EXIT-chart properties of the highest-rate LDPC code with desired convergence behavior

We consider uniparametric LDPC decoding schemes, i.e., the class of decoding algorithms for which an extrinsic information transfer (EXIT) chart analysis of the decoder is exact. We treat the general case of code design for a desired convergence behavior and provide necessary conditions and sufficient conditions that the EXIT chart of the maximum rate low-density parity-check code must satisfy. Our results generalize some of the existing results for the binary erasure channel: our results apply to all uniparametric decoding schemes and they apply to any desired convergence behavior.