How often is hard-decision decoding enough?

The problem of decoding binary linear block codes has received much attention; the two extremes are optimal, high-complexity soft-decision (or maximum-likelihood) decoding and lower performance, much lower complexity hard-decision (or algebraic) decoding. This article considers a class of decoders which first implements hard-decision decoding; second, tests to see if that is enough, that its result matches the result of soft-decision decoding; and third, continues to search if a match is not found. The advantage of such a testing procedure is that if the hard-decision decoding result is found to be enough (called a success for the test), then the computational effort expended by the decoder is low. The performance, as measured by the probability of a success, of a variety of simple tests of the hard-decision codeword are analyzed.