Sufficient conditions for ruling-but useless iterative steps in a class ofiterative decoding algorithms

In this paper, we consider sufficient conditions for ruling out some useles s iteration steps in a class of soft-decision iterative decoding algorithms for binary block codes used over the AWGN channel using BPSK signaling. Su fficient conditions for ruling out the next single decoding step, called ru ling-out conditions and those for ruling out all the subsequent iteration s teps, called early termination conditions, are formulated in a unified way without degradation of error performance. These conditions are shown to be a type of integer programming problems. Several techniques for reducing suc h an integer programming problem to a set of subprograms with smaller compu tational complexities are presented. As an example, an early termination co ndition for Chase-type decoding algorithm is presented. Simulation results for the (64, 42, 8) Reed-Muller code and (64, 45, 8) extended BCH code show that the early termination condition combined with a ruling-out condition proposed previously is considerably effective in reducing the number of tes t error patterns, especially as the total number of test error patterns con cerned grows.