1. A maximum a posteriori (MAP) decoding apparatus comprising: a table generation unit to generate a state table and a branch table; a metric difference vector generation unit to generate a state metric difference vector based on state table and generate a branch metric difference vector based on the branch table; a first calculation unit to calculate a metric of a path formed through a combination of a state and a branch each having a maximum metric; a comparison unit to compare the state metric difference vector with the branch metric difference vector; a second calculation unit to calculate an index value and a metric of a current state to which a calculation value is to be applied through an increase of an index value of the branch metric difference vector according to a result of the comparison; and a third calculation unit to calculate the index value and the metric of the current state to which a calculation value is to be applied through an increase of an index value of the state metric difference vector according to a result of the comparison.