1. A transmitting/receiving data processing system comprising: an encoding apparatus which encodes data; and a decoding apparatus which decodes the encoded data, wherein: said encoding apparatus comprises: a first codebook storage apparatus storing a codebook; encoding unit which encodes the data by using the codebook required for encoding the data, and outputs the encoded data, the encoded data including a code and a differential vector; and encoding-information updating unit, connected to the encoding unit and the first codebook storage apparatus, which updates the codebook in the first codebook storage apparatus based on the code and the differential vector; and said decoding apparatus comprises: second codebook storage apparatus storing the codebook; decoding unit which decodes the encoded data by using the codebook required for decoding the encoded data, decoded data including the code and the differential vector; and decoding-information updating unit, connected to the decoding unit and the second codebook storage apparatus which updates the codebook in the second codebook storage apparatus based on the code and the differential vector.