Approximate cycle extrinsic message degree regular quasi circulant LDPC codes

We propose a new class of quasi circulant matrices for high rate (R≥½), by applying the approximate cycle extrinsic message degree (ACE) algorithm, which not only avoids cycles of certain length but also increases the extrinsic message degree (EMD) of stopping sets in a quasi circulant matrix. This novel technique avoids cycles of length four in its primary designing stage, while conditioning on higher length cycles increases the size of a stopping set in the parity check matrix and, hence, lowers the error floor. Appropriate cycle conditioning on quasi circulant matrices in comparison with quasi circulant, irregular and regular matrices (with or without cycle conditioning) yields codes with the lowest error floors under belief propagation decoding for the fading channel. A significant gain of ≈5 dB is observed at bit error 10^-4 under the Jake´s fading channel model.