According to one embodiment, a maximum likelihood decoder includes a branch metric calculator, a processor configured to perform addition, comparison, and selection of an output from the branch metric calculator and a path metric memory, and outputs a selection signal for identifying a selection result, a path memory configured to store a time variation of the selection signal, and a path detection module configured to detect a decoding signal based on the time variation of the stored selection signal. A decoding method includes selecting operation modes of at least one of the branch metric calculator, the processor, and the path memory between a first operation mode in which an operation is performed at a channel rate frequency and a second operation mode in which an operation is performed at a specific frequency lower than the channel rate frequency.