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This paper describes a concatenated code method where the outer decoder hypothesizes possible block symbol values for the inner code to make a likelihood retest from its original soft information. These hypotheses come from low density check sets where the probability is significant that there is only one error in the check set, whose value would be the syndrome for that check. The method has an advantage over pure verifications in converting errors into erasures. Also, it is shown that, if the inner decoder can supply a list of two decisions for each symbol, the decoding method, for large first choice symbol error probability p, allows reliable communication at rates substantially exceeding the (1-p) log2Q QSC per symbol channel capacity with b-bit symbols.