We consider sufficient conditions for ruling out some useless iteration steps or all subsequent iteration steps without degradation of error performance in soft-decision iterative decoding algorithms for binary block codes used over the AWGN channel using BPSK signaling. Then the derivation of such sufficient conditions and the selection of centers of search regions in iterative steps are formulated uniformly as a type of integer programming problems. Several techniques for reducing such an integer programming problem to a set of subprograms with smaller computational complexities are presented.
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