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Look at the classical block codes... they are designed based combinatorics and polynomial interpolation over Galois fields mostly. Their decoding algorithms are naturally hard-decision because they require precise values for computation. Soft-decision block decoding requires an iterated approach, and
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More about this... the traditional notion of error-correction capability is that a code with
Hamming distance d can correct up to d/2 errors. However, other than for perfect codes, the channel capacity allows for much better error recovery, and this is enabled particularly through soft decoding, but
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this is pursued only recently again, starting with the turbo and LDPC codes. Again, if you think may claim is so dubious, than please justify yourself the addition of your fact? template.
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Of course this is not really true... you could do soft decoding without iterations, and you could use
Viterbi-like decoding. However, this is not typically done because of its complexity.
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this is only recently done to improve the performance such as of RS codes. What is the doubt that you have?
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