Pseudo-binomial degree distributions from derivative matching

In this paper, a method to design check-concentrated LDPC degree distributions for the erasure channel is proposed. This method is obtained taking a derivative matching approach. It consists of matching the first and high-order derivatives of the variable node decoder EXIT function and inverse check node decoder EXIT function in order to reduce the gap between the two curves in the EXIT chart. A sufficient condition for a check-concentrated distribution to achieve derivative matching up to some order is first developed, and then a design algorithm is proposed exploiting this sufficient condition. A comparison with other deterministic design techniques is provided, revealing the potentialities of the proposed algorithm.