Encoding device and method including encoding of error transform coefficients

An encoding apparatus comprising:

• a base layer encoder that encodes an input signal to acquire base layer encoded data;
• a base layer decoder that decodes the base layer encoded data to acquire a base layer decoded signal;
• and
• an enhancement layer encoder that encodes error transform coefficients to acquire enhancement layer encoded data, the error transform coefficients being a frequency domain signal of a residual signal representing a difference between the input signal and the base layer decoded signal,
• wherein the enhancement layer encoder comprises:
• a divider that divides the error transform coefficient into a plurality of subbands;
• a first shape vector encoder that performs shape vector quantization with respect to the error transform coefficients of each of the plurality of subbands to acquire first shape encoded information, and that calculates target gains of each of the error transform coefficients of the plurality of subbands based on the first shape encoded information after the shape vector quantization;
• a gain vector former that forms one gain vector using the plurality of target gains calculated by the first shape vector encoder;
• and
• a gain vector encoder that encodes the gain vector formed by the gain vector former, to acquire first gain encoded information.