect and construct codes with good cycle properties is proposed. A geometrical approach to design codes with good girth properties is then presented and illustrated, through the definition of rules for the design of parity check matrices without short length cycles. An upper bound on the minimal distance of the proposed structured code is also derived. The information provided by this bound can help the construction of the parity check matrices, in order to achieve a target minimum distance.