Method and apparatus to search fixed codebook and method and apparatus to encode/decode a speech signal using the method and apparatus to search fixed codebook

A method and an apparatus to encode and decode a speech signal using a code excited linear prediction (CELP) algorithm. In order to reduce a bit rate without degrading performance in an enhancement layer based on CELP, each of a fixed codebook of a core layer and a fixed codebook of the enhancement layer is divided into a plurality of spaces. The spaces of the fixed codebook of the enhancement layer excludes a space corresponding to a least distorted space determined from among the spaces of the fixed codebook of the core layer are searched.