An approach is introduced towards generalised threshold decoding, in which the threshold value is not necessarily a majority element. This approach can help extend the threshold decoding method to more types of code in order to benefit from having low decoding complexities. With the motivation of finding codes decodable by applying the general threshold decoding rule, a class of block codes, called parity-check-based codes, is investigated. The method of constructing this class of codes differs from traditional approaches, i.e. the encoding procedure is based on the given parity- check symbols, instead of information symbols, with the aim of having a simple decoding algorithm. Better code performance can be achieved with some of these codes than those using similar decoding methods.
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