A hierarchical lossless encoding and decoding technology for digital signals such as of music data, audio data, or the like. A lossless reproduced signal is made identical to an input signal even when the processing accuracy in an encoding apparatus and the processing accuracy in a decoding apparatus are different from each other. the encoding apparatus transmits low-bit-rate encoded data produced by encoding an input signal, lossless encoded data produced by effecting lossless encoding on a differential signal between a low-bit-rate decoded signal decoded from the low-bit-rate encoded data and the input signal, and corrective information extracted from the low-bit-rate decoded signal to respective input terminals of the decoding apparatus. A low-bit-rate decoder decodes the low-bit-rate encoded data. A lossless decoder decodes the differential signal. A corrector corrects the low-bit-rate decoded signal based on the corrective information. An adder adds the differential signal and the corrected low-bit-rate decoded signal into a lossless reproduced signal.