The least stringent sufficient condition on the optimality of suboptimally decoded codewords

The number of iterations of an iterative optimal or suboptimal decoding scheme for binary linear block codes without any effect on its error performance can be reduced by testing a sufficient condition on the optimality of a candidate codeword. The least stringent sufficient condition on the optimality of a decoded codeword is investigated under the assumption that the available information on the code is restricted to (1) the minimum weight or the distance profile and (2) for a given positive integer h, h or fewer already generated candidate codewords. The least stringent sufficient conditions of optimality for 1⩽h⩽3 are presented. Cond₁ is the same as the one given by Taipale and Pursley (1991), Cond₂ is less stringent than the one given by Kaneko, Nishijima, Inazumi and Hirasawa (see IEEE Trans. Inform. Theory, vol.IT-40, no.3, p.320, 1994), and Cond₁ and Cond₂ are derived from Cond₃ as special cases. These conditions can be used effectively to save computer simulation time for evaluating the error probability for maximum likelihood decoding