Decoding method, decoding apparatus and digital transmission system of product code

A decoding apparatus generates error position sets of data sequence by generating a codeword from positions of soft input values output from a low reliability position detecting circuit (38) and from syndromes computed by a syndrome calculation circuit (40). The recording apparatus further includes a codeword candidate generating circuit (43) that computes correlation mismatch amounts by adding soft input values at the error positions contained in the error position sets, and updates the correction information according to the error position sets and correlation mismatch amounts. The decoding apparatus can calculate the soft output values accurately by utilizing the generated codeword candidates efficiently, and reduce the circuit scale by decreasing the amount of computation.