The design of protograph-based low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. We show by example that protograph-based EXIT (PEXIT) analysis is not sufficiently reliable in the finite-iteration case, and develop a new technique which, similarly to PEXIT analysis, uses the mutual information (MI) as a tool in order to predict the performance of ensembles based on protographs. In contrast to PEXIT analysis, in which a critical value of the MI is used to define the decoding threshold, in our technique we examine the behavior of the MI over a range of channel parameters in order to define the threshold. Using this new definition of the iteration-constrained threshold, we perform a search over a large family of protographs in order to find the protograph with the highest iteration-constrained threshold for a finite number of iterations over the BEC.
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