Selection of excitation vectors for the CELP coders

The authors investigate several algorithms that construct the input for the synthesis filter in the CELP coder, they present them under the same formalism, and compare their performances. They model the excitation vector by a linear combination of K signals, which are issued from K codebooks and multiplied by K associated gains. They demonstrate that this generalized form incorporates several particular coders such as code excited linear predictive coders, multipulse coders, self excited vocoders, etc. The least squares minimization problem is presented afterwards. In the case of orthogonal codebooks, they show that the optimal solution of this least squares problem is equivalent to orthogonal transform coding. They use the Karhunen-Loeve transform to design the corresponding orthogonal codebooks. In the case of nonorthogonal codebooks, they are restricted to suboptimal iterative algorithms for index selection and gain computation. They present some new algorithms based on orthogonalization procedures and QR factorizations that attempt to reduce this suboptimality. In a particular case, when the excitation is modeled using one gain coefficient (for example, ternary excitation or concatenation of short codebook vectors), an iterative angle minimization algorithm is proposed for index selection. The different extraction algorithms are compared with regard to the resulting coder complexity and synthetic speech quality. They find a particularly attractive method that consists of modeling the excitation with one unique gain.